VoMP: Predicting Volumetric Mechanical Property Fields
Authors: Rishit Dagli
Donglai Xiang
Vismay Modi
Charles Loop
Clement Fuji Tsang
Anka He Chen
Anita Hu
Gavriel State
David Levin I.W.
Maria Shugrina
Venue: ICLR 2026 Poster (2026)
Keywords: Physics-based Modeling
3D Dynamics
Primary area: applications to computer vision, audio, language, and other modalities
TL;DR: We introduce a framework that estimates fine-grained volumetric physically-valid mechanical properties that can be used in a simulator to produce realistic interaction.

Abstract: Physical simulation relies on spatially-varying mechanical properties, typically laboriously hand-crafted. We present the first feed-forward model to predict fine-grained mechanical properties, Young’s modulus ($E$), Poisson’s ratio ($\nu$), and density ($\rho$), throughout *the volume* of 3D objects. Our model supports any 3D representation that can be rendered and voxelized, including Signed Distance Fields (SDFs), Gaussian Splats and Neural Radiance Fields (NeRFs). To achieve this, we aggregate per-voxel multi-view features for any input, which are passed to our trained Geometry Transformer to predict per-voxel material latent codes. These latents reside on the trained manifold of physically plausible materials, which we train on a real-world dataset, guaranteeing the validity of decoded per-voxel materials. To obtain object-level training data, we propose an annotation pipeline combining knowledge from segmented 3D datasets, material databases, and a vision-language model. Experiments show that VoMP estimates accurate volumetric properties and can convert 3D objects into simulation-ready assets, resulting in realistic deformable simulations and far outperforming prior art.

Published as a conference paper at ICLR 2026
VOMP: PREDICTING VOLUMETRIC MECHANICAL PROPERTY FIELDS
Rishit Dagli'. Dongaii Xiang'
Vismay Modi Charles Loop'
Clement Fuji Tsang'
Anka He Chen'
Anita Hu'
Gavriel State'
David I.W. Levin 1.
Maria Shugrina'
INVIDIA University of Toronto
Realistic
Material
Values
VoMP
VoMP
3D
concreto
Mesh
Propert Fickd
mematl
metil beditume
Gaussian Splats
Young's s ModulusiPoisson Raiio
Density
Young's Modulus Poisson's Ralio
Density
A bowling ball falling bed
65 Beuses falling into container
Figure 1: VoMP predicts physically accurate volumetric mechanical property fields across representations in just a few seconds (top), enabling their use in realistic deformable simulations (bottom).
ABSTRACT
Physical simulation relies apatially-varying mechanical properties, often labo- riously hand-crafted. VoMP a feed-forward method trained to predict Young's s modulus (E)), Poisson's ratio (v), and density (p) throughout the volume of 3D objects, in any representation that can be rendered and voxelized. VoMP ag- gregates per-voxel multi-view features and passes them our trained Geometry Transformer to predict pox-voxel material latent codes. These latents reside on a space of physically plausible materials, which we learn from real-world dataset. guaranteeing the validity of decoded voxel materials. To obtain object-level training data, we propose an annotation pipeline combining knowledge from seg- mented 3D datasets, material databases, and vision- languan model, along with a new benchmark. Experiments show that VoMP estimates accurate volumetric properties, far outperforming prior art in accuracy and speed.
INTRODUCTION
Accurate physics simulation is critical part of modern design and engineering, for example, in workflows like creating Digital Twins (virtual replicas of real systems) (Grieves & Vickers 2017). Real-2-Sim (generating digital simulation from the real world) (NVIDIA 2019), and Sim-2-Real (transferring policies trained in simulation to real-world deployment) (Rudin et al. 2021). However, setting up reliable simulations remains intoo-intensive, partially due the necessity provide ac- curate mechanical properties throughout the volume of every object, namely the spatially-varying Young's 's Modulus (F.), Poisson's ratio (v), and density (p). Common capture methods (Kerbll al. 2023) and 3D repositories (Deitke et al. 2023) rarely contain such annotations, forcing artists and engineers to guess or copy-paste coarse material presets subjective, time-consuming pro- We focus automatic prediction of these parameters, addressing important limitations of prior art.
We propose VoMP, the first feed-forward model trained estimate simulation-ready mechanical property fields (E, v. p) within the volume of 3D objects across representations. Rather than spe- cializing inputs like Gaussian Splats (Shuii al. 2025 Xie al. 2024), method works

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Published as a conference paper at ICLR 2026
for any geometry that can be voxelized and rendered from turnaround views, including meshes, Gaussian Splats, NeRFs and SDFs (Fig. [].. Unlike virtually all prior works, VoMP fully feed-
forward, requiring per-object optimization of feature fields (Zhi et al. 2024 Shuai et al. 2025) or run-time aggregation of Vision-Language Model (VLM) (Lin et al. 2025a or Video Model (Lin et al. 20256) supervision. Uniquely among others, VoMP outputs true mechanical properties (a.k.a. material parameters), like those measured in the real world. Many existing pipelines target fast. approximate simulators, resulting simulator-specifie parameters (Zhang al. 2023 Huang al.) 2024b) that may not transfer reliably across frameworks (Fig. 2. whereas our result is directly compatible with any accurate simulator. Finally, unlike prior art, our method designed to assign materials throughout the object volume, which is critical for simulation fidelity.
To enable learning physically valid mechanical properties, we first train a latent space on a database of real-world values (F, v/ using variational auto-encoder MatVAE ($3). To predict mechanical property fields for 3D objects, our method first voxelizes the input geometry and aggregates multi- view image features across the voxels ($4.1). This process accepts many representations and is fast, unlike optimization used in concurrent work (Le et al. 2025). We pass the voxel features through the Geometry Transformer ($4.2). trained output per-voxel material latents. The MatVAE latent space decouples learning material assignments for objects from learning what materials are valid, ensuring that the final volumetric properties (E, v. p) decoded by MatVAE are physically valid, even in the case of interpolation. To create material property fields for training, we propose a pipeline ($5) combining the knowledge from part-segmented 3D assets, material databases, visual textures, and a VLM. Our experiments (56) show that VoMP estimates simulation-readyy spatially-varying mechanical properties across range of object classes and representations, resulting in realistic elastodynamic simulations. We evaluate our method on an existing mass prediction benchmark and contribute a new material estimation benchmark ($6.3), consistently outperforming prior (Shuai Lin et al. 2025a Zhai et al., 2024). In summary, our contributions are:
al. 2025
The first (to our knowledge) method to estimate object mechanical material property fields that (1) is a trained feed-forward model with minimal preprocessing, (2) generalizes across 3D represen- tations, (3) predicts physically valid properties that can be used with accurate simulator, and (4) predicts mechanical properties within the volume of objects ($4).
The first (to our knowledge) mechanical properties latent space
An automatic data annotation pipeline and new benchmark volumetric physics materials ($5)
Thorough evaluation through high-fidelity simulations and quantitative metrics on existing and new benchmarks, significantly outperforming the prior art ($6).
2
RELATED WORK
BACKGROUND
All algorithms for continuum-basee based simulation of solids and liquids require material models as imput. The material, or con- stitutive, model is the function that determines the force re- sponse of a class of materials (e.g., rubbers, snow, water) to internal strains and strain rates. To produce the correct consti- tutive behavior for given material, the model requires an ac- curate set of corresponding material parameters for every point in the simulated volume. For locally isotropic material models, Young's 's modulus (E, in the ID linear regime, the proportion- ality constant between stress and strain), Poisson's ratio (v, the negative ratio of transverse to axial strain under uniaxial loading) and density (p. unit mass per volume) are ubiquitous. Given an accurate and valid triplet (E, v, p) along with a rea- sonable material model, a consistent numerical simulation can produce accurate predictions of an object's behavior under load.
XPRE
MPM
Figure 2:
Simulator differences when dropping solid sphere with (E, p) = (10*Pa, 0.3, 10 kg/m" ) with XPBD (Macklin al. (016)) and MPM (Sulsky et 1994) vs. more curate FEM.
Measured, real-world parameters
We deseribe available methods for meshes, SDFs, and NcRFs, and present method for Splats in 66.1
2

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portable to any consistent simulation algorithm (we use high-resolution Finite Element Meth- ods). Further, they are portable across any material model that relies on density, Young's s modulus and Poisson's ratio, derived quantities, such shear or bulk modulus (e.g.. Neo-Hookean, St. Venant-Kirchhoff,
AeRiiiddAs-Possiblll Co-Rotated Elastic, Mooney-Rivlin, and Ogden models). On the other hand, many physics simulation algorithms are implemented applied in consis- tent fashion, favoring speed over accuracy (Macklin et al., 2016) (Sussky et al. 1994). In these cases, material parameters must be modified to avoid inaccurate behavior (Fig.
2.2 INFERRING MECHANICAL PROPERTIES OF STATIC OBJECTS
Our goal is to predict volumetric mechanical properties given only shape and appearance, a challeng-
ing inverse problem, which research suggests humans learn good intuition about (Adelson [
Fleming 2014 Fleming et al. 22033; (hharan et al. 2009). However, progress in learning-based ap-
proaches has been hampered by limited data. Existing datasets are small (Gao et al. 2022 Downs
et al.
2022| Chen et al. 2025c), contain noisy labels (Lin et al. (0018), , use simulator- siettoo- param-
2022
eters
Mishraa| [202]] Xie et al. 2025 Belikov et al.] (015)) provide only coarse annotations (Ahmed
et al.
2025 Slim et al. 2023 Li ei al.) 2022) are biased towards rigid or man-made objects (Cao 2025).. J. Worse, data collection is difficult, relying on rigorous physical experiments (ASTM
et al.
Committee D20, [2022, ASTM Committee E28 2024 Pai 2000),, and even then lacking spatial
material fields (Loveday et al. (2044) due to digitization and annotation challenges.
As a result, works that infer physical properties from appearance often leverage knowledge from large pre-trained models. NeRF2Physics (Zhai et al. 2024) and PUGS (Shuai et al. 2025) opti- mize language-embedded feature fields for NeRF (Mildenhall al. 2020) or 3D Gaussians (Kerbl et al. 2023). respectively, to predict coarse stiffness categories and density, but require per-object optimization and are limited in their ability to predict values inside objects due to the lack of mean- ingful features inside NeRFs or splats. Many approaches distill signals from Video Generation Model and optimize physics parameters by backpropagating through fast, approximate physics sim- ulators, resulting in slow optimization process, yiclding materials deviating from real-world values and overfit to a specific simulation setup (Zhang et al., 2025| HHuan et al.] 2024b; Liu et al. 2025
Cleac h et al. 2023] Liu et al. [2024a] Lin al. 2025b)
(221)) Many methods
also tailored to
specific 3D representation or time simulation implementations, such as Splats (Xie et al.) 2024) or explicit Material Point Methods (Sulsky et al.
1994 Le al. 2025), or work with coarse material
categories (Fischer et al. 2024 Hsu et al.] 2024 Lin et al.] 2025a] Xia et al. 2025) that must be manually mapped to simulation parameters. Instead, we aim to augment objects across 3D repre- sentations with fine-grained spatially-varying mechanical properties that are physically accurate and compatible across accurate simulators. Like our method, many techniques leverage vision-language (VLM) models. PhysGen (Liu et al. (2024b) and PhysGen3D (Chen et al.] (022a)) use a VLM to infer mass, elasticity, and friction for segmented parts of single image. Phys4DGen (Lin et al.) 2025a) uses a VLM to annotate parts of a 3D model with coarse material labels, which are then mapped to physical parameters, a baseline used in our evaluation. Most works above rely on aggregation of large model outputs for every input shape, which can be brittle and can only leverage external segmentation. Instead, our method uses a VLM paired with other data sources annotate training dataset for feed-forward model leveraging 3D data to annotate and learn internal material composition.
at run-time, and
Like our method, SOPHY (Cao & Kalogerakis 2025). PhysX-3D (Cao al., 2025). ). PhysSplat
(Zhao et al. 2024a b) (a. SimAnything) and the concurrent Pixie (Le et al. 2025) leverage pre- trained models and 3D data to annotate a training dataset with physical materials. PhysSplat trains a network to predict spatially-varying simulator-specific material offset weights for MPM by using outputs from video distillation (Liu al., (2024)). not focusing on material accuracy. SOPHY and PhysX-3D are 3D generative models, designed to generate new shapes augmented with physical attributes, and cannot augment existing assets, which is our goal. Still, we detail similar aspects of these works. Like these works, our method uses a VLM to annotate 3D objects with Young's 's Mod- ulus, Poisson's 's ratio, and density, but we do not rely on the saman--n-the-lowe and instead leverage multiple data sources, not just VLM knowledge, to ensure more accurate physical properties. As baseline, SOPHY does implement a material decoder, but it has not been made available, and only considers object surface, while we aim estimate volumetric properties. Like method, PhysX- 3D adopts the structural latent space of TRELLIS, but trains a joint generative model over these and learned awape physical properties latents in order generate physics- augmente shapes from
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MarVAE
Nhe 2od GPs
Dec.
Geometry
Mesh
SDF 3DGS NeRF
Voxelize
Transformer
Per-Voxel
Input
Propertics
DINOV2
Ray-Voxel Intersection
MatVAE
led GR
Reconsiructed Image
Dec.
Figure 3: VoMP Overview. For any input geometry, aggregate multi-view DINOv2 features across its
volumetric voxelization ($4.I). trained GeometryTransforme ($4.2) predicts per-voxel material latents,
decoded by MatVAE into mechanical properties (E, v. p).
scratch. contrast, we treat material prediction deterministic inference for simplicity, and further adjust the TRELLIS pipeline to facilitate accurate material prediction inside the object. Pixie (Le) 2025), a concurrent work and the only other feed-forward approach, is trained on semantically- segmented objects and uses points from filtering NeRF densities. Thus, Pixie is trained on segments biased toward the surface, as we show Fig. 15 while we demonstrate being able to estimate volumetric properties with internal structures. Furthermore, unlike Pixie, we specifically focus on estimating physically plausible material properties, such as those measured in the real world.
3 MECHANICAL PROPERTIES LATENT SPACE
To learn latent space of valid Young's modulus, Poisson's ratio, and density triplets (E, V, p) (1..)) we propose MatVAE, a variational autoencoder (VAE) trained on a dataset of real-world values (m, (F,, Vi; p:)} (55.1). The model's objective is map these triplets into 2- dimensional latent space, E I from which they can be accurately reconstructed. While this offers only minor compression (IR + R²), this latent 2D space of material properties is now easy to visualize, sample, and interpolate within, and results in consistent distances between material triplets with disparate units (Fig. 6.44. MatVAE acts like continuous tokenizer that allows us to always ensure VoMP output properties that fall inside the range of some materials.
We build on VAE (Kingma & Welling 2022), with the reconstruction component the loss defined as mean-squared error between the input (E,, Pi) and reconstructed material values (E,, 1,, P:):
N
RRcon
Σ
((E - ((É,, Ds, P:) 1=1
(1)
N
where T denotes transpose and N per-property normalization. where E and are first log- transformed (logı0 (E), lo then normalized to [0, 1], while is directly normalized to [o, 1].
We find other normalization schemes without log-tra transfonffom or standard z-score normalization in- duce a heavy-tailed feature distribution, which is poorly conditioned for learning ($C).
We make several modifications over standard VAE. First, to capture complex posterior beyond a simple Gaussian, the encoder's output is transformed by a (radial) Normalizing Flow (Rezende) & Mohamed 2015), giving us more flexible variational distribution {0(z/m) since we observe heavy-tailed distribution for Young's 's Modulus and Density while Poisson's Ratio concentrates near the boundaries after normalization. Second, we decompose the KL-divergence term of the ELBO following (Chen et al. 20188. This allows us to directly penalize the total correlation {0())) where 7s(2) is the aggregated posterior, 2j is the j (1,2)-th coordinate of the latent vector z. Penalizing TC allowed tween latent coordinates which caused MatVAE to encode density both dimensions. Third, we observe imbalanced reconstruction, i.e. the latent space collapses reconstruction errors for one property and high reconstruction error for others ($C). Thus, to ensure the 2 latent dimensions actively utilized, introduce capacity constraint (5 2dim) based
TC(=) (L(
to reduce the high dependence be-
property, giving us low
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on (Higgins et al. 2017).
resulting in the following final objective:
Latent Space Regalarization
M CRecon +
MI
+ B (c) +
max(6, (L())(z)) (p(2))))
(2)
Mutual Information
Total Correlation
-=1
Dimension-wise KL
where we set 7/ P, a (1.0, 2.0, 1.0), with free nats constraint 8 0.1. See F for more details.
4 PREDICTING MECHANICAL PROPERTY FIELDS
To predict volumetric mechanical properties across 3D representation, VoMP first aggregates volu- metric features for the input geometry ($4.1). which are then processed by a trained feed-forward transformer model ($4 4.2) that learns in the latent space of MatVAE ($3). See 2.2
4.1 AGGREGATING FEATURES
Our method accepts any 3D representation that can be voxelized and rendered from multiple views. Following recent works Waan et al. [023]] Dutt et al. 2024; Xiang et al. 2025), we compute rich DINOv2 (Oquab et al. 2024) image features across 3D views and lift them to 3D by projecting each voxel center into every view using the camera parameters to retrieve the corresponding image features. The retreived image features are then averaged to obtain feature for every voxel. A critical difference with these prior works is that we also voxelize and process the interior of the objects and not just their surface, which allows for voxelization schemes and see FF3 for details on voxelization for training). Let's denote all active voxel center positions in a 3D grid of size N {p.} where L denotes the number of voxels, P: E IS denotes the voxel center, and 11, R + [-1, 1J2 the camera projection for view j E J where J is the set of rendered views. Let the DINOv2 patch-token map be T₃ E 1024 xxxn
learn and predict material properties inside the objects (See
which bilinearly sampled to get a feature map F, : [-1, 1, 1]2 - 1024 Then for each voxel e (1.2, L}. we obtain feature f,:
f Average(C; =
(P:)),(P))) (F
E J}) 1024
(3)
This propagates multi- information the voxels in the interior of the object, encoding useful information that our model learns to process to predict internal material composition.
4.2 GEOMETRY TRANSFORMER
The main component of VoMP is a Transformer that maps voxelized image features our trained material latent representation. The backbone of our model follows TRELLIS (Xiang et al., (025) encoder/decoder, and the backbone layers of our model are initialized with TRELLIS weights. The encoder processes variable-length set of active voxels, represented by their positions and features X= (Pr,, H To make this data suitable for a Transformer, we first serialize the voxel features into a sequence and then inject spatial awareness by adding sinusoidal positional encodings derived from each voxel's 3D coordinates. Similar to TRELLIS and state-of-the-arr 3D Transformers, we adopt 3D shifted window attention mechanism (Liu al. 2021 Yang al., (025).. Contrary to TRELLIS (Xiang et al.] 2025). to handle assets of various sizes, we define a maximum sequence length of LN. For assets with fewer voxels L Ln. we use the complete set. However, for larger assets where L > LN. we use a stochastic sampling strategy, selecting a random subset of LN voxels the start of each training epoch. This dynamic resampling ensures the model is exposed to different parts of the asset over epochs and have a larger number of "effective" max voxels.
For each training asset, we first define as the set of voxel indices to be processed in the current iteration. The corresponding sequence of image features Xs obtained from voxel features ($4.1). passed to F. The resulting latent representation then fed into the frozen decoder of pre-trained Mat VAE to predict material properties. The MatVAE is run L times i.e. once per voxel, which gives us material triplets (E, v, p) for each voxel. We train this transformer with the mean squared error between the predicted materials and the ground truth materials, averaged over all voxels in the set S,
L S
Σ || (F(xs)))) ((E,, M4 (.P...) 1
(4)
5

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where (-(-) denotes the output of the frozen MatVAE decoder, ((E,, 14, MT is the ground truth material vector for voxel i, and F(Xs); is the latent representation for voxel
To transfer voxel materials back to the original representation (i.e. splat means, tets for FEM sim- ulation, quadrature points for simulation, etc.), we use nearest neighbour interpolation as outlined in $ The per-voxel latents are passed into the decoder model of MatVAE ($3). which yields per voxel material triplets, as shown in 2.2
5 TRAINING DATA GENERATION
5.1 MATERIAL TRIPLETS DATASET (MTD)
To train MatVAE ) collect Material Triplet Dataset(MTDD, containing 100,562 triplets
(E, p) for real-world materials, We first collect a dataset of measured material properties from multiple online databases (MatWeb, LLC| 2025 Wikipedia contributors 2024a b The Engineer- ing Toolbox, 2024] Department of Engineering, University of Cambridge (2011) containing values
obtained experimentally, typically with valid ranges for all three properties for all materials. We sample numeric triplets from each material, with the number of samples proportional to the range size. Finally, we filter out duplicates resulting from overlapping ranges for some materials.
5.2 GROMETRY WITH VOLUMETRIC MATERIALS (GVM) DATASET
To train Geometry Transformer $$. develop an automatic annotation pipeline to overcome the limited availability of detailed volumetric material datasets ($2.2). Like prior works (Lin et al., [2025]]
Jodles Iuly
aaalaa lnndle
high quality uerets
plalic Aeu
Wada,
rives
detailed volumetric parts (+ material names)
Cao & Kalogerakis 2025 Le et 2025). we lever- age a pre-trained VLM, but overcome its limita- tions by introducing additional sources of knowl- edge present in our 3D dataset and the MTD($5.1)
YKS
M8:035 .035 RHO 2w0lkii
material ranges database
extracted textures
VL.
part-wise mechanical properiiss
We collect high-quality 3D meshes from (NVIDIA
Figure 4: Training Data annotation leverages ac- curate 3D data labels together with VLM.
Corporation| 2225a c, NVIDIA Developer 20255
NVIDIA Corporation 2025d), containing 1624 part-
segmentated 3D models, with total of 8089 parts, and treat each part having isotropic material. Each part contains an English material name and its own realistic PBR texture, which can be used as additional cues to the VLM. For each part in each object, pass the following information to the VLM: rendering of the full object, detail rendering of the part's visual material mapped onto a sphere (showing visual aspects that tend correlate with material composition), the material names, and the ranges of three closest woal-world materials in the MTD 1 based on the material names (See 4ig detailed prompt in Fig. 23 The vision-lann languuge model then outputs material triplets for each part, and we map to all volumetric voxels within it, resulting in a total of 37M voxels annotated with (E, v, p). By guiding VLM with real-world material values and extra clues, we avoid inaccuracies and implausible material values. See additional details in 6.
6 EXPERIMENTS AND RESULTS
We evaluate VoMP end-to-end, showing diverse realistic simulations in $6.2 Quantitative results presented in $6.3 with MatVAE evaluated separately in $6.4 See video and & for many additional results, $ for extra comparisons with concurrent work and $ for ablations.
6.1 IMPLEMENTATION DETAILS
Voxelization: For voxelizing 3D Gaussian splats (Kerbl et al. 2023). we present a new voxelizer, that works in three phases: (1) 3D Gaussians are voxelized over 3D grid as solid ellipsoids defined by the 99th percentile iso-surface, (2) this set of voxels is rendered from several dozen viewpoints sampled over sphere to form depth maps, (3) these depthmaps used to carve away empty space around the exterior the object, but leaving unseen interior voxels to form a solid approximation of the object. We then sample this solid jittered sample points regular grid. We employ

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Published as a conference paper at ICLR 2026
stack of oranges Falling down
18 dog luys falling through paclinko
Figure 5: Simulation-ready physics materials of VoMP enable realistic simulations for meshes and splats.
octrees as acceleration structures and GPU implementations for both phases. Our test objects can be voxelized in 31 ms (see Tb. D. To voxelize meshes and SDFs we use standard methods (see FF.3)
Data and Training: For material annotation, we experimentally choose Qwen 2.5 VI.-2BB VLM (Bai et al. 2023 2025). We partition our MTD and GVM datasets ($5) into 80-10-10 train, validation, and test sets. See {Elfor data details. For rendering we use Omniverse (NVIDIA Corpora-
tion 2025b) and Blender (Blender Online Community) (021). and for DINOv2 we use optimized implementation (NVIDIA 2025). During training and testing, we set the maximum number non- empty voxels per object Ln 32768 (sampled stochastically, $4.2), and sparse data structures for efficiency. See forr more details. All experiments were performed on a machine with four 80GB A100 GPUs, where training took about 12 hours for MatVAE and days for the Transformer.
Simulation:
We used FEM simulator for meshes and sparse Simplicits (Modi et al. 2024
Fuji Tsang al.) for our large-scale simulations combining splats and meshes. Details in SG
6.2 END-TO-END QUALITATIVE EVALUATION
We qualitatively evaluate VoMP by using it to annotate volumetric mechanical fields for several meshes and 3D Gaussian Splats, and running physics simulation with these exact spatially vary- ing (E, v. p) values, resulting in realistic simulations without any hand-tweaks (Fig. 5 Fig. 0:36). We also show that our approach can work across more representations, including meshes, 3D
Gaussian Splats, SDF, and NeRFs Fig. Sa with additional results in $A.2
6.3 QUANTITATIVE EVALUATION
Datasets and Metrics: The 10% hold-out test set of GVM ($5) consists of 166 high-quality 3D objects with per-voxel mechanical properties for total of 4.9 million point annotations, significantly larger than previous works, e.g. 31 points across 11 objects (Zhai et al. 2004)). We contribute this as new benchmark and use it for evaluation against baselines. We measure standard metrics, Average Log Displacement Error (ALDE), Average Displacement Error (ADE), Average Log Relative Error (ALRE), and Average Relative Error (ARE) for each mechanical property, further detailed in $D.1 We provide additional intuition for interpreting these errors through targeted simulations in $D.4
Table Wall-clock comparisons and breakdown.
We compare against prior art NeRF2Physics (Zhai et al., 2024) and PUGS (Shuai et al., (025), where look up material proper- ties at the voxel locations (with proper scaling) using their optimized representations. Note that these techniques do not output Poisson's ratio. Phys4DGen (Lin al. (025a) an important baseline, aggregating VLM prediction directly, but does not provide code. We used our best effort to replicate their method and used prompts provided by the authors, designating this implementation Phys4DGen*. More bascline details in (F.5). We also include early comparisons against concurrent with additional explorations in B
Baselines:
Method
Time (s)
NeRP2Physies
1454.55 (1:1118)
PUGS
1058.33 (b6.4)
Pixie
201.63 (127.744
Phys4DGen*
51.65 (1:000)
Ours
3.59
Rendering
2.1 (#-00040)
Voxelization
0.03 (=00001))
DINO-v2 Computation
0,86 (=00000)
DINO-v2 Reconstruction
0.58 (1000053)
Geometry Transformer
0.0082 (1000063)
MaIVAE
0. 0.00032 (40000026)
(and yet unpublished) Pixie (L al. 2025)
Estimating Mechanical Properties: Quantitative evaluation of material estimates (E, v. p) of our method against prior art our detailed benchmark shows a dramatic quality boost across all properties and metrics (Fig.(6b). According to our explorations ($D.4). ALRE under 0.05 for E and ARE under 0.15 5 for other properties result in similar simulations, suggesting that our materials will

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Published as a conference paper at ICLR 2026
Table 2: Mechanical Property Estimates of method on the publicly released dataset are very close to the
full dataset. Per-voxel error rate first computed per object, then averaged across all objects the test set to avoid weighing some objects more. Global voxel-level normalization yields similar results, see Supplement
Th.
Method
Young's s Modulus Pa (E)
Poisson's Ratio (v)
Density Eg (p)
ALDE (U)
ALRE (L)
ADE (1)
ARE (L)
ADE (4)
ARE (L)
NeRF2Physics
2.8000 (2:106)
0.1346 (20000))
1432.0343 (=9664 88)
1.0365 (#:063)
PUGS
3.3942 (2:172)
0.1688 (10.10)
3568. 2150 (2:2839 13)
3.2429 (13356
PhysiIGenn
4.8967 (#3.17)
0.2227 (+0.14)
0.0407 (H0.4)
0.1467 (#0.38)
1865.5673 (#2176690)
1.4394 (#235)
Ours
0.3794 (1:0.29)
0.0409 (2:0.84)
0.0241 (1.0.01)
0.0818 (110.83)
142.7017 (=166332)
0.0921 (:1007)
lead to more faithful simulations than competitors when using an accurate simulator. Qualitatively (Fig. baa. we observe that this performance difference may be due baselines occasionally misla- beling segments (e.g. by Phys4DGen), due to noisy estimates (e.g. NeRF2Physics and PUGS), and less accurate values in the objects' interior due to the baselines' design.
We are unable to make the vegetation subset of our dataset publicly available. Thus, we compute the mechanical property estimations on the public version of the dataset Tb. Tb.2amm and We find that our results averaged over the public dataset are highly similar to the full dataset.
Run-Time: To show approximate speed difference, we report average material estimate speeds across 100 runs on objects with an average of 53.9K Gaussians for our method and the baselines in T To ensure fair compute between CPU and GPU heavy methods, we ran this experiment on a machine with only one A100 GPU and 64 CPUs. While we do not provide timing breakdown of the other methods, this result suggests a speed up of 5-100x achieved by our method, which not sur- prising given that it is the only forwad model among previous work. Concurrent Pixie, which is also feed-fdr involves a heavier pre- processssn step, including per-object optimization, af- fecting its end-to-end time. In the timing breakdown of our method, rendering and pre-processing take the most time, and could be further optimized.
Following NeRF2Physics (Zhai al. 2024) and PUGS (Shuai et al. 2025), also evaluate our dataset on the ABO-500 (Collins et al. following the evaluation protocol of PUGS. We run our model to estimate density p for upto 32678 voxels per object, then average these values and multiply by the known object volume to obtain mass. While this is only an imperfect proxy for measuring the accuracy of volumetric density p. is a benchmark used by prior works, and we include it for completeness. We achieve better or on-par performance across most metries (Fig. 6cp. with qualitative results in $A.3
Mass Estimation:
2022) object mass estimation benchmark,
Validity: To gauge how well different methods are at predicting realistic materials, such as those measured in the real world, which is our goal, we leverage our MTD dataset of real materials. First, we run all methods on GVM test set objects, and for each test voxel compute relative errors to the nearest possible material range from MTD (error is O for estimates within an existing material range). These errors are averaged across all the voxels and reported in Fig. 6d We observe that our method, on average, outputs much more realistic matcrials, as it was explicitly designed to do so.
6.4 RECONSTRUCTINS AND GENERATING MATERIALS WITH MATVAE
Given no prior works exploring latent space of material triplets (E, v, p). evaluate MatVAE on the MTD test set ()..I). achieving low reconstruction errors in Fig. 7a (See Appendix D.I Appendix[.A. for metrics). Further, in Fig. 7 we show the desirable properties of this learned latent space. In (a), samples throughout the 2D latent space map to real-world material ranges in MTD. In (b), we show that (E, v, p)values of real materials encoded the latent space vary smoothly. Further, the latent space ensures valid interpolation points between materials (c), facilitating valid assignment from predicted voxel materials back to the original geometry. We include detailed ablations of VAE design ($C), and additional latent space explorations AA.4
DISCUSSION
We introduce a representation-aguee aggoosic method that maps any 3D asset (mesh, SDF, Gaussian splat, or voxel grid) to a volumetric field of physically valid mechanical properties (E,u,)) We show
8

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NoRF2Plissies
PUGS
Plos4DGet
NGRF2Fhysics
PLGS
Plys
VIMP
Young's Modulus
Young" Modulus
Paisson's 5 Ratio
ouppee
alminum mecal
(xcrew)
Density
copper mettal
plastic
plastic (shelf)
NoRi2Pbysics
PUGS
PhyslDXim
Ous
NeRFEPhysics
PUGS
PlystDGen
VoMP
Density
Young's S Modulus
Tigll
plattic
foam
Soura
platic
(a) Qualitative Comparison: We show that qualitiative VoMP tends provide less noisy volumetric? values
compared the baselines. We show the color coded fields and slice planes through the fields.
Method
Young's Modulus Pa (E)
Poisson's 's Ratio (1)
Density Eg (p)
ALDE (L)
ALRE (L)
ADE (1)
ARE (L)
ADE
ARE
NeRF2Physics
2,8000 (21.06
0.1346 (20.06)
1432.0343 (25564 88)
1.0365 (1:63)
PUGS
3.3942
0.1688 (10.10)
3568,2150 (1:2839 13)
3.2429 (13356)
Phys4DGen*
4.8967 (#3.17)
0.2227 (#0.14)
0.0407 (20.44)
0.1467 (b0.18)
1865.5673
(#217690)
1.4394 (#235)
Ours
0.3793 (#:0299
0.0409 (#0.44)
0.0241 (20.00)
0.0818 (20,33)
142.6949
(=16630)
0.0921 (=100))
(b) Mechanical Property Estimates of our method significantly outperform the baselines all metrics. Per- voxel eтror rate is first computed per object, then averaged across all objects in the test set avoid weighing
some objects more. Global voxel-level normalization yields similar results, see Supplement Tb 4
Method
log(E)(
p(1)
Method
ALDE (1)
ADE (J)
ARE (L)
MoRE (1)
NcRF2Physics
1.62 (:436)
19.75 (=4600)
NcRF2Physics
0.236
12.725
PUGS
1.87 (1450
13.24 (21233)
PhysADGen*
PUGS
0.664
0.661
9.961
9.461
0.825
0.767
0.576
0.566
Phys4DGen*
1.77
0.85
39.49
Pixie
11.90 (11744)
3.46
(1444)
46.58
96.3)
Ours
0.631
8.433
0.887
0.576
Ours
0.29 (::33))
0.00 (1000)
11.75 (2402))
(c) Mass Estimate: We show the errors for estimat- ing mass of objects the ABO-500 (Collins al.) 2022) dataset, the only existing benchmark, approxi- mating the accuracy of our p estimates.
(d) Material Validity: We report mean values and relative errors (in %) with the closest physically mea- sured material range in MTD ($5.).
Quantitative Results and Comparisons: We compare our method against prior art NeRF2Physics (Zhai al. (2024). PUGS (Shuai et al. 2025) and Phys4DGen (Lin et al. (025a). and include limited early results comparing with concurrent method Pixie (Le et al. (005)..
Figure 6:
that method significantly outperforms prior art in accuracy and speed, lowering the barrier for integrating accurate physics into digital workflows across 3D representations, with potential impact across digital twins, robotics, and beyond.
While we show important advances over existing works, our method is not without limitations, which we hope will open exciting avenues of future research. Due fixed-grid voxelization, our output resolution is limited, causing oversmoothing in highly heterogeneous regions, and may result in approximation errors when transferring results more detailed input geometry. During annota- tion, we assume part-level materials are isotropic, which is not a true assumption for some common materials like wood. Further, future work could extend our method to predict additional properties like yield strength, shear modulus and thermal expansion, or to adapt true material properties output by our method to simulator-speciff scales required for faster algorithms or implementations. We hope to support future directions in this area by releasing our material estimation benchmark, and trained models.

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Published as a conference paper at ICLR 2026
[og(E) (3)
(1)
(4)
(Bp) (
(G) ())
()
L.S. (1)
E.A.
Bray Curtis (.)
0.0034
0.0426
0.0330
0.0054
0.0036
0.0036
0.0131
0.4439
0.0411
(a) Va shows excellent reconstruction errors on MTD test set across metrics.
#000lgo
(c) Encoding real materials results in smoothly varying E,
P. values throughout the 2D latent space.
Start Value
MatVAE Interpolation
End Valne
Carboo Fiber
Carbon Fiber
Aerographite
Carhon Nitride
Diamond
(high strength)
(high modulus)
0.001 GPa
235.0 GPa
400.0 GPa
822.0 GPa
1220.0 0 GPa
Rake
Baarky Flalo (PM0))
0.25
0.25
Nindo
0.2 kg/m
1775 kg/m
1800 kein
3200 ke/m
3500 kg/m
Start Value
Naive Interpolation
End Value
Aerographite
Invalid (K)
Invalid (X)
Invalid (X)
Diamond
Stdl
Teakker
0.001 GPa
GPa
Gdd
Tapgee
0.25
0.24
0.23
0.21
0.20
Hoce
0.2 kg/m
875 875 kg/m 3
1750 kglm
2625 kg/m
3500 kg/m
Cfoposdente Onnn
(b) Decoding latent samples leads to plausible (d) Interpolating in latent space results valid intermediate (E, v, P) values within real-world materials. materials, unlike naive (E, p) interpolation.
Figure 7: Material Latent Space learned by MatVAE ($3) ensures faithful (a), valid (b), smoothly varying (c),
and interpolatable (d) materials. "Invalid" values (c) fall outside all material ranges in MTD ($5.T)
ACKNOWLEDGMENTS
We thank Gilles Daviet for help in setting up of the simulations. We thank Caan-Francois Lafleche for help with rendering. We thank Beau Perschall for help in using the datasets.
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Supplementary Material for VoMP: Predicting Volumetric Mechanical Property Fields
SUPPLEMENTARY CONTENTS
Additional Results
22
A.I
End-to-end Examples with Simulation
22
A.2 More Mechanical Property Prediction Results
22
A.3
Mass Estimation Example Results
22
Additional MatVAE Results
27
Comparison with Concurrent work
29
Ablations
30
Metries
D.I Metrics for Mass and Field Estimation
31
D.2 Metrics to Mcasure Differences Mechanical Properties
................................
32
D.3 Metries to Measure Differences in Distributions
32
D.4 Interpreting Errors for Material Property Estimation
33
Dataset Details
34
Annotation with Vision-L.anguag Model
35
2
Dataset Statisties
36
Additional Implementation Details
38
Design of MatVAE
38
Network Design
41
3
Training
Simulation and Rendering
44
F5
Baselines
44
Additional Details on the Simulations
44
Interpolation Scheme
45
G.2
Preparing Scenes and Assigning Materials for the FEM Solver
45
Details of the FEM Solver
46
G.4
Preparing Scenes and Assigning Materials for the Simplicits Solver
47
G.5
Deforming Splats and Rendering Deformed Splats
48
G.6
Details of the Simplicits Solver
48
G.7
Preparing Scenes and Assigning Materials for the XPBI) Solver
49
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G.8 Preparing Scenes and Assigning Materials for the MPM Solver
49
Other Related Works
50
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Table 3: Voxel Mechanical Property Estimation. Errors for predicting mechanical properties the publicly released dataset, which does not include the vegetation subset. are very close to the full dataset. These metrics are computed by averaging across all voxels across all 3D objects in the public test set.
Method
Young's 's Modulus Pa (E)
Poisson's 's Ratio (V)
Density m (p)
ALDE ())
ALRE (L)
ADE (L)
ARE (L)
ADE (4)
ARE (L)
NeRF2Physics
2,8000 (#1.05)
0. 146 (#0.05)
1432.0343 (=964 88)
1.0365 (#:033)
PUGS
3.3942 (#1.72)
0.1688 (#0.30)
3568,2150 (#2839113)
3.2429 (#3356)
Phys4IGenn*
4.8967 (#3.77)
0.2227 (+0.14)
0.0407 (+0.44
0.1467 (+0.18)
1865.5673
(#2176.90)
1.4394 (#2335
Ours
0.3766 (1:0.39)
0.0421 (1:0.85) 0.0250 (100.01)
0.0837 (1.083)
113,4683
(=:30219))
0.0909 (20.14)
A
ADDITIONAL RESULTS
A.1 END-TO-END EXAMPLES WITH SIMULATION
We demonstrate the process that enables creating simulation-ready, realistic assets from Gaussian Splats and meshes in Fig. 8 demonstrating convincing simulations without any fine-tuning. For example, in Fig. 8c we first capture a video of an object, and then train a 3D Gaussian Splatting model. Then, we pass it to VoMP which estimates the mechanical properties in a couple of seconds. We then use these properties in a simulator to produce realistic (see : 0:36), greatly reducing the barrier toward constructing realistic interactive digital worlds directly from our physical reality. We demonstrate a Gaussian Splat scene with multiple simulated objects each of which has properties estimated with VoMP, we then place a robot in the scene interacting with the splats Fig. [4 Through experiments Gaussian Splats we find the Gaussian Splat voxelization scheme 1 we introduce empirically qualitatively accurately voxelizes complex, noisy real-world splat objects.
A.2 MORE MECHANICAL PROPERTY PREDICTION RESULTS
We show qualitative results for inferring mechanical property fields in Fig. and 10 from Fig. row 1, column 2 that our model can pick up small details like the stem of the orange at the top of the object, which is given a different Young's ' modulus, though it only spans a few voxels (see : 1:38). We notice from Fig. 9 row 2, column 2 that our model finds that the space inside the pot should be made up of properties that fall in the range of dirt, even though the inside of the pot was not observed through external renders (see : 1:50). We notice from Fig. 9 row 3, column 2 that our model can tolerate some noise in assets such as the Gaussian splat of a bowl with fruits segmented from larger Gaussian splat (see 2:01). We notice from Fig, 10 row 1, column that our model can accurately predict thin segments and thin boundaries, like for the seat of the chair (see 2:10). We notice from Fig. 9 row 3, column 2 that our models can handle complex assets and complex materials like trees and accurately handle fine details, such as understanding where all the leaves lie and giving them different material properties than wood (see 2:16). We notice from Fig. row 4, column 1 that our models can handle complex volumetric materials, such as annotating the properties of wood under the flowers (see =: 2:28). We notice from Fig. | row 4, column 2 that our models can handle thin materials and identify the vein of the leaves (see 2:35). For completeness, we also include our metrics normalized by total test set voxels in Tb. 4 and observe the same performance boost compared to prior art as with the per-object normalization as presented in the main paper Fig. 6b
We notice
We present dataset voxel-averaged results on the publicly-released dataset in Tb. The publicly-
released dataset does not include the vegetation subset.
A.3 MASS ESTIMATION EXAMPLE RESULTS
We show qualitative results from our model on mass estimation on the ABO-500 (Collins et al. 2022) dataset in Fig. II
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Mesh
Property Fields
SDF
Property Fields
NeRF
Property Fields
Splat
Propent Fields
(a) Inference across representations: We show that VoMP can operate any geometry that can be voxelized and rendered, including meshes, SDF, NeRFs, and Gaussian Splats (o: 1:30).
Am anmchair falling the ground
A bowling ball falling armehair
(b) Simulating meshes: We show realistic simulations for meshes using predicted material values (O) 3:40),
Gaussian Splat
Simulator
Young's Modulus
Poisson's 's Ratio
Density
Vaxelized
Fields
(c) Simulating captured Gaussian Splat model: In this example, we apply VoMP to this Gaussian Splat model that we captured using commercial app. Our method converts this model into a simulation-ready asset 0:36).
dog tays Falling through pachinko (d) Simulating meshes and splats: We show realistic simulations for meshes (left) and splats (right) using predicted material values (a) 3:20).
stack of 3 oranges falling down
placie
Density
YM
Mechanical
MD Clenesaa Splant (MMcchSDD:Neelt
Property Fields
Poisson 's Ratio
Density
YM
concrese
dist
Volumetric
Poisson's 's Ratio
Property
(e) Simulating Gaussian Splats at scale: elastodynamic simulation of Gaussian Splat bulldozer going through a forest 100 Gaussian splat ficuses in the presence of wind; materials predicted by ( 3:00).
We test VoMP material estimates on variety of input representations (a), and show realistic simulations without any hand-tuning for meshes and splats across diverse scenarios. No hand- tuning of our predicted material parameters performed, showing that VoMP directly predicts simulation- ready parameters. See our video for simulation of these examples.
Figure 8: End To End Results:
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Object
Young's Modulus
Poisson's Ratio (1)
Density kg (p. m
Object
Young's Modulus (E. Pa)
Poisson's Ratio (2/
Density kg (p. m3
(E, Pa)
Figure 9: Inferred Mechanical Property Fields. We show additional mechnical property fields and slice planes through mechanical property fields estimated by VoMP 1:40).
Table 4: Voxel Mechanical Property Estimation. Errors for predicting mechanical properties from 3D objects averaged across all voxels in the test set.
Method
Young's Modulus Pa (E)
Poisson's 's Ratiu (or)
Density by
ALDE (1)
ALRE (1)
ADE (1)
ARB (1)
ADE (1)
ARE (1)
NcRF22Passiss PUGS (Shuai of ai 2025
2024
2,5719 (#1.5))
(6608)
(=131571))
(e0.7)
3.8619 (#200)
0.4512 (#6.))
3641.0715 (=382077))
4.0413 (e4.66)
Phys4DGGr
2025g
(#3.36)
(86.1)
(6005)
0.1425 (6:22)
(=119818))
(#2.53)
Ours
0.3765 (1..290)
0.0421
(1BA5)
0.0250
(1800)
0.0837 (LBAT)
113.3807
(1.31.90)
0.0900
(18.6))
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Object
Young's Modulus (E, Pa)
Poisson's Ratio (1)
Density kg (p,
Object
Young's Modulus (E. Pa)
Poisson's Ratio (z/
Density (p. kg
Figure 10: Inferred Mechanical Property Fields. We show additional mechnical property fields and slice
planes through mechanical property fields estimated by VoMP 2:10).
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Predicted: 1.58 kg
Predicted: 0.01 kg
Predicted: 0.02 kg
Predicted: 0.71 kg
Ground Truth: 1.58 kg
Ground Truth: 0.01 kg
Ground Truth: 0.01 kg
Ground Truth: 0.70 kg
Predicted: 9.09 kg
Predicted: 0.37 kg
Predicted: 7.52 kg Ground Truth: 7.54 kg
Predicted: 14 kg
Ground Truth: 9.07 kg
Ground Truth: 0.34 kg
Ground Truth: 0.10 kg
Predicted: 0.38 kg
Predicted: 0.25 kg
Predicted: 0.05 kg
Predicted: 0.19 kg
Ground Truth: 0.32 kg
Ground Truth: 0.19 kg
Ground Truth: 0.11 kg Ground Truth: 0. kg
Predicted: 7.68 kg
Predicted: 4.56 kg
Predicted: 1.23 kg
Predicted: 0.80 kg
Ground Truth: 7.60 kg
Ground Truth: 4.65 kg Ground Truth: 1.12 kg
Ground Truth: 0.91 kg
Predicted: 4.47 kg
Predicted: 0.42 kg
Predicted: 2.40 kg
Predicted: 2.85 kg
Ground Truth: 4.36 kg
Ground Truth: 0.29 kg Ground Truth: 2.27 kg
Ground Truth: 2.72 kg
Figure Mass Estimation. show qualitative results of estimating mass from ABO-500 (Collins et al. 2022) dataset.
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Table 5: Distribution learned by MatVAE compared to the distribution of MTD test set.
Young's Modulus (E)
Poisson's 's Ratio
Density (p)
W1 (J)
Wa (L)
DKL (4)
W1 ())
W2 (
DXL ())
W1 (L)
W2 (L)
DKL ())
0.0405
0.0798
0.1379
0.0317
0,0437
0.0342
0.0132
0.0172
0.0260
A.4
ADDITIONAL MATVAE RESULTS
A.4.1 DISTRIBUTION LEARNED BY MATVAE
We measure standard metries used for measuring the difference in the distribution learned by Mat- VAE and the distribution the test set in Tb. observing small errors which suggest that Mat VAE leamned good approximation of the true material distribution.
A.4.2 MOVING ACROSS MATVAE LATENT SPACE
We show an example of moving our latent space and move across both of its dimensions to obtain multiple smoothly varying material properties. We apply these properties a bunny and simulate dropping simulator and these various material properties. The color plots show the average displacements of the mesh from its state across simulation steps (c.g. Fig. T3)) demonstrating that even the actual physical behavior correlates with the dimensions of the latent space. Thus, we find that MatVAE learns a rich, meaningful latent space with smooth interpolation and ensures generating physically valid material triplets.
the latent space in Fig. 13 For each setting, we take point in
the ground with FEM
A.4.3 INTERPOLATION WITH VAT
We show additional examples of interpolating in the MatVAE latent space (66.4) in Fig. 12
Start Value
MaIVAR Interpolation
End Value
Stynokoum
Vanacium
Rhodium
Tungslen
Osaiuum
0.002 GPa
128.0 GPa
275.0 GPa
411.0 GPs
550.0 GPa
0.33
0.37
0.30
0.26
0.25
P
25 kg/m
6110 ke/m
12430 kgimn 19250 kg/m
22570 ke/m
Value
Nuive Interpolation
End
Styrofoam
Lnvaled (X)
Invaled (X)
Invalid (X)
Osmium
0.002 GPa
137.5 GPa
275.0 GPa
412.5
550.0
2 0.33
0.31
0.29
0.27
0.25
P kg/mn
5861 kg/m" 11298 kg/m²
16934 kg/m²
22570 kg/m"
Figure 12: Interpolating in MatVAF latent space: an additional example of interpolation, complementary to Fig.
7d
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Sctting
Young's Modulus (Pa)
Poisson's
Danity (kgla))
Interpolased
Range
Interpolased
Range
Interpolated
Range
Top-len )
Acnographiti
10x
Top right )
Polyureihane Team
10xx
5.0
0.304
0.30 0.30
298.2.0
50 300
Botton-led left (
Rulber (sott)
3.1 x 10
x.xx 1If
5.0
10P
0.885
0,48-11.50
952.0
950-950
Bottom-iggt (
Styrofaum
1.0 x 10
10x 100-0.000
0
100
0.322
0,3-0.35
22.6
15-35
Fig 13
Top-len )
Acrogel
x 13
10x UP
10
10r
0.257
0.2-0.3
1.0
10-1,
Top-right (
Neoppene
1.0 10
100 10
-1 1.0 107
0.994
0.45-0.5
1252.0
1250-1250
Botiom left
EPDM Rubber
10
5.0 1P
10
10"
0.69 0.49
11009
1100 1100
right
(Plsticiee))
10P
0,45-0.45
Top R
Polystyrene
10
Top-right (
Chinroprese Rubberr (Ncopuenc)
5.0
0,49-1449
12008
1200-12089
nottom-lett (
Pelystgmee (Fram)
2.5 10"
7.00--700000
0.34004
34.8
Bottom-right (
Polybutylme (PB)
2.5 10"
2.5 10"
-300
108
0.400
04-0144
932.0
930-950
(a) Corner Materials for our experiments on moving across the latent space (Fig. 13b to
13d
Lane D
Laser Dineniie
3:0 0000 5.0 122 10
1.5%% 10 1955 10"
5-13 oo 1.0 20 tub 10 1.25 x 10 faus to
1.77 10 1.00 00 1.00 x TAIL 1.31
120 1. 1.5 1.2 1.4
1.13 1/0 but 6,79
5.35
2.57 10
30 1120 12 1.30 10 in 1137
1.1 in 100 6.t0x 7.00 3.90
Baaxx 435 vi 1.00 1.80
116 3a 1 11"
LITK 10" T
+ or am 2 tasx 10
LaT un
244 ca 1.0 x Lin 10 120x an
(b) Setting
(c) Setting 2.
(d) Setting
Figure 13: Moving Across MatVAE latent space. We sample different valid mechanical property triplets (E, p) (Setting 1,2,3), corresponding to the middle square in the three color diagrams. We encode cach of these triplets with MatVAF, and then traverse the 2D latent space build 5 5 grid of latents around the starting value, which each decoded to actual mechanical properties. To visualize if latent space dimensions correlate with actual simulation performance, we apply each meachnical property triplet a dropping bunny simulation and measure its mean displacement from rest, which is color coded in the graphs below. Each diagram (b, c, d) thus corresponds to 25 simulation runs with different parameters. We observe a clear correlation between latent dimensions and simulation behavior. (a) 4:40)
D
time
Young's Modulus
Density
Poisson's Ratio
Voxelized Splats
Figure 14: Simulating Large Gaussian Splat Scene. We demonstrate elastodynamic simulation of
large Gaussian Splat scene with multiple objects segmented out and being assigned properties with VoMP.
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stitch frame
egs
cushion
Object
VoMP
blown-up VoMP
Pixie
blown-up Pixie
(voxelizing meshes)
Figure 15: Data Annotation. We compare data annotation process of VoMP and Pixie.
Table Comparison of Mapped Material Properties between Pixie's 's in-context physies examples <Le et al.
2025
and the datasets of known material properties.
Bizm
Mappail Mateiials
Pisic y
Datasct P
Pisic E
Daisset E
Pisaz
Datsect ar
Clay Brick
[1900, 1900)
12,000-009 6.000e+051
10.20. 0.20
tnce/pool
Porzzlan (Cemmiic)
(400, 400]
23000
P20000-08 2.00c+005]
P.000=10,
1000=+00
[0:40, 0.40)
2.20
Conmiic
[2000 2600
19 10000==10, 1.000+11]
[0.24,
18,000-009 1.100=+101
10.30
trchhuuk
Ouk
12.00-0066
0:40)
Mayle (Sugua)
[I [1,000s10, 1.300+100
[0.30
monilaaoss
2000 200)
[2 02.00-004, 2,002,00000000000 2.00c0044)
[0:40, 0.400
towershaae
Claas (Soda Lime)
Cilasi (Bocosilicate)
[500,
[2700, 2300)
[2500, 2500)
11,000e05, 1.000e+000)
17.200e+10.
[6.200ee 8.100ce 10)
7:400ce 10)
10.30,0.30)
[0.20. 0.20]
[0.23, 0.23]
Rowersllowers
[100, 100]
11,000e-04, 1.000)2404)
0.40)
Jlmbiiius
[300, 300]
700, 700
[I (1,000-05, 1.000c405)
[8,000=000, 10100+100
[0:35,00 0.35)
[0.30, 0.50
shubbhwgg
250. 250]
700,
[6 (6,000e+04, 6.000ee044)
[8,000e00W, 1.10ee100
(0.38,0.30)
[0.30. 0.50
shuubliliage
12.000-04, 2.00022004)
0.40)
Rutber (sofi)
1950, 950
[3,000-006 000e=00)
[0.48,
gnow/hlades
EPDM Rublier
[80, B0]
[1100. 1100)
[1.00e+04, 1.000c+04)
[1000ea07. 1 (.0004077
10.45, [0.45,0.45 0.45)
[0.49, 0.49)
Neoprene
[1230, 1250)
[10000e00. 1 1000044777
[0.45, 0.50]
snil vidble)
Sundy Leaa
[1200) 1200))
[1600, 1800)
15.000-405, 5.000:+055
[1 1000000888 5 5.000406)
[0.30, 0.30)
[0.31, 0.31]
Rubber (soft)
(960, 950]
33000e-000 5.000e+06)
[0.48, 0.50)
robber drcks and Inpolay
Nesgrme
EPDM Rubber
(90) 150)
11000 1100)
1250)
(3,000e-44, 000ce044)
II 10000=+07 1.000etth]
100000066 (000:4177
(0:40, 0.45)
10, 11.99 (.299
0.500
(Plasticized)
[1200, 14000
2.000cw07. 1.0002408)
[0.45,
(soft)
5.000++066
EFDM
[80,
11000
(3.000=-04, 6.00022044
100000007.
[0.49.
Neoprene
12500
1.000ea06. 1.00024077
Alaminium
22700 2700)
7,000=110. 7 7.000c
[0.85, 0.35)
Alaninum 2024-73
12600, 2800]
[2780. 2750)
15.000e 10, K.000c 10
17 17240e=10. 72240x 10]
10.25, 0.35)
[0.33, 0.33)
Alaninum 7073-36
12 2810)
7.100e=10. 7.100ce 10]
[0.33, 0.33]
Studl
[7700, 7700))
2,00ss111 2000c+11]
[0.31, 0.31]
nntel_enteskaal
Stinless Stedi 17-7PS
[2500, 2900]
[7800, 7800)
(8.000e-07, 1.200c+055
2.000e111 2.00c+111
10.25, 0.35)
10.30. 0.30
Stáilees Steel 440A
[7800) 7800)
2.000=111 2.000ee11]
[0.30, 0.30
sudbaad
Sundl
[1800, 2200)
[1600, 1800)
[4.000=007. 6.000c+077
[1,000a08, 5.000405)
10:25, 0.35)
[0.31, 0.31]
Jelio Nock/eello
[40, 60)
[0,000e02, 1.200e+003
10,25, 0,35)
mudisoow
12000 3000)
[1600, 1800)
[8.000e-04, 1.200ev05)
|1,000e00,,
10.15.0.25
10.31.
B COMPARISON WITH CONCURRENT WORK
Although Pixie (Le et al. 2025 is concurrent with us, we still compare aspects of our approach with Pixie. We discuss differences with Pixie in $2.2
Data Annotation Process. We compare data annotation process with the annotation process of Pixie (Le et al. 2025) in Fig. [5] Our method performs annotation from meshes while Pixie (Le) al. 2025) gets points from training NeRF, which often produces noisy points, and the segmen- tation is performed based on CLIP features, which often produces noisy segmentation for difficult objects.
Validity of Materials for Data Annotation. Although we do not have access to the Pixie (Le) et al. 2025) dataset, Pixie uses in-context physics examples, which include material names and ranges of mechanical property triplets in the annotation process. We analyze these in-context physics examples and compare them with real material ranges from MTD ($5.1) in Tb. We find that some of these in-context properties might create pleasing simulations with a particular simulator but can fall outside the range of real materials.
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wood
VoMP
fabric
Young's Modulus
Poisson' Ratio
Density
Pixic
plastic
Young's Modalus
Poisson's s Ratio
Density
Figure 16: Comparing Estimations. We compare property estimates hetween VoMP and Pixie for mesh.
Comparison of Outputs. Although Pixie (Lee et al. 2025) concurrent with us, we still compare the outputs of Pixic with VoMP one object in Fig. 16
C ABLATIONS
We provide an in-depth analysis motivating our MatVAE and Geometry Transformer training scheme by ablating each component in Tb. 7 and Our ablations require changing the hyper- parameters for fair comparisons; thus, for each ablation, we tune our hyperparameters within an identical compute budget.
MatVAE vs Vanilla VAE. Technically, MatVAE ($3) is built on top of the vanilla VAE (Kingma & Welling 2022) and we can use a vanilla VAE (Kingma & Welling 2022) in its place. In Tb. we show material property reconstruction and distributional metrics between vanilla VAE and our MatVAE. MatVAE outperforms the vanilla VAE almost all metrics. We find that Vanilla VAE collapses to the Young's Modulus property, giving us a low reconstruction error for Young's Modulus but significantly higher errors other properties.
Image Features. For aggregating image features 44.11. we experiment with using DI- NOv2 (Qquab et al., 2024), CLIP (Radford et al. 2021). and RGB colors by average pooling in the voxel. The results are shown in Tb. Our model had many layers in the Geometry Transformer F.2) initialized from a generation model (Xiang et al. 2025). This set of abla- tions was trained starting from random weights, due to the absence of generation weights for these settings. We find that using DINOv2 (Oquab et al., 2024 and CLIP (Radford et al. (02II) without initializing the weights from TRELLIS (Xiang et al. 2025 performs slightly worse, whereas simply using RGB colors performs significantly worse.
and appendix
MatVAE. While MatVAE acts as continuous tokenizer, it is possible to have the Geometry Trans- former directly predict R vector i.e. directly predict the material triplets. We find this produces significantly worse results for Young's Modulus estimation and Poisson's 's Ratio estimation.
Normalization Scheme. We experiment with different normalization schemes ($3) like Z-score, and not using log-space transform for either Young's 's Modulus Density. All of these normalization schemes lead to a significant degradation in performance. Most notably, removing the logarithmic scaling for Young's Modulus (w/o log(E) E)) or using simple Z-score severely harms prediction accuracy.
Loss. Our Geometry Transformer 4.2 is trained with &g loss for reconstruction (Equation We test the effect of replacing this with an & loss. This change results in a substantial drop in performance across all metrics, with errors increasing by factor of 2-3x for most properties. This indicates that the squared error penalty the E, loss is more effective for this material property regression task.
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D METRICS
We present explanation of the metrics use, and experiments interpreting these metrics.
D.1 METRICS FOR MASS AND FIELD ESTIMATION
To evaluate the accuracy of predicted scalar quantities such as object mass, well as continuous scalar fields like density or stiffness, we use several commonly adopted metrics. Let y denote ground-truth scalar value or voxel-wise field (c.g., density), and ÿ its predicted counterpart.
Absolute Difference Error (ADE). The average absolute error between predicted and ground- truth values:
N
ADE
U1
8s1-
(5)
N
This metric is scale-sensitive and reports the error in physical units (e.g., kg/m² for density, kg for mass).
Absolute Log Difference Error (ALDE).
The average absolute error in logarithmic space: log y: log 0sl-
ALDE
This metric captures multiplicative error and is particularly useful for quantities that vary cral orders of magnitude.
Average Relative Error (ARE). The mean relative deviation between predictions and ground truth:
N
Vi
ARE
N
This dimensionless metric penalizes over- and under-estimates proportionally, making it appropriate for comparing across varying scales.
Minimum Ratio Error (MnRE). A symmetric and bounded measure of relative accuracy:
N
MrRE Σ
min
(8)
This metric ranges from and is maximized when predictions are perfectly accurate. As sug- gested in prior work (Standley et al.) (2017). MrRE avoids bias toward systematic over- or under- estimation and reduces sensitivity to outliers, making it particularly effective for evaluating physical quantity predictions across heterogeneous samples.
Table 7: MatVAE Ablation. We ablate MatVAE by comparing it against a vanilla VAE and present reconstruc- tion and distirbutional metries.
Model
Modilus
Poisson's
Dessity
W;
Dxa
Wg
W
Manilla Welling MarVAF
0.0668
0,0840
0.044
0J8175
8.87%
0J1342
IU0122
0.0260
0.0445
TC penalty
0.109
wlo free zats
0.0099
0.1168
0.1311
0,2014
0.2064
0.6376
0.0121
0.0007
0.0223
E3
F.)
(())
log( (1)
Jog (
(A)
LS.(U
E.A. (1)
Bray Curtis (L)
Nanilla VAE
Kingma Welling 2022
B,012
15366.8730
0.336
0.0442
0,0544
00847
0.2384
2.1893
0.4690
MoVAF
IU0834
0,8426
RUM154
0.0036
0J0131
R.4439
8JHTT
(-0.085)
(413665)
(40.998)
(0.0419
(-0055))
(-U911)
(40.225)
(-1.745)
(-0-25)
Wub NP
01022
pan
011150
0L0033
0.0021
0.0021
020086
0L1729
010234
wis TC penalty
0.4999
15567 0086
0,8398
0.0377
0.0530
0.0437
0.2383
2.1514
0-4522
voo
0.0066
16332.7829
0,0276
0.0053
0.0041
0.2966
0.0436
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Table 8: Ablations. We ablate VoMP with choice of image features, using MatVAE. normalization scheme, choice of loss function. We report the voxel-level mechanical property difference errors.
Method
Young's Modulus (F)
(or)
Density Ag (p)
ALDE (
ALRE (?)
ADE (U)
ARE (1)
ADE (3)
ARE (})
Image Features (Geometry Transfomeer start from random weights,
w/ DINOv2 (Oquab al. 2024
0.2888
0.0536
0
0.0803
373.5183 (1:6780))
0.3126
w/ CLIP Radford of al. 2021
0,2695 (=
0.0508 (+906))
0.0250 (20
0.0771
(=
383.5844 (=776441)
0.3110 (+:685)
w/ RGB colors
1.2176
0.6593
0.1379
1644
3678.4451
4.7430 (1:485)
MaIVAE
(10.2))
0.1289 (18,8))
0.0480
0.1638 (1000))
917.5879 (1442.50)
0.86337 (1
Normalization Schemne
w/ 2-score
0.8838 (+0,6))
0.0996
(4:888)
0.0814
(2004))
0.2938
5269.2900
(#:96603)
6.4656
(5:4.0))
w/o logip)
0.6654 (19.4))
0.0748
0.0542
0.1806
549,9512 (1:513.57)
0.5976
wio log(E)
0.9033 (:0000))
0.1024
(4:889)
0.1182
(2006))
0.4189
4051.9121
(#838199)
5.0428
(4:322)
Loss w/
0.8947 (29422)
0.1038 (1:009)
0.0468
CERDN
0. 166666
568.7543
(2775111)
0.6337
(2:8,85
0.3765 (19.39)
0.0250 CE0D0
0.0837
113,3807
CL (919
(1..94)
D.2 METRICS TO MEASURE DIFFERENCES IN MECHANICAL PROPERTIES
We use multiple commonly used metrics for measuring differences between mechanical properties.
Relative Error in log( E). Relative error between predicted and true values of the logarithm of Young's modulus E reported in units of Pa. This captures relative error in material stiffness across several orders of magnitude.
Relative Error v. Relative Error in linear space for Poisson's ratio v, a dimensionless measure of lateral contraction under uniaxial loading.
Relative Error in p. Relative Error between predicted and true values of material density p. re- ported in units of kg/m sg/m3.
Relative Error in log(E/p). Relative Error in the logarithm of specific modulus, where E is Young's modulus and p is density. Reflects relative deviation in stiffness-to-weiglle efficiency.
Relative Error in log(G). Relative Error in the logarithm of shear modulus G 2(1+b) repre-
senting resistance to shear deformation.
Relative Error in log(K). Relative Error in the logarithm of bulk modulus K terizing resistance to uniform volumetric compression.
321-20j+ charac-
E
Lightweight Stiffness Ashby Index (P E1/2/pp) The Relative Error in log(P), where P / p, reflecting relative error in predicting material efficiency for maximizing stiffness per unit weight (Ashby Cebon 1993).
Energy Absorption Ashby Index (P /1/3/p). The Relative Error in log(P), where P
E1/3 p. quantifying relative deviation predicted energy absorption efficiency (Ashby & Cebon
1993
Bray-Curtis dissimilarity. Bray- Curtiss dissimilarity (Bray Curtis 1957) between predicted and ground-truth property vectors and y:
BC(x,y) Σ, lo yil E, + v))
A normalized, dimensionless measure in [0, 1] capturing overall distributional divergence across multiple material properties.
D.3 METRICS TO MEASURE DIFFERENCES IN DISTRIBUTIONS
We multiple commonly-used metrics for measuring differences between distributions.
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time
Simulations Interpret Errors. We demonstrate simulations performed show the relation between relative error simulation error.
Figure 17:
Wasserstein-1 Distance (W1). For probability measures μ,, v space X,
Wi Wi(,, inf 7El((a.)) xxx
||x yll dy(,,)),
(10)
where T( 2) is the of all couplings of y and Wi equals the minimum average "work" to move mass from to v.
Wasserstein-2 Distance (W2). For probability measures μu, v on a space X,
inf /
||x - y/l dy(x, v) 1/2
v) (ET((u.)) xxx
(II)
where [1(,, v/) is the set of all couplings of and v. The cot-mean-sqqaat transport cost between a and v.
Kullback-Leibler Divergence (DRL). For densities p, X,
(xl())lg) / p(z) log g(x))
p(x) dx.
(12)
DKL measures the expected extra log-lik log-likelihood of data drawn from when it is coded using instead of p.
D.4 INTERPRETING ERRORS FOR MATERIAL PROPERTY ESTIMATION
We experimentally demonstrate an interpretation of how relative changes material properties af- fect simulations of the finite element method (FEM) solver. We do so by simulating the deformation of unit cubes under many different material properties and scenarios with an FEM solver.
For each baseline triplet (Eo, Vo, Po) representing Young's modulus, Poisson's 's ratio, and density, we introduce variations following the scaling laws: density variations follow linear scaling Prew Po A). Poisson's ratio variations use the same linear relationship Vnew vo (1 + A), while Young's 's modulus variations use exponential scaling Enew = Ege to accommodate the wide range of stiffness values. We then apply every such unique material triplet to unit cube and perform simulation under some external forces.
During each of these simulations, measure the final volume and potential energy of the cube after the Newton iterations have converged.
Measuring Volume. For a body undergoing deformation, the deformation gradient Vu + maps material points from the reference to the current configuration, where represents the dis- placement field and I is the 3 x 3 identity tensor. The local volume change is quantified by the Jacobian J = det(F), which represents the ratio of deformed reference volume at each material point. The total deformed volume is: Vaet = Jn, J dV, where On denotes the reference configura- tion. The relative volume change, defined as AV/V (Vier Vo)/V,, Vo. provides dimensionless measure of volumetric deformation.
Measuring Potential Energy. We compute the total potential energy by combining clastic strain energy and sinetic-potentin contributions. We use corotated linear elasticity, where we calculate the Vu II and symmetric strain tensor [ + FT) energy density = μ (r²) + (tr(S))?, with Lamé parameters f1 and À derived from the Young's modulus and Poisson's ratio. We three distinct contributions in the kinetic-potential term:
deformation gradient
obtain the
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Young's s Modulus (E)
Poisson's Ratio (v)
Density (p)
10
03
0.01
3.
0.0
-32
-0.02
-0.
-1.0
-0.03
-0.3
-02
-01
0.0
0.1
0.
0.3
(x207)
0.4
20
15
1-
0.0
0.
-1
-0A
-2
0.0
-0.3 -0.2
-9.1
0.3
Figure 18: Gripping Force by Robots. demonstrate the relation between relative errors materials and relative change P.E. (top) and volume (bottom). We then show the confidence bounds in light shaded regions.
inertial component Emsnnia Sa |u u 2 dV that captures displacement changes between iterations our quasi-static solver, a gravitational potential Egaavity - So u g dV accounting for body forces, and an external work term Fiex = Sn u feu dV representing the applied loads. We thus compute the total potential energy as Evoal = Ja W dV Einenia + Egravity - Eext, evaluated at the converged displacement field.
We perform the simulations in the following scenarios,
Gripping foree by robots. We simulate 140 N compressive force, which is common in robotic gripping applications, for example,
Franka Emika (frankaemika) 2025) "Hand" end effector applies maximum of 70 N per finger with maximum clamping force of I40 N. We demonstrate the results from 486 simulations in this setting, all of which were run to convergence in Fig. [8
Impact Foree Dropping Objects. We simulate 120 N impact force that simulates package drop scenarios, calculated from the impact dynamics of a kg package dropped from 0.6 m height with 5 em deformation distance. We demonstrate the results from 486 simulations in this setting, all of which were run to convergence in Fig. 19
Tensile Testing Machines. We simulate 330 N force corresponding to standard tensile testing conditions employed in bench-top universal testing machines (ASTM Committee D20 2022 ASTM Committee E28 2024). We demonstrate the results from 486 simulations in this setting, all of which were run to convergence in Fig. 20
Tension. We simulate 200 N force, which represents typical pretension in tendon- robotic
systems, where continuum arms and wearable assistive devices maintain structural stiffness through cable tensions (Schäffer et al. 2024). We demonstrate the results from 486 simulations in this setting all of which were run to convergence in Fig. 21
E DATASET DETAILS
We present additional details about our datasets for training MatVAE ($3 and Geometry Trans- former 44.2
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Young's Modulus (E)
Poisson's Ratio (v)
Density (p)
34
0.5
1.2
0.5
0.0
-31
-02
-03
-003
8.
1.0
-0.3
-02
-01
0.0
0.1
0.2
0.3
(x200))
01 [1x201
1.0
-1-
-0.3
-0.2
-0.1
0.3
Figure 19: Impact Force on Dropping Objects. demonstrate the relation between relative errors in ma- terials and relative change in P.E. (top) and volume (bottom), We show the confidence bounds in light shaded regions.
Young's Modulus (F)
Poisson's 's Ratio (V)
Density (p)
5.1
0.3
0.1
8.0
-01
-01
0.3
0,0075
5.2
0.1
0.3
-01
0.0
0.1
0.2
0.3
8 1x109
2 1x:0
10.0
2.0
75
82
1.5
5.0
25
1.0
00
-33
35
3.0
-32
-01
3.0
0.1
0.2
0.3
-0.3
-2.2
-2.1
0.0
0.2
0.2
0.3
Figure 20: Tensile Testing Machine. We demonstrate the relation between relative errors in materials and relative change in P.E. (top) and volume (bottom). We show the confidence bounds in light shaded regions.
E.
ANNOTATION WITH VISION-LANGUAGGE MODEL.
To create our training dataset ($5) for the Geometry Transformer, we use Vision-Language Model (VLM) coupled with multiple other data sources like 3D assets, component-wise part segmenta- tions, material databases ($5.I), visual textures, and material names to annotate our dataset. We run the VLM on every segment of every object individually. We experiment with Qwen2.5-VI 7B,
Qwen2.5-Vi VL 32B, Qwen2.5-V. VL 72B (Bai et al. 2023 2025). VL-Rethinker (Wang et al. 2023), GPT (Cheng al.) 2024), and Cosmos Nemotron (Lin al.) 2024a). We experimentally
choose Qwen2.5-VE 72B for the data annotation. We show the system prompts and the user prompts
that in Fig. 22
25
We find the best performing system prompts with TextGrad (Yuksek-
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Young's s Modulus (E)
Poisson's Ratio (v)
Density (p)
5.4
0.020
93
0.4
0.015
52
81.
02
0.200
0.05
0.000
0.055
-02
0,000
-0.015
-03
-22
-01
0.0
011
02
033
18107)
2.4
2.0
531
1.5
0.055
81
1.0
0.000
0.0
0.05
0.5
-0.10
84
-33
003
-02
0.1
0.0
0.1
02
0.3
Figure 21: Tension. We demonstrate relation between relative errors materials relative change in P.E. (top) and volume (bottom), We show the confidence bounds in light shaded regions.
Table 9: VLM Annotation Errors. Errors for the VLM annotation for mechanical property annotation.
log(E) (U)
x (1)
(L)
log(E/p) (1) log(G) ())
log(K) (U) L.S. (J)
E.A. (.)
Bray CurtiCsrti (C)
0.0295
0.0426
0.1348
0.1961
0.0303
0.0330
0.2022
0.2162
0.2342
gonul et al.
2025).
We show a response from the model for one of the segments from an object in
dataset
Fig. and 27
We construct a tiny dataset consisting of complex objects that are manually annotated and compare these properties with the annotations from the VLM (Qwen2.5-VL 72B Tb. 9 We observe that the VLM, given significant additional information as we provide, performs close to human annotator performance. We report the commonly used metrics we list in Appendix D.2 for measuring differences in mechanical properties.
E.2 DATASET STATISTICS
Our dataset comprises a diverse collection of 1,692 objects, sourced from four datasets: sim- ready (NVIDIA Developer 2025), residential (NVIDIA Corporation) 2025c), vegetation (NVIDIA Corporation (002dd), and commercial (NVIDIA Corporation| (2025a). As shown in Tb. [10] the ma- jority of objects belong the simready and residential categories, with vegetation and commercial objects providing additional variety. Each object is decomposed into multiple segments, with a total of 8,128 segments across the dataset. Most parts are labeled with English material names, and for few parts that do not have these material names, we infer these from the PBR texture names that were applied to these parts. To characterize the physical realism and diversity of the dataset, we analyze the distribution of key material properties for all segments in Tb. II The wide range of material properties highlights the heterogeneity the dataset, which is essential for robust learning and evaluation of material-aware models. We summarize the most frequent material categories (e.g., metal, plastic, wood, cardboard) and object classes (e.g., residential, shelf, container), along with their respective counts and proportions in Tb. [2]
We report the statistics of our Material Triplet dataset in Tb. To train MatVAE, we use the "Filtered Dataset".
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System Prompt.
You are materials science expert specializing in analyzing material properties from visual appearances and physical data. Your task is to provide precise numerical estimates for Young's 's modulus, Poisson's ratio, and density based on the images and context provided.
Important Context:
The material segment you are analyzing may be an internal component or structure that is not visible from the outside of the object. For example:
Internal support structures, frames, or reinforcements
Hidden layers core materials
Components enclosed within the outer shell
Structural elements that are only visible when the object disassembled
When analyzing:
Consider that the material might be completely hidden from external view
Use the semantic usage and material type hints infer properties internal components
Internal structural components often have different properties than visible surfaces
For example, soft exterior might hide a rigid internal frame
Critical Instruction: You MUST provide numerical estimates for ALL materials, even organic, biological, unusual materials like leaves, feathers, or paper. For organic materials, estimate properties based on similar natural materials with known values
For leaves, consider them as thin plant fiber composites with values similar to paper or dried plant fibers
Never respond with "N/A" or any non nom-ric value in your property estimates
When analyzing materials, use step-by-step reasoning:
First identify the likely material class and subtype based on visual appearance (if visible) contextual clues (if internal)
Consider how texture, color, and reflectivity inform your understanding the material (when visible)
Incorporate the provided physical properties and contextual usage information
4. For each mechanical property, reason through how the visual and physical attributes lead to your estimate
Consider how the material compares to reference materials with known properties
6. If the material appears to be internal/hidden, use the object type and usage context to make informed estimates
Important Formatting Requirements:
Young's 's modulus must be provided in scientific notation followed by "Pa" (e.g.. 2.0e11 Pa) Poisson's ratio must simple decimal between 0.0 and 0.5 with no units (e.g., 0.34)
Density must be provided in kg/m/3 (e.g.. 7800 kg/m^3)
Each property must be on its own line with exactly the label shown the examples or parenthetical notes after the values
-Do not include explanatory
-LLWAYS provide numerical values, never text like "N/A" or "unknown"
Figure 22: System Prompt. The System Prompt we use every segment every object.
A12
0.39
B16-
6.2
812-
1/6
8:K-
8M-
Vengi tha
Priwe Baii
Figure 28: Young's Modulus Pa Figure 29: Poisson's Ratio (v). Figure 30: Density Histogram
(E), Histogram of Young's Modu- Histogram of Poisson's Ratio in our lus in our Geometry with Volumet- Geometry with Volumetric Materi- of Density in our Geometry with Volumetric Materials Dataset ($5).
ric Materials Dataset
Dataset (55)
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Table 10: Dataset Statistics. Number of objects, total segments, total points, average segments per object (std.
dev.), average points per object (std. dev.) for each dataset.
Dataset
Total Objects
Segments (%)
Voxels (%)
Avg. Segments/Object
Avg. Voxels/Object
commercial
82
650 (8.0)
1,812,064 (4.9)
7.93 (#7.199
22.098 (=:22,74))
residential
449
4225 (52.2)
9,109,380 (24.4)
9.41 (12188)
20,288 (1.11,114)
simready
1029
2544 (31.5)
24,148, 660 (64.7)
2.47 (21133)
23,468 (=225,03))
vegetation
104
670 (8.3)
2,267,848 (6.1)
6.44 (2:4.3)
21,806
(2:19,428)
train
1333
6477 1)).))
28,709,19 199, (76.9)
4.86 (1.12.6)
21,537
(122,433)
validation
165
552 (6.8)
3,719.996 (10.0)
3.35 (#:3.19)
22,545 (=233095)
test
166
1060 (13.1)
4,908, 766 (13.1)
6.39 (#:1333)
29,571 (2:25,07)
Total
1664
8089 (100.0) 37,337,952 (100.0)
4.86 (1:11.97)
22,439 (123,786)
Table 1I: Material property statistics for all segments in the dataset. We report the minimum, maximum, mean, median, standard deviation, and outlier count (% of values outside +30) for Young's s modulus, Poisson's ratio, and Density.
Property
Max
Mean
Median
Std Dev
Outliers (%)
Density (mm
5.0 x 10a
1.93 x 104
2.28 x 10
1.20 x 10a
2.44 10a
25 (0.3)
Young's Modulus (Pa)
1.0 x 10
2.8 x 10
4.19 x 10
1.0 x 10
6.53 x 10
165 (2.0)
Poisson's Ratio
1.6 10
4.9 10
3.36 10
3.5 10
4.36 10
88 (1.1)
F ADDITIONAL IMPLEMENTATION DETAILS
We present additional implementation details.
F.1 DESIGN OF MATVAE
We explain the motivation behind the design of MatVAE.
Normalizing Flow. Material triplets remain statistically non-Gaussian even after normaliza- tion (beavy-talle//multimmooal log10 E, log oi boundary-conneentaaed
[0, 0.5)), diagonal (s(= m) tends to mode-average and miscalibrate tails. We therefore param- eterize the posterior with a bijective normalizing flow (Rezende & Mohamed 2015) fo where is the parameter of the flow network f, and & is the space of all parameters V. This fy applied
(aangg(()) (m)). set = = (u(,), and to a Gaussian base lo sample u ~ (u( m) = No diag o
compute the density by change of variables
log (=(= m) log 4o (5. (z) m) + log det J 5- (:)
hase density
log Jacobrian
(13)
log qo m)
log det Jf (w)) lu (==)=((>)
base density
Ing. Jacobian
with a standard normal prior p(z) (O, I) and decoder likelihood pa (m 2).
Table 12: Most frequent high-level material categories and object classes. We report the top high-level material categories (aggregated and deduplicated) and the most common object classes the datasct, with their respective counts and percentages.
Mat. Category
Count (%)
Object Class
Count (%)
Metal
1434 (17.7)
residential
477 (28.2)
Plastic
553 (6.8)
shelf
250 (14.8)
Wood
707 (8.7)
container
193 (11.4)
Cardboard
315 (3.9)
cardboard box
106 (6.3)
Leather
140 (1.7)
vegetation
105 (6.2)
Chrome
171 (2.1)
crate
101 (6.0)
Glass
(1.0)
commercial
82 (4.8)
Fabric
60 (0.7)
pallet
67 (4.0)
Rubber
55 (0.7)
barricade tape
59 (3.5)
Stone
40 (0.5)
inclined plane
22 (1.3)
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Table 13: Dataset Details. We present statistics of our dataset for training MatVAE
Dataset
Size
Material Ranges
249
Extracted Materials
105456
Filtered Materials 101517
This keeps the ELBO form unchanged while strictly enlarging the variational family (the identity map recovers the Gaussian case), allowing de to match the true posterior and avoid mode- mode-averaging on (E, V4 p). We instantiate fv as a single radial flow,
displacement
(u) - u + Bl(w) (u - 20),
(14)
radiaa scale
h(u) (a + ||u 20l12)
whose log-determinant has the closed form (substitute h' = -h in the closed form from (Rezende
Mohamed] 2015)),
log det J (u) (D 1) log ++(hw))
angular
+ log 1 + Bh(u) - 8
(15)
radial
r(u) ||u 20
where D is the dimensionality of the latent space and 20 is a trainable D-dimensional vector (one per flow layer) representing the centre of the deformation.
Radial flows are invertible iff > and 3 > -a, we satisfy these by softplus(ā), 8 -a -a+ softplus(() (}) (Rezende & Mohamed, 2015) with unconstrained trainable parameters ā, B E R. We show our implementation Algorithm
Penalizing TC. We observed high dependence between latent coordinates in the aggregated pos- terior (2) (both dimensions tended to encode p). Thus, we decompose the KL-divergence term of the ELBO following (Chen al. 2018). For MatVAE, this allows to directly penalize the total correlation TC(=) = (L II, (zy)) where 7s(2) is the aggregated posterior, 2j is the j E 21, coordinate of the latent vector 2. This allowed us to reduce the high dependence between latent coordinates, causing both dimensions to encode density. During training, we fol- low (Chen et al. (2018) and approximate the aggregated posterior (2(2) Emoopacta [90(2 m)]
using samples from a mini-bate where Paota is the empirical data distribution.
Preventing Posterior Collapse.
For fixed m, define per-dimension marginals go(z) m) and (16)
KLy(2 m) = KL (go(2) m) p(2,))
Then, for each m,
KT (go(2 (z m) [|((=)) Σ (Ty(m)
(17)
TC TC (qo(= mm)=
<L((g(= m)) II, (m()mm)
So the total KL contains per-dimension rate term plus per-sample total correlation. In the Gaus- sian (no-flow) case, KL,(2 m) = (H,(m)² 2 (m) - log oy (m)² 1), whose gradients
drive (4 -> 0, a - under posterior collapse. We therefore impose capacity constraint ("free nats") on the dim-wis wise term to prevent collapse:
max (8, Epan. Kl
(18)
free-nats
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Algorithm MatVAE posterior update with a radial normalizing flow.
Require:
Batch x E R2x3
Encoder outputs (x()) E Bx
Encoder outputs log 0² (x) E Rx
Flow param 2g E R1xD
Flow param log E R
Flow param 3rw
Prior p(z) (0, I)
Ensure:
Flowed latent E R Post-flow log-density log ((= x)) E B
KL term denoted KL Reconstruction loss Lreoon
1: > Encode and reparameterize
2: μ f Encoder, (xx
3: log σ² +- Encodering (z)
4: N/ I)
5: Zbase +- exp( log o²) O
6:
7: Base posterior log-density
8: log q0 Edt log (i pdd, exp(log x
9:
Radial flow parameters (a 0, a.)
11: a + softplus(log a) + Ea
3 -a softplus(3rm)
13:
14: & Radial flow transform
15: diff + Zbase 20
16: r + |diff]| E,
17: h t (atr)
+ Zhase + +Bx x h diff
19:
20: Log dogedenermnnant of Jacobian
21: bh 8 x h
22: bbaah +- clamp (bh, -c, c)
log(1 bhat 24: terma < log(1 + bhitab - 33 h2
23: term, < (D
25: A log []| < term; + term2
26:
27: Change of variables and KL pieces
28: log + log 90- - A log |/]
29: logp: t Ed=1 log 0,
30:
31: Losses (non-relevant details shown as ...)
32: (É,,,,...) t- Decoder(z)
33: Creenn t- MSE/NLL in transformed space (...)
34: KL+
log Pz
35: Ereenn +
36: return (z, log g. KT, Crecm)
which enforces minimum information budget 8 0.1 per coordinate (zero subgradient below 8). This allows us to fix the empirically observed imbalance where one latent carried most information and the other collapsed. An aggregated alternative consistent with the KL decomposition is max(Ø- d, Σ, (L(gs(z,) p(2;)))
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Table 14: Training Hyperparameters. We show the hyperparameters for the MatVAE and Geometry Trans- former.
MatVAE
Geometry Transformer
Training Precision
FP-32
Training Precision
FP-16
Hidden Width
256
Voxel Grid Resolution
64
Network Depth
(x2)
Input Channels
1024
Latent Dimensions
Model Channels
768
Dropout Rate
0.05
Latent Channels
Epochs
850
Transformer Blocks
12
Batch Size
256
Attention Heads
12
Optimizer
AdamW 10-4
MLP Ratio
4
Learning Rate
Attention Mode
Swin
Weight Decay
10-1
Window Size
LR Scheduler
Cosine Annealing
Max Training Steps
200,000
Final Learning Rate
10-5
Batch Size per GPU
4
Gradient Clipping
5.0
Total Batch Size
16
a = 1.0 (KL)
Optimizer
Adam W
B-TC Loss Weights
B 2.0 (TC)
Learning Rate
10-4
7 = 1.0 (MI)
Weight Decay
5 x 10-2
Free Nats
0.1
Gradient Clipping
1.0
KL Annealing Epochs
200
Loss Function
&g
Data Normalization
Log Min-Max
EMA Rate
0.9999
F.2
NETWORK DESIGN
We now present our network architecture
The encoder architecture begins by projecting the 3-dimensional material triplet through a linear transformation into 256-dimensional hidden space, followed by SiLU activation. The resulting representation then passes through three "ResidualBlocks" each using a bottleneck design that compresses the 256-dimensional vector to 128 dimensions via LayerNorm and SiLU activation, applies another linear transformation, and restores the original dimensionality through second LayerNorm-Sil.U sequence. Each "ResidualBlock" maintains skip connection that adds the input directly to the final output. The encoder finally has separate linear heads that project the processed representation into the latent space parameters: one head predicts the posterior mean No (m) and another predicts the log- variance log o (m) for the 2-dimensional latent code
MatVAE.
The decoder mirrors this architecture reverse, beginning with a linear projection from the 2- dimensional latent space back to the 256-dimensional hidden representation, followed by SiLU ac- tivation. The latent encoding then goes through three "ResidualBlocks" with an identical bottleneck structure and skip connections the encoder. Finally, three separate linear heads decode the pro- cessed representation into the reconstructed material properties: Young's 's modulus, Poisson's 's ratio, and density, each predicted scalar values in the normalized space.
Geometry Transformer. Our model is based on TRELLIS (Xiang et al., 2025). We use a transformer-based architecture specifically designed for processing sparse voxel representations with associated material properties. The model operates on a 643 resolution voxel grid, accept- ing di24-dimeniional DINOv2 visual features as input and compressing them to compact 2- dimensional latent representation through 12-layer transformer backbone. Each transformer block utilizes 12 attention heads with 4:1 MLP expansion ratio, using Swin attention with 8x8 local win- dows. During training, the Geometry Transformer operates in conjunction with a frozen MatVAE that decodes the latent into material properties.
F.3 TRAINING
We present our voxelization scheme for training on meshes Algorithms and 3
We present the
hyperparameters used for training MatVAE and Geometry Transformer in Tb 14
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Algorithm 2 Segment-aware volumetric voxelization for meshes.
Require:
Full-mesh vertices Van E Nx3 faces Fan
Segments {(V, RNNx3, Fú, Ii Grid resolution r E N (voxel pitch h = 1/r) Per-segment cap Keg E N
Global cap Kan E N
Ensure:
Combined voxel centers Call R2 within [-0.5, 0.5] Segment identifiers sidall E {str} L
Discretized centers Can E R2x3 on an r grid
1: > Global normalization from the full mesh
2: Umin min( Van)
3: Umax f- max(Van)
4: (Vmin Vmmax 1/2
5: + max(Umax Umin)
6: 10-6
7:
8: Case +
9: sidace + []
for to M do
11:
Normalize segment to [-0.5, 0.5) and ensure triangles V + clip((V, -c)/s, -0.5 + E, 0.5 =)
12:
13:
Fy triangulate(F:)
14:
15:
Voxelize segment and solid-fill (Algorithm (C,, Y;) + VOXELIZESOLID(V', Fy, r)
16:
17:
if Keey is given and |C,| Keg then
18:
- Choice([C.]. Kegg without replacement)
C; C,[4]
20:
if [C]] = then
21:
continue
22:
Cece Bec-append (C;)
23:
sidace aaieeeappendd( ((si.) cil)
24:
25: if [Cnel = 0 then
26:
return (Ø, Ø, 2)
27: Call + concat (Cace)
28: sidall <- concat(sidaed.
29:
30: Optional global subsampling
31: if Kal is given and |Caul Kau then
32:
I choice(|Canl, Kan, without replacement)
33:
Cal - Canl7]
34: sidai [7]
35:
36: Discretize to 7 grid aligned with [-0.5, 0.5]
37: J + clip(((CCan 0.5) -r), 0, r r-1)
38: C.n + J/r 0.5
39: return (Can, sidan, Can)
Voxelization For Training. Our training dataset contains Universal Scene Description (USD) files with multi-segment meshes. Each mesh is normalized to the range [-0.5, 0.5] using a global bound- ing box computed across all segments to preserve relative spatial relationships. We volumetric voxelization using a regular 3D grid with a resolution of हq. where each voxel center is tested for interior containment within the mesh volume through point-in-polyhedron testing, followed by vol-
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Algorithm 3 Voxelization and flood fill primitives for meshes.
1:
procedure VOXELIZESOLID(V, F, r)
2:
Grid setup over a padded mesh AABB
3:
h 1--17 1/r
4:
amin - min( V); dmax + max(V)
5: Amin -- Omin h
6:
Umax f Omax +
7:
frr (Omaxx, Dunin,x) )
8:
f (0max,y Umin,y) /
9:
Tg [bmax, Umin,
10:
S S Ryg Uz] f false
X [22, Bys nz]
false
12:
Triangle rasterization: mark surface cells for each triangle = (vo, 22) E F do
14:
15:
Compute triangle AABB [fmins tmax] world coordinates
16:
Convert to grid index ranges (Amin &max: Jmin Imaxi Kmin kmax) for i imin to 1maa do for j = Juin to Jmax do for lt = kimin to kmax do
17:
18:
19:
20:
Cell box B (mmn ki,,, bmin + (i 1, + 1)4) if TTTRIANGLBBXXXTTRRREEEE
21:
B) then
S k] true
23:
24:
Exterior marking by flood fill non-surface cells Initialize queue Q with boundary indices (i, k) where Sli, k:] ffase
25:
26:
while Q empty do
27:
+ Q.pop()
28:
if [[]] then
29:
continue
30:
X[u] + true
31:
for each 6-neighbor of u within bounds do
32:
S'v] = false and X(v] = false then Q-push(r)
33:
35:
Solid fill (interior) and center extraction
36:
Y 1--XA-S
37:
C+
38:
for all indices (i.j, k) where Yii,j, k] = true do
39:
C Dini + (i + 0.5, j 0.5, h: 0.5) C.append
40:
41:
return (C, Y)
umetric filling to generate solid voxel representations rather than surface-only discretizations. All the voxels inside given segment receive the material properties the segment they lie in.
Rendering for Training. For multi-view image rendering of meshes, we use a path-tracing ren- derer produce photorealistic renderings 3D objects. Camera viewpoints are sampled using quasi-random Hammersley sequence distributed uniformly across a sphere. For training and testing, we render 150 views, though our method can work by rendering as many views as needed, with cam- eras positioned at a fixed radius of 2 units from the object center and configured with a 40-degree field of view. Images are rendered at 512x512 pixel resolution. The rendering pipeline outputs both the RGB images and the corresponding camera extrinsics and intrinsics. For rendering splats, simply replace the renderer with the 3D Gaussian Splat renderer (Kerbl et al. 2023) in our workflow. For rendering SDFs, render meshes using many points collected from the SDF, For rendering NeRFs (Mildenhall et al. 2020), we simply replace the renderer with serfstudia (Tancik et al. 2023 in workflow.
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Feature Aggregation. For visual feature extraction, employ DINOv2-ViT-L/I (Oquab al. 2024) with registers. We use a patch size of 14x14 pixels and process imput images resized to 518x518 pixels, resulting in 37 x37 patch. We use the nv-dinov (VVIDI INVIDI 2025 implemen- tation.
F.4 SIMULATION AND RENDERING
For our mesh simulations FFig. we simulate with the finite-llement method (FEM) using the libuipe (Huang et al. 2025 2024a) implementation, and we render the simulations in a path-
tracing-base -baee renderer. While comparing with other simulators (Fig. [ we use MPM (Sulsky et al. 1994) using ta ch -mpm (Hu & contributors] 2018). XPBD (Macklin et al. 2016) us-
ing Posiiioinni PositiooBaseeDDnamic.... [Bender & contributors 2015). and FEM using Warp (Macklin 2022).
For our large-scale splat simulations or splat + mesh simulations, we use Simplicits (Modi et al. 2024) using the sparse simplicits implementation using Kaolin (Modi et al.) 2024 Fuji Tsang al.) For rendering our large-scale splat simulations or splat + mesh simulations, we use Polyscope (Sharp) ct al., 2019) and composite splat renders from gsplat (Ye et al. 2024). For these simulations, we apply material property tolerances to reduce numerical noise: voxels with Young's modulus differing by less than 10a Pa, Poisson's ratio by less than 10-3, or density by less than 10 kg/m² are assigned identical values for the respective property. We present additional details for deforming and rendering deformed Gaussian Splats in Appendix G.5
F.5 BASELINES
Converting Hardness to Young's Modulus. NeRF2Physies (Zhai et al. (2224) does not estimate a numerical value of Young's 's Modulus, but instead predicts Shore A-Shore hardness. Thus, to compare our method with NeRF2Physics (Zhai et al. 2024) we convert these Shore hardness values to average Young's 's Modulus values.
Shore A. For Shore A hardness, we follow (ASTM International 2013) and use: EMPa e (S. x0.0255)-0.640:
(19)
where SA is the Shore A hardness value and EMra is Young's modulus in megapascals.
Shore D. For Shore D hardness, we follow (ASTM International 2015) and use: ExPa ((SD x0.0235)
(20)
where Sp the Shore D hardness value and EMPa is Young's modulus in megapascals.
Point Voxel Sampling. The baselines NeRF2Physics (Zai al. 2024 and PUGS (Shuai et al., 2025) in their methods sample points from the NeRF or Gaussian splat, respectively, and predict mechanical properties at those points. To ensure fair comparisons in Tb, 4 and Fig. 6b we explicitly make these methods work on the same set of points in the object on which our method is evaluated.
Implementation details of Baselines. The baseline NeRF2Physics Zhai et al. 2024 uses gpt-3. -urbbo for certain parts their pipeline. We replace gpt 3. 5 turbo in their pipeline with better performing model, GPT-4o (OpenAl & et al. 2024). The baseline Phys4DGen (Liu et al.; 22244) does not have code available. Thus, we faithfully reproduce the parts, "Material Grouping and Internal Discovery" and "MILLMs-Guided Material Identification". We produce these parts of their pipeline using GPT-4o (OpenAl et al. 2024) for the MI.LMs-Guided Material Identification. Furthermore, we obtained the prompts from the authors Phys4DGen (Liu et al. 2024b) and use the same prompts.
G ADDITIONAL DETAILS ON THE SIMULATIONS
We experiment with Simplicits (Modi et al. 2024), a reduced- -rddr simulator (Fig. | and accurate finite-element method (FEM) simulator (Fig. and 8b) with our material prop-
8c and Seh
https:://buiii wtt.:/t.......ooaoaaoaaea a/nv nov2
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Table 13: Hyperparameters for FEM simulation.
Hyperparameter
Value
Hyperparameter
Value
Time Integrator
Backward Euler
Linear Solver
pre-conditioned CG
Nonlinear Solver
Newton's 's w/ line search
Linear tolerance
10-3
Newton iters.
1024
Line search
Velocity tol.
0.05 ms-1
max iters
8
CCD tol.
1.0
Collision
Transform rate tol.
0.1/s
Friction
0.5
dt
0.02
Contact Resistance
1.0
Gravity
0..0- -9.,
d
0.01
erties. We also use a FEM simulator for our experiments on interpreting errors in properties (Ap- pendix D.4). We use a material point method (MPM) (Sulsky et al., 1994), and an Extended Position compare between
Based Dynamics (XPBD) (Macklin al. 2016) simulator for our experiments simulators (Fig. 2). We share details on these simulations. We also share details on the interpolation we use across all our simulations. We share the hyperparameters used for all the FEM simulations in Tb. 15
G.1 INTERPOLATION SCHEME
Our simulations receive material field sampled on voxel grid predicted by VoMP, i.c., values m(X;) given at lattice points { C Q. When the simulator needs material values at arbitrary query locations X (e.g.. clement centroids or vertices), we evaluate nearest-neighhour interpolation of the voxel field:
i' (X) arg min X - X2I12,
(21)
(xx) = X xx
We intentionally avoid higher-order interpolation of material fields since real objects are piecewise- constant across label regions, and convex blending across parts of the objects invents intermediate materials. These intermediate materials might not be physically present or admissible, while our out- puts fall into a valid material due to the MatVAE ($3). Nearest-neighhour preserves sharp interfaces and is usually robust for arbitrary query locations.
G.2 PREPARING SCENES AND ASSIGNING MATERIALS FOR THE FEM SOLVER
Mechanical properties are set either uniformly (like in Appendix D.4 or heterogeneously from voxel field. For uniform assignment, given and v we compute Lamé parameters
Ev
E
A v)(v 2v)
(22)
2(1
which are used elementwise together with a constant mass density
For heterogeneous assignment, a voxel lattice provides E(X), vXX), and p(X) at voxel centers. After applying the same rigid/scale transform as the mesh, each tetrahedron takes A, /u from the nearest voxel to its centroid, and each vertex takes p from the nearest voxel to its position. This produces per-tetrahedron À, and per-vertex p fields that directly used in the clastic strain energy density per unit reference volume (W), first variation of the incremental potential (R), and Newton- Jacobian (AC).
During simulation, a visual mesh embedded into the physics mesh by assigning each visual vertex x, to containing (or nearest) tetrahedron with vertices (X,)4 and barycentric weights {wa)) ) satisfying Σ. un and Σ. Wa X, X,; its deformed position then the barycentric interpo- lation of current nodal positions [x=]
def Σ W. X
(23)
The state update our simulation experiments is computed time-step by time-step. and we also deform and move the visual mesh according the physics mesh each time step.
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G.3 DETAILS OF THE FEM SOLVER
For FEM simulations, we use simulator based on the libuipe (Huang et al. 2025 2024a)
implementation and the Warp (warp. fem) (Macklin 2022 implementation. We first explain the details for our simulations in $D.4
We consider deformable continuum body with reference configuration ! C R3 and boundary O = Tn U Tw, where Pn denotes boundary points with Dirichlet boundary conditions, and I'v denotes boundary points with Neumann boundary conditions. The unknown solve for is the displacement field
+ IR3 Time is discretized into frames with a fixed step At. At each frame compute increment Au that advances the configuration <- Au while enforcing Dirichlet constraints on I' D. The deformation map is (XX) = x with deformation gradient F(u) + Vu, Jacobian modeling, we use the stretch tensor from the polar/SVD decomposition: F U diag(or) V then S V diag( ④ VT. Given Young's modulus E and Poisson ratio v, the Lamé parameters = (1 + (1 2v)) and E/(2(1 +)). Here V denotes the gradient with respect to reference coordinates, A:B tr B) is the Frobenius inner product, and ||-|| is the Euclidean norm.
det F, and isochoric invariant Te tr(FT F). For corotational
The elastic response we use is the corotational Hookean model. Define the small strain The strain energy density and Kirchhoff stress are
S I.
(CR(S)
Ne:E
ir(e))
shear (devintoric)
volumetric
(24)
T(S) 24 Atr(e)
volumetric
with a consistent linearization obtained via the variation of with respect to and projected to maintain symmetry and positive semidefiniteness.
Each frame solves an incremental variational problem. Given the previous increment A-n we
seek Au" " that approximately minimizes the incremental potential
Au
An"
IT (T)
p
A
dv
inertial regularization
pg Au fxt Au) dv
budy and external work
(25)
WeR (S(u"~1 Au)) dV
elustic energy
(Au)
interionthwunddary regularization
where p is the mass density, g is the gravitational acceleration vector, fxt denotes preseribed vol- umetric loads, and Im denotes any interior/boundary regularization term (e.g., a jump penalty in discontinuous settings). The admissible test function v is any sufficiently smooth virtual displace- ment that vanishes pp. The first variation (TT v) 0 for all such yields the residual
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functional
Au Au au n-1
R[Au)[v]= =
vdv
At2 inertia
+
(
pg v fext v) dv
bodylexternal
(26)
T (S(u"~11 + Au)) VvdV
(internal) virtual
+ Rint (Au)(v).
regularication
which is set to zero for all v. Newton's method is applied to R(Au) 0. At iterate Au (R) we assemble the consistent tangent operator A. = DR DR[Aut Au [3) (the Gàteaux derivative of R) and solve the linear system
K ju = - RR(Au Au (=)),
(27)
Au (k+1) Au (k) + a Su
where a E (0, is chosen by a backtracking Armijo rule to guarantee sufficient decrease of 11. The operator X. contains an inertial mass-like term Ja P At du vdV, the consistent elastic tangent from the linearization of (((()), and any interior/boundary penalty contributions. This procedure repeated until the update norm or residual falls below prescribed tolerance.
For all our other simulations (i.e. except the simulations $D.4) we use a closely related variant whose differences are in the constitutive law, material assignment, mesh preparation/ineerooattoo and contact handling. First, the stored energy and stress are taken to be compressible Neo-Hookean with volumetric regularization. Writing C F and B FFT, the energy and Kirchhoff stress are
WNH
(tr C
2 J) + JI
(28)
(F) μ (B 1) + II
This change only affects the elastic terms in II, R, and K;; the kinematics and inertial terms remain the same. For the simulation experiments, we also use IPC (L al. 2020a) for collision handling.
G.4 PREPARING SCENES AND ASSIGNING MATERIALS FOR THE SIMPLICITS SOLVER
Each object is specified by set of quadrature points Q {X,) that sample its volume (used for elasticity and inertia), a set of collision particles = {X.} for contact, and a set of visual vertices for rendering. We position objects with rigid transform (origin and rotation) and an object scale; these transforms are applied consistently when evaluating kinematics, gravity, and material fields.
We embed all objects into a regular grid domain and attach this grid low-dimensional Simplicits subspace. The displacement basis is the product of a trilinear grid shape and a per-object handle shape, with multiple duplicated handles per grid vertex. each quadrature point, evaluate and cache por-node subspace weights and their spatial gradients. These weights modulate the duplicated handle functions during assembly, instantiating the Simplicits subspace the grid.
Material parameters are assigned per quadrature point from a voxel lattice providing E(X). (XX,, and p (X).. After applying the same rigid/scale transform as the object, each quadrature location X, takes its material from the nearest voxel to Xg. We compute Lamé parameters per point as
E(X,) v(X))
Xy + (X,, () 2 2 (X,))
(29)
E(X,)
Mq 2(1 v(x,))
and use Pq p(X,) in the inertial terms.
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The quadrature weights set uniformly
Wg
(30)
where is the object volume estimate and [Q] is the number of quadrature points. This makes clastic and inertial energies invariant to the sampling density.
Collision particles C are used for detecting and resolving contact against other particles and reg- istered kinematic triangle meshes (containers and obstacles). We use an IPC-style barrier with Coulomb friction, and scale the contact stiffness by object volume and the number of collision particles to obtain comparable penalties across scenes.
G.5 DEFORMING SPLATS AND RENDERING DEFORMED SPLATS
We render each object set of anisotropic Gaussian splats. At rest, a splat is parameterized by its mean poo E IR3, a unit quaternion qo (with rotation Ro E SO(3)), and axis scales So E R We define the rest-frame shape operator
Ro diag(so).
(31)
rest anisotropy
During simulation, the displacement field yields world-space deformation gradient
at
local deformation
the splat center and a world-space position (obtained by evaluating the embedded deformation at the visual vertex). We map the anisotropy through the local deformation obtain the world- space covariance of the splat as
deformed ases
Σ
F
FLL
(32)
world covariance Here >> 0 is small scalar that guarantees positive-definitnnes under extreme compression.
deformed
padding
For rasterization we pass μ and Σ to the Gaussian renderer. The renderer (gsplat et al. 2024))
expects symmetric 6-vector parameterization; we therefore pack the lower-triangular entries as
[2n E12, V1s. D22,
233
(33)
packed covariance
Color appearance (spherical harmonni coefficients) and opacity are carried from the rest representa- tion; only the mean fs and covariance change over time. We also support scalar scale multiplier applied to for interactive control in qualitative visualizations.
Given the view (extrinsic) matrix V and vertical feld-of-view, we synthesize camera intrinsics
fz
Cy
K =
0
f9
Gy
0
1
(34)
fr
fo
lowa
tani lov
tan(
2
Go W Cy 2
with image size (W, H). We then render the set of splats {u, c) under (V,K) to produce RGB (and depth) frames. At every frame, we interpolate and F at the visual vertices, form Σ F + I. pack it as c, and feed the Gaussian rasterizer together with the stored colors and opacities.
G.6 DETAILS THE SIMPLICITS SOLVER
We use the Simplicits (Modi et al. 2024) simulator based on the implementation in Kaolin (Fuji Tsang et al.). Simplicits solves for a displacement field represented in low- dimensional subspace attached to a regular grid. This subspace is a product basis between trilin- grid polynomials and duplicated per-vertex "handle" functions whose influence is modulated by per- per-point weights and weight gradients evaluated at quadrature points. We assemble inertia and compressible Neo-Hookean elasticity this subspace, using the per-quadrature Lamé parameters
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(Ag. My) and measures wy- Each frame performs Newton steps the incremental potential with backtracking line search. Linear systems are solved by preconditioned conjugate gradients.
In the Kaolin implementation, splat-splat contact positions Xa, X3, and contact radius r, we set n. = (Xa /x,)/ | - xxll. Te = r, and use the relative offset o.(Au) = Au, Aug, so that de De. (Xa xx) and Vt.c measures tangential slip between the two.
particle pairs: for pair (a, 6) with current
However, in our implemennaatin,, pplat-mesh contact is handled differently than splat-splat contact. For splat-mesh contact, instead of using the collision points, we use triangle meshes as kinematic and its closest point p on nearby triangle (with interpolated mesh normal/velocity ne. Vm), we take = 2r and
colliders: for particle
(u(Au) = Au + (l|x pll - n. Auj n. Vm de = ||x - pll n Vm Only the simulated-object DOFs enter o,; mesh or splat motion appears through Vm.
(35)
These terms are used in the Newton system
K K + CH'CH,
r
g
(36)
contact stiffieess
Force
where H is the Jacobian of contact offsets, and g: C are the per-contact gradient/Hessian with spect to Og. For splat-mesh contacts only the simulated-object block H is present; for splat-splat contacts the two object blocks appear with opposite signs.
G.7 PREPARING SCENES AND ASSIGNING MATERIALS FOR THE XPBD SOLVER
We also use an Extended Position-Bast -Bseed Dynamics (XPBD) solver (Macklin et al. 2016) based on PositionBasedee wettiiioBBdeDDammm..... (Bender & contributors, 2015).
Particles and initialization. Objects are represented by particles positioned at rest locations {X;}, For each particle we initialize position x; f X; and a previous position equal to X; (Verlet), mass and inverse mass 1/m; (pinned points use 0). A soft sphere uses one center particle and a set of surface particles sampled on UV sphere; the center forms simple tetrahedra with nearby surface points for volume preservation.
Material parameters and compliance. To target an elastic behavior with Young's modulus E' and Poisson ratio (bulk modulus K E/(3(1 2v))), we choose distance- and volume-constrr compliances Oddist, Qval inversely proportional to E and K. XPBD uses the scaled compliance aa = // A/2 so that smaller a yields stiffer response.
Prediction, projections, and updates. Each frame predicts positions with Verlet integration, then iteratively projects distance, volume, and collision constraints. For pairwise distance constraint, the XPBD update displaces endpoints along the edge with factor
a
X;
X, x1,l'
Wi
Ax, x C
Ax
AX.
(37)
as + w. wy
|
Wj
with the analogous formulation for volume constraints using their gradients. After projections, we update positions and apply ground-plane contact with Coulomb friction.
Visualization. We track the evolving surface by updating a triangular mesh whose vertices coin- cide with the surface particles.
G.8 PREPARING SCENES AND ASSIGNING MATERIALS FOR THE MPM SOLVER
We use a material point method (MPM) simulator Sulsky et al. 1994 based on tai taichi mpm Hm
& contributors 2018). Scenes are specified by a uniform Cartesian grid, set of particles sampling each object's 's volume, and per-object mechanical properties.
Domain, grid, and timestep. We embed all objects in a unit cube domain discretized by an Agrid X Ngrid X ngrid grid (cell size Az 1/ngria). We use fixed time step At small enough for stability (e.g., At = 5 10-5 in experiments).
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Particles and initialization. Each object is sampled with material points (particles) positioned rest locations {Xp}- For each partiele we initialize position Xp < Xp, velocity Vp + 0, affine velocity field Cp < O, and deformation gradient F, f I. Mass is set as m, Vp with density and particle volume Vp consistent with the grid resolution. In the simple drop test, we sample a sphere at height and let gravity act.
Material parameters and constitutive law. son ratio v, compute Lamé parameters 1 E/(2(1 + v)) and Ev/((1 ((1 + 1) 2x) and use fast corotated (FCR) elastic model. With polar/SVD decomposition
We assign per-object Young's s modulus E and Pois-
U diag( V
and
rotation R UVT, the Kirchhoff stress is TFCR(F)
2p (F R) + (J
=
(38)
Transfers and updates. Each step performs Particle-to-Grid (P2G) transfers using quadratic B- spline weights: we scatter particle mass, momentum, and internal forces ~V, T Vw to grid nodes. On the grid, we (i) convert momentum to velocity, (ii) add gravity, and (iii) enforce box boundary conditions by clamping outward normal velocities to zero. We then perform Grid-to-Particle (G2P) to interpolate grid velocities back particles, update the affine field, and integrate
Xp Xp + V.. F f (I AI VV)
(39)
Visualization. We embed a coarse surface at rest, align it to the particle center mass, and update its vertices via interpolation of nearby particle displacements.
H OTHER RELATED WORKS
For completeness, include other tangentially related works here. A different setting from
is inferring physical properties given additional observations, such as video (Davis et al. 2015
Mottaghi al. 2016 Bhat et al.
2002 Chen al., 2025b Liu et al. [024a]] Xue al. [023]] Li
et al. 2025 |025 Brubaker et al. [2099]
Yildirim et al. 2016 Li et al. [2023] 2020b][wraaa et al. 2016 2015
2017 Xia et al.
2024 Xu al.
2019 Feng et al. 2024 Lin et al. 2024b) or physical manipulation
of real objects Yu et al. 2024
Pai et al.) 2001
Lang et al. 2003 Lloyd & Pai 2001 Pai et al.)
2008 Pai 2000 Yao & Hauser 2023 Pinto et al. (016). Other related works focus on generating
new physically plausible shapes, e.g. stable under gravity other interactions, but cannot augment
existing 3D assets with mechanical properties, which is our goal (Lin et al. 2025b Guo al. 2024
Chen et al.] 2024] Ni et al. [2024 Yang et al. 2024]] Mezghanni al.) 2022 Chen et al. 202 Cao
et al. 2025 Cao & Kalogerakis 2025). Other methods predict displacements (Zhang et al.
2024
Shi al. 2023), bypassing mechanical properties, focus other aspects such articulation
X1a
et al. 2025).
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User Prompt.
You are materials science expert analyzing two images:
1. A photo of the full object (showing how the material appears in context).
2. A sphere with the material's texture (showing color/rouginessiielcctttty isolation).
Using both images and the information below, identify the real-world material and estimate its mechanical properties.
Material context:
*Material type: fill in from dataset
*Opacity: fill in from dataset
*Dnssiyy: fill in from dataset kg/m²3
*ynamiic friction: fill in from dataset
SSatiic friction: fill in from dataset
*Restitution: fill in from dataset
* Usage:
fill from dataset
Your task is to provide three specific properties: Young's modulus (in Pa using scientific notation)
2. Poisson's ' ratio (a value between 0.0 and 0.5) Density (in kg/m33 using scientific notation)
Additional reference material property ranges to help you make accurate estimations:
closest match from material database
Young's modulus range fill in
Poisson's ratio
range fill in Density range fill in kg/m/3
closest match from material database Young's modulus range
fill
Poisson's ratio
range fill in Density range fill in kg/m^3
closest match from material database Young's modulus range fill GPa, Poisson's 's ratio
range
fill in Density range fill in kg/m²3
Example 1:
Material: metal
Opacity: opaque
Density: 7800 kg/m²3
Dynamic friction: 0.3
Static friction: 0.4
Restitution: 0.3
Usage: structural component
Analysis:
Step 1: Based on the images, this appears be standard structural steel with a matte gray finish.
Step 2: The surface has medium roughness with some subtle texture visible in the reflection pattern.
The physical properties (density, friction values, restitution) are consistent with carbon steel.
Step 3:
Step 4: Considering the usage and measured properties:
High stiffness (Young's modulus 200 GPa) based on typical steel values
Medium Poisson's ratio typical metals
High density matching the measured 7800 kg/m33
Young's modulus: 2.0e11 Pa
Poisson's ratio: 0.29
Density: 7800 kg/m33
Figure 23: User Prompt I. The User Prompt use for every segment of every object.
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User Prompt Continued.
Example
Material: plastic
Opacity: opaque
Density: 950 kg/m^3
Dynamic friction: 0.25
Static friction: 0.35
Restitution: 0.6
Usage: household container
Analysis:
The material shows the characteristic smooth, uniform appearance of a consumer plastic.
Step 1:
Step 2: It has moderate gloss with some translucency and slight texture.
Step The physical properties (medium-low density, moderate friction, higher restitution) match polypropylene.
Step 4: Based on these observations and measurements:
Medium-low stiffness typical of polyolefin plastics
Higher Poisson's ratio indicating good lateral deformation
Density matching the measured 950 kg/m/3
Young's 's modulus: 1.3e9 Pa
Poisson's ratio: 0.42
Density: 950 kg/m²3
Example 3:
Material: fabric
Opacity: opaque
Density: 300 kg/m/3
Dynamic friction: 0.55
Static friction: 0.75
Restitution: 0.2
Usage: furniture covering
Analysis:
Step 1: The material shows a woven textile structure with visible fibers.
Step 2: The surface has significant texture with matte appearance and no specular highlights.
Step 3: The physical properties (low density, high friction, low restitution) match a woven textile.
Step 4: Based on these observations and measurements:
Low stiffness as expected for flexible textiles
Medium-high Poisson's 's ratio from the woven structure
Density matching the measured 300 kg/m33
Young's s modulus: 1.2c8 Pa
Poisson's ratio: 0.38
Density: 300 kg/m33
Figure User Prompt The User Prompt we for every segment of every object.
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User Prompt Continued.
Example
Material: organic
Opacity: opaque
Density: 400 kg/m^3
Dynamic friction: 0.45
Static friction: 0.65
Restitution: 0.15
Usage: decorative element
Analysis:
Step 1: This is an organic material with the characteristic structure of natural fibers.
Step 2: The surface shows natural pattern, matte finish, and relatively brittle structure.
Step 3: The physical properties (low density, moderate-high friction, low restitution) align with plant-based materials.
Step 4: Considering similar organic materials and the measured properties:
Low-medium stiffness in the fiber direction
Medium Poisson's ratio reflecting the fibrous structure
Density matching the measured 400 kg/m33
Young's s modulus: 2.5e9 Pa
Poisson's ratio: 0.30
Density: 400 kg/m/3
Based on the provided images and context information, analyze the material properties. Note: The material segment might be internal to the object and not visible from the outside.
Respond using EXACTLY the following format (do not deviate from this structure):
Analysis:
Step I: Identify the material class/type based visual appearance
Step 2: Describe the surface characteristics (texture, reflectivity, color)
Step 3: Determine the specific material subtype considering its physical properties
Step 4: Reason through each property estimate based on visual and measured data
Young's 's modulus: <value in scientific notation> Pa
Poisson's ratio: <single decimal value between 0.0 and 0.5> Density: <value in scientific notation> kg/m"3
Critical Instructions:
You MUST provide numerical estimates for ALL materials, including organic or unusual materials
For natural materials like leaves, wood, or paper, provide estimates based on similar mate- rials with known properties
Never use "N/A", "unknown", or any non-numeris responses for the material properties
4. For Poisson's ratio, provide simple decimal number (like 0.3 0.42)
Each property should be on its own line with exact formatting shown above
Figure 25: User Prompt III. The User Prompt use for every segment every object.
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Object.
VLM Response.
Step I: Identify the material class/type based on visual appearance
The material appears be metallic, specifically aluminum, given the context of it being used a pallet and the provided density value which matches aluminum.
Describe the surface characteristics (texture, reflectivity, color) The surface is smooth with matte finish, showing minimal reflectivity. The color uniform light gray, typical of aluminum.
Step 2:
Step 3: Determine the specific material subtype considering its physical properties
Considering the density 2700 kg/m², the material is most likely aluminum, a common choice for pallets due to its lightweight yet durable properties.
Step 4: Reason through each property estimate based on visual and measured data
** Young's 's modulus+:; Aluminum typically has a Young's modulus around 70 GPa. Given the usage pallet, it needs be stiff but not overly so, supporting the estimate of 70 GPa. ** Poisson's ratio*#: Aluminum generally has Poisson's 's ratio around 0.33, which is typical for many metals.
**Density*:; The provided density is 2700 kg/m/3, which is consistent with aluminum.
Young's 's modulus: 7.0e10 Pa Poisson's ratio: 0.33 Density: 2.7e3 kg/m33
Figure Example Response We demonstrate an example response segment from one of objects from our dataset. The given object has one part.
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estimate within the upper range of Published as a conference paper at ICLR 2026
Object.
VLM Response.
Step I: Identify the material class/type based on visual appearance
The material appears to be type of rubber, specifically used for antiskid caps based on the context provided. The surface of the sphere suggests a matte finish, which is common for rubber materials designed for grip and friction.
Step 2: Describe the surface characteristics (texture, reflectivity, color)
The surface of the sphere is matte with a uniform gray color, indicating lack of significant reflectivity. There is a slight texture visible, suggesting it is perfectly smooth, which consistent with rubber materials intended for anti-slip applications.
Step 3: Determine the specific material subtype considering its physical properties Given the usage as an antiskid cap and the provided physical properties such density (1100.0 kg/m/3), dynamic and static friction (both 0.7), and restitution (0.8), the material is likely type rubber with good elasticity and frictional properties. The density matches well with EPDM rubber, which is commonly used for such applications due to its durability and resistance to environmental factors.
Step 4: Reason through each property estimate based on visual and measured data
**Yuun''s modulus**; Considering the material is rubber used for antiskid purposes, it needs to be flexible yet provide sufficient stiffiness to maintain shape under load. The given density and usage suggest medium-hard rubber, rubber's Young's modulus is uppropriate.
**Poisson's 's ratio**; Rubbers typically exhibit high Poisson's 's ratios close to 0.5, indicating significant lateral expansion when compressed. Given the material's ss flexibility and the need for good grip, value near the upper end of the rubber range is suitable.
**Densty***; The provided density is already specified as 100.0 kg/m*3, which aligns well with EPDM rubber.
Young's 's modulus: 1.0e8 Pa Poisson's ratio: 0.49 Density: 1.1e3 kg/m33
Figure 27: Example Response II. We demonstrate example response for segment from of the objects from our dataset. The given object has two parts, and we show response "rubber cap" part.
55


Reviews:
[{"review_id": "gWl9xR0nNT", "reviewer": "Reviewer_2WjH", "summary": "The paper proposes VoMP, a feed-forward system that predicts volumetric mechanical property fields including Young's modulus, Poisson's ratio and density- for 3D objects across multiple 3D representations (meshes, Gaussian splats, SDFs, NeRFs). The pipeline first voxelizes the object, lifts multi-view DINO image features into the volume, and feeds per-voxel features to a transformer trained to output material latent codes. MatVAE is a VAE trained on a database of real-world materials so that the decoding process guarantees materials lie on a learned manifold of physically plausible parameters. The authors construct a Geometry with Volumetric Materials (GVM) dataset via a VLM-assisted annotation pipeline that leverages part segmentations, PBR textures, and real-material ranges. VoMP generalizes across 3D formats and produces simulation-ready fields that drive high-fidelity FEM / simplicits simulations without tuning, outperforming recent baselines both in accuracy and speed.", "questions": "1. Generalizability of Voxelization: The feature aggregation step requires solid voxelization, especially challenging for sparse representations like NeRFs and GSs which are fundamentally surface or density fields. Given the extensive training data is derived from high-quality segmented meshes (GVM), how reliable is the voxelization scheme for novel, noisy, or incomplete real-world captured NeRFs/GSs? Does the current method of voxelizing 3D Gaussian splats via rendering depth maps and carving space introduce artifacts or inconsistencies that affect the predicted internal properties in practice?", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "1.  New Dataset: The GVM pipeline combines part segmentation + PBR textures + VLM prompts constrained by a curated materials range table to annotate 37M voxels, a scale jump over earlier works that only annotated sparse points. This will be useful to the community and encourage future research in this under-explored area.\n2. Volumetric Representation: Unlike previous models that focus heavily on surface properties or struggle with interior prediction (e.g., NeRF2Physics and PUGS due to feature field limitations), VoMP is designed to predict materials throughout the object volume. The system uses a unified multi-view rendering and voxelization pipeline, successfully handling meshes, SDFs, NeRFs, and 3D Gaussian Splats.\n3. MatVAE: The introduction of MatVAE- a VAE used to learn a low-dimensional latent space of valid real-world material triplets- is a significant contribution. This component ensures that the decoded per-voxel materials are physically plausible, even during interpolation or sampling, a guarantee largely absent in prior methods that may output simulator-specific or non-physical parameters. The paper explicitly shows that interpolation in the latent space yields valid materials, unlike naive linear interpolation in the material space.", "weaknesses": "I do not have a major concern, several minor points:\n1. Reliance on Approximate Input and Voxelization Resolution: The final output resolution is limited by the fixed-grid voxelization. This can lead to oversmoothing in highly heterogeneous regions and approximation errors when mapping results back to highly detailed input geometry, especially for thin structures or internal complexities. Also the authors do not provide a comprehensive study on the impact of input & output resolution.\n2. Assumption of Isotropic Materials: The annotation pipeline and the resulting model fundamentally assume that materials at the part level are isotropic (properties are uniform in all directions). This is a critical limitation for common composite or natural materials, such as wood or carbon fiber, whose physical behavior depends strongly on direction (anisotropy). The model cannot currently capture this crucial complexity.\n3. While the VLM is carefully guided by MTD and visual cues, the core physical property assignment for 37M voxels relies on the VLM's inference capabilities. Failure cases in similar VLM-based approaches (like Phys4DGen's dependency on MLLM consensus) highlight the brittleness of this approach. The use of a VLM introduces a reliance on an external, possibly inaccurate, source of physical knowledge, rather than deriving parameters purely from visual features and learned physics principles. I would like to see more discussions with regard to this.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "hHYba7JIgh", "reviewer": "Reviewer_vFJr", "summary": "VoMP predicts spatially varying volumetric mechanical properties—Young’s modulus, Poisson’s ratio, and density—from 3D assets, taking any renderable and voxelizable representation as input and outputting per-voxel fields ready for accurate simulation. It aggregates multi-view DINOv2 features into a voxel grid and uses a TRELLIS Geometry Transformer to produce per-voxel material latents. These latents are decoded by a 2D MatVAE trained on real-world triplets, which enforces physically valid material values. A data pipeline combines part segmentations, material databases, textures, and a vision–language model to create large-scale volumetric supervision and a new benchmark. Experiments show lower errors than NeRF2Physics, PUGS, Phys4DGen, and Pixie, while running in a few seconds per object and enabling realistic deformable simulations. Overall, the work delivers a fast, representation-agnostic, feed-forward approach to simulation-ready material fields via multi-view voxel features and a physically grounded latent material prior.", "questions": "To what extent does the method capture discontinuities at part boundaries without “bleeding” material across seams, and is there any explicit penalty encouraging jumps where appropriate?\n\nDoes the model predict uncertainties per voxel (e.g., variance over E, ν, ρ)", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "- Representation-agnostic, feed-forward pipeline that predicts per-voxel mechanical properties in seconds, with outputs directly usable in simulators.\n- Data contribution: a VLM-based pipeline that annotates ~1.6K part-segmented 3D shapes with **volumetric** materials; unlike PIXIE’s Pixelverse (surface-biased), this provides volumetric supervision.\n- Extensive quantitative and qualitative results with detailed ablations, plus realistic FEM simulations.\n- Clear writing and thorough explanations.", "weaknesses": "- Scalability is limited by the size and diversity of the training set (≈1.3K shapes) and the need for part-segmented annotations, making it harder to scale than methods that avoid volumetric labeling.\n- Most experiments use author-curated data; because the test set follows a similar distribution, generalization to independent datasets (e.g., Objaverse) is uncertain.\n- Resolution is bounded by fixed-grid voxelization, which restricts fine-detail fidelity.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "lCR1R2nyUQ", "reviewer": "Reviewer_6Gxe", "summary": "This paper presents a novel feed-forward model (VoMP) to automatically predict the physical properties for 3D objects, which is an interesting and core problem for setting up the physical simulations requiring these properties. It proposes two important modules, MatVAE and Geometry Transformer, to map the interior voxel to mechanical values in a physically valid manner. The experiments demonstrate the effectiveness and speed of the proposed model.", "questions": "1. The Geometry Transformer's architecture uses $64^3$ voxel grid, which seems a limitation. What are the bottlenecks preventing scaling this transformer up to $128^3$ or even $256^3$? Would this influence fine-grained detail prediction? It's interesting to analyze whether the performance could also scale up with respect to the resolution.\n2. A remaining concern is the material annotation accuracy. Although there is external knowledge to help with the annotation, how can to guarantee the correctness for training and evaluation? Is there any small expert-annotated dataset including these three values that can be used to serve as an independent test of physical accuracy? This problem seems implied in Figure 6, where in (b), VoMP outperforms all previous approaches significantly, while in (c) ABO-500 benchmark, the improvement is not obvious. How to demonstrate that the model is not mimicking the VLM-predicted behavior but truly learning from physics.\n3. The model allows internal structure prediction. How to deal with the situations of occlusion?", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The core design is novel and effective. The problem is decoupled into two parts, which guarantee valid physical latent space learning and fast plausible prediction. The ablation study confirms the superiority of the proposed architecture\n2. The feedforward nature achieves inference in seconds compared to the previous optimization approach, making it a useful tool for scalable simulation pipeline setup\n3. The paper includes a comprehensive set of experiments, including strong quantitative comparisons, ablation studies that justify the design choices.", "weaknesses": "1. One remaining concern is the reliance on VLM-generated ground-truth. An expert-annotated dataset is hard to get; hence, the usage of VLMs and external knowledge is an interesting point for data construction. But how to guarantee the correctness of the VLM predicted value is also crucial, especially for real future downstream task usage. \n2. The Geometry Transformer is trained using a fixed $64^3$ voxel grid, which is rather low resolution for complex 3D assets. This seems like a major bottleneck that prevents the model from capturing fine-grained material details.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "yvkxF0tAQ8", "reviewer": "Reviewer_HQpe", "summary": "This paper proposes VoMP, an end-to-end framework that predicts voxel-wise physical property fields from a voxelized 3D representation aggregated from unprojected 2D features. The method employs a MatVAE trained on real material databases to ensure physically plausible outputs, a Geometry Transformer that transforms the input features to predict per-voxel latent codes in the material space, and uses a decoder to reconstruct continuous volumetric material fields from these latents. To train this model, the authors construct a large-scale GVM dataset with voxel-level annotations generated via VLM guidance. Experiments across various 3D inputs demonstrate generalization and physically consistent simulation results.", "questions": "A bit of concern around L244: Since transformers inherently support variable-length sequences, why is cropping necessary in your implementation? What specific limitation or efficiency concern motivates this design choice? The explanation that “dynamic resampling ensures the model is exposed to different parts of the asset over epochs and has a larger number of effective max voxels” seems counterintuitive. Random subsampling may lead to distribution shift during full-sequence inference, effectively making inference out-of-distribution compared to training. Moreover, if subsampling changes which spatial regions of the object are visible or centered, the geometric semantics of each cropped region could shift, potentially confusing the model. How do you ensure consistency of geometry–material correspondence under such random cropping or resampling?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- Proposes a framework for predicting voxel-level material properties from arbitrary 3D representations, defining a novel and important task in 3D physical modeling.\n- Introduces a MatVAE that maps material parameters into a physically valid latent space, effectively smoothing predictions and constraining outputs to realistic ranges.\n- Employs a VLM to automatically construct large-scale annotated datasets, with the resulting GVM dataset being valuable for future research and other methods.\n- Demonstrates higher overall quality than prior methods, with notable improvements in physical consistency and simulation fidelity.", "weaknesses": "- Although interior structure plays a crucial role in physical simulation, the current voxelization approach (projecting 2D multi-view features) is not well-suited for capturing internal geometry variations, leading to limited understanding of interior geometry.\n- The voxelization process may cause significant information loss in high-frequency or fine geometric regions, reducing the spatial precision of the predicted material fields.\n- The transformer design uses only Swin-Attention without the hierarchical downsampling (and upsampling) scheme of a full Swin-Transformer, which restricts the receptive field and may limit the model’s ability to capture long-range structural dependencies. The VAE of TRELLIS is only for local geometry encoding and compression, and using that structure for global material property prediction is not suitable.\n- The task and dataset inherently probably contain inconsistencies due to the semantic labeling process based on VLM and the task’s inherent ambiguity. A pure regression formulation may not be ideal for modeling such uncertainty, even with the help of a latent MatVAE. Would a generative or probabilistic approach better capture these ambiguities?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)