Gaussian-Augmented Physics Simulation and System Identification with Complex Colliders
Authors: Federico Vasile
Ri-Zhao Qiu
Lorenzo Natale
Xiaolong Wang
Venue: NeurIPS 2025 poster ()
Keywords: System Identifications from Videos
Gaussian Splatting
Physics Simulation
Primary area: applications
TL;DR: System identification from videos during collisions with arbitrarily shaped rigid bodies.

Abstract: System identification involving the geometry, appearance, and physical properties from video observations is a challenging task with applications in robotics and graphics. Recent approaches have relied on fully differentiable Material Point Method (MPM) and rendering for simultaneous optimization of these properties. However, they are limited to simplified object-environment interactions with planar colliders and fail in more challenging scenarios where objects collide with non-planar surfaces. We propose AS-DiffMPM, a differentiable MPM framework that enables physical property estimation with arbitrarily shaped colliders. Our approach extends existing methods by incorporating a differentiable collision handling mechanism, allowing the target object to interact with complex rigid bodies while maintaining end-to-end optimization. We show AS-DiffMPM can be easily interfaced with various novel view synthesis methods as a framework for system identification from visual observations.

Gaussian-Aummented Physics Simulation and System Identification with Complex Colliders
Federico Vasile
Ri-Zhao Qiu
Lorenzo Natale' Xiaolong Wang?
Istituto Italiano di Tecnologia. PUC San Diego
setess//asddffffn github.ic
Figure 1: We present the Any-Shape Differentiable Material Point Method (AS-DifMMPM), a particle-based framework for simulating collisions with arbitrarily shaped rigid bodies. When integrated with Gaussian-based rendering, it enables physically plausible animation and system identification (estimation of object physical parameters from visual observations).
Abstract
System identification involving the geometry, appearance, and physical properties from video observations is challenging task with applications in robotics and graphics. Recent approaches have relied on fully differentiable Material Point Method (MPM) and rendering for simultaneous optimization of these properties. However, they are limited to simplified object-environment interactions with planar colliders and fail in more challenging scenarios where objects collide with non- planar surfaces. We propose AS- AS-DifiMPM, a differentiable MPM framework that enables physical property estimation with arbitrarily shaped colliders. Our approach extends existing methods by incorporating differentiable collision handling mechanism, allowing the target object to interact with complex rigid bodies while maintaining end-to-end optimization. We show AS-DifIMPM can be easily interfaced with various novel view synthesis methods as framework for system identification from visual observations.
1 Introduction
Bending but not breaking, branch dances with the wind-yielding to its force yet never surrendering. From the gentle drift of a balloon the violent shatter of glass, the world reveals its hidden truths through motion. We, too, learn not only by seeing but by umderstanding-trrati movement the forces that shaped it. In this work, give machines this power: see, reason, and uncover the physical essence of objects through their dance with the world, recovering their hidden properties from mere pixels.
back from
Estimating the physical parameters of objects from visual observations is a challenging task in computer vision, with applications in robotics, virtual reality, and graphics. While existing methods
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

such as PhysGaussian []] can animate static scenes by simulating plausible dynamics, they do not support the identification of object properties from dynamic scenes. Humans naturally infer an object's 8 geometry and dynamics through two-step process. First, they recognize and understand its shape (e- a ball). Then, by observing its interactions with the environment (e.g., let the ball fall on the ground), they deduce its physical properties. Inspired by this intuition, modern system identification methods follow a similar paradigm, combining two components: a rendering model to reconstruct geometry from images and physics engine to simulate motion, enabling the estimation of physical properties from video sequences.
Recent advances in scene representations particularly point-based models (2 and particle-based physics simulation [3], have facilitated the animation of static geometry with physics grounded motion. This process involves establishing correspondences between the points used for rendering and the particles in simulation, allowing the radiance field to animated by applying the motion derived from simulated particle trajectories. As a result, for physical properties estimation, this approach can be applied by reconstructing the object's geometry, initializing an estimate of its physical parameters, and refining them through gradient-based optimization, comparing simulated motion against real-world observations.
PAC-NeRF 4 is a pioneering model for system identification from visual observations; combining voxel-based radiance fields [5] with a Differentiable Material Point Method (DiffMPM) [ to enable gradient- based optimization of physical parameters from images. However, this approach, along with other recent works g 9 share a significant limitation: they perform system identification only when the object interacts with simple boundaries such as the ground. While effective, this setup fails to capture more complex scenarios, where objects interact with arbitrarily shaped rigid bodies.
In this work, we extend system identification beyond simple boundary interactions, enabling estima- tion of physical properties in more complex settings. To the best of our knowledge, this problem has not been previously addressed, primarily due to two key limitations: (i) existing system identification methods are restricted to interactions with a planar boundary 4 7 g 9 and (ii) available MPM-based simulators that accurately handle arbitrarily shaped colliders are not differentiable [10] thus not suitable for physical parameters optimization. Our contribution is threefold:
1. Any-Shape Differentiable MPM. We propose AS-DiffMPM, a Differentiable MPM capable of handling collisions between the target object and arbitrarily shaped colliders. Quantitative experiments on Newtonian, non-Newtonian and granular materials demonstrate the necessity of an ad hoc solution for rigid body interactions, which previous system identification methods have overlooked.
2. Versatile Collision Handling Framework. We design a general interface to integrate colliders of various formats (i.e., mesh and 2D Gaussians (T) into AS-DifIMPM.
3. Kendering-Physste Integration for System Identification. We combine our AS- SS-DiffMPM with multiple rendering models and establish benchmark for system identification from visual observations when the object collides with arbitrarily shaped rigid bodies.
2 Related Work
Scene Representations for Photorealistic Rendering. The topic of scene reconstruction and synthesizing photorealistic novel views has been studied in the computer vision community for decades [12 13 [14. Recently, there has been a growing interest in using learning-basee differentiable
rendering or rasterization for such a purpose (2 15 16 [8]. These methods are often categorized
into implicit rendering methods based on ray-marching queries [65] 17 [8] or explicit rasterization methods [_. To manipulate and animate these static scene representations, researchers have shown that it is possible to edit both implicit methods (often via remapping voxel-based representations [4] 19] and explicit methods (via direct manipulation of explicit units [8] (0).. Our method is mostly orthogonal to the development in scene representations. The AS-DiIIMPM is a plug-and-play module to both NeRF- and 3DGS-basse methods, as quantitatively shown in the experiment.
Physics-integraedd Scene Synthesis. While high-qualit, reconstruction methods offer pathway to synthesize static scenes from set of images in novel viewpoints, they are limited to understanding static appearances. Humans, on the other hand, have the ability to picture physically plausible interactions with the scenes. To equip machines with such an intelligence, researchers have sought to animate static scenes with physics simulators generate animated scenes that are both visually and

---

20G5
Col 5on
P2G GRID-OP G2P
Multi-view input images
Continuum Material
Physically plausible animation
Rendering
AS-DIRMMP
Update Particle P Physics
Figure 2: Overview. Given multi-view input images, we separately reconstruct the continuum object
using a rendering model (c.g.. (T and the rigid body collider with 2DGS [.]. Particle trajectories are subsequently advected using AS-DiffMPM. Finally, the updated particle positions are mapped back to rendering primitives for photorealistic and physically plausible animation.
Due to the indirection caused by implicitness, few methods animate implicit NeRFs 233 Many researchers have combined Material Point Method [] with Gaussian Splatting (2) due to their naturally aligned point- representations. These methods have shown to provide photorealistic animations [ 25 with extensions to VR applications [22], language-driven animations [20], and complex fluid dynamics (21). However, these methods provide physically plausible animations of static scenes rather than estimating physical parameters of objects. Another line of work leverages object dynamics priors from video generative models endow static 3D objects with interactive behaviors [26 27 28 29]. While effective for visually realistic interactions- in applications such as content creation- they may fail in domains like robotics, where precise physical understanding is necessary. In contrast, our work aims to recover accurate physical parameters of objects from visual observations.
physically appealing [1 21 20 22
23
24
System Identification from Videos. The identification of dynamic systems goes beyond simple animation, it requires not only visually plausible animations but also accurate physical properties that replicate the behavior of the reference system. Prior to the introduction of photorealistic differentiable rendering [15), system identifications from videos have been difficult due to the optimization of physical parameters through differentiable rendering and simulation for system identification. PAC-NeRF [4) is a representative method that combines a voxel-based NeRF [5] and DifIMPM for this task. Following up this work, GIC [ introduces novel scene representation method upon 3DGS 12 to improve the supervisory signal from visual observations. Additionally, [9] replaces MPM with Spring-Mass representation model elastic objects. However, these methods focus on system identification under the assumption of object interactions with planar surfaces, as the underlying physies simulator does not support complex colliders. Our AS- AS-DiffMPM bridges this gap by supporting system identification under more realistic conditions, such as collisions with complex colliders.
coupling of appearance and dynamics 30 Recent works have leveraged gradient-
Preliminary
3.1 Material Point Method
The Material Point Method (MPM) 31
32 3 is a widely adopted approach to simulate the dynamics of continuum materials. It combines the strengths of both Lagrangian particles and Fulerian grid by discretizing the continuum as a set particles carrying physical information such as position, velocity, and mass. For every update step, these properties are transferred to the Eulerian background grid to solve the equations of motion on the grid nodes. Finally, the resulting nodal velocities on the grid nodes are interpolated back to the Lagrangian particles, thus updating the state of the material. MPM operates in three stages: Particle-to-Grit (P2G) transfer, Grid Operations (G-OP), and -arrtiice (G2P) transfer.
Specifically, considering toy example where an object subject to gravity, we represent the object as set of particles carrying the following Lagrangian quantities: the particle position Xp. velocity vp. and mass my- These particles interact with an Fulerian grid, which stores nodal quantities: the position Xg, mass my and velocity V, at the grid node g.

---

At each time step, the simulation proceeds through the following stages:
Particle-to- setticle-to-riie Grid (P2G): Physical quantities from particles are transferred to nearby grid nodes using weighting function wy (x(X, Xp). The mass and momentum of each particle contribute to the grid:
mgg Σ mp - Xp), Vg P
Σ mp MipppWyXx - Xp).
(I)
mg
Grid Operations (G-OP): Once the mass and momentum fields are constructed on the grid, forces such as gravity g are applied to update velocities at grid nodes: V. <- Vg + Alg. Next, boundary conditions are enforced to ensure that the object correctly interacts with obstacles in the scene. In this example, we consider a sticky ground, meaning any particle colliding with the surface loses velocity upon impact. The ground is represented as a plane defined by a point X5 and a normal n, A grid node is in contact with the ground (x, xx) n, I 0, in which case its velocity is set to zero, i.e., V 0.
Grid-to-Parie Partiiate (G2P): The velocity field from the grid nodes is interpolated back to the particles update their state. Each partiele gathers velocity from the surrounding grid nodes:
Vp Σ VoWg((g -xp).
(2)
9
The particle positions are then updated: x, t X, + Atvp
3.2 System identification
System identification aims to estimate the geometric structure and physical properties of dynamic objects from multi-view video sequences. Following prior works 4 7,8 assume that the object material (e.g., Newtonian) is known and that its behavior adheres to continuum mechanics
32 33
Rigid Body Colliders
4.1 Collision Resolution in MPM
common approach for handling collisions between the continuum material and a rigid body is to apply velocity corrections during the G-OP stage, introduced in See. [..] Specifically, level sets (or signed distance functions) are used to classify each grid node as inside or outside the collider and adjust the nodal velocity accordingly [3 Although straightforward and effective, this method fails with complex geometries (e.g., open surfaces, sharp boundaries), since all the particles in the same grid-cell region share single velocity field. In contrast, Compatible Particle-in-Cell (CPIC) (IO) handles collisions in a particle-wise manner during the P2G and G2P steps. It partitions grid nodes and partieles into compatible or incompatible sets relative to the boundary's surface, allowing more precise velocity corrections for each particle colliding with the rigid body.
method to project the rigid body onto grid-based distance field (Sec. 4.1.1). ). This information is transferred to the continuum material (Sec. [41.2) and used to possibly apply velocity corrections on particles based on their relationship with neighboring grid nodes (Sec.) 4.1.3.
Hereafter, we detail the CPIC 10
4.1.1 Project Rigid Body to Collision Grid
Following prior work [10], we represent the rigid body collider mesh and project it onto grid that encodes propertics for collision handling. We define Collision Grid with the same resolution as the MPM Eulerian grid and store the following quantities at each grid node: (i) the affinity flag Ag indicating whether the grid node g is near the boundary, (ii) the unsigned distance dg from the grid node to the boundary, (ii) tag Tg denoting which side of the boundary the grid node on and (iv) normal n, retrieved from the boundary. The projection process follows three key steps: sampling rigid particles, identifying affinity nodes and reconstructing the Collision Grid.
Sampling rigid partieles. To map the rigid body's surface onto nearby grid nodes, the collider is treated collection of primitives, thus, sample predefined number of rigid particles on each

---

face 5' of the mesh representing the rigid body. Moreover, we define {(xxp) as the face to which the rigid particle X,p belongs.
Identifying affinity nodes. In order to identify all the grid nodes surrounding the rigid body, we map each Xrp to the 3x3x3 grid of neighboring grid nodes denoted as (xrp). For each grid node E N (xrp), its position Xg is projected onto the plane defined by the face {(xpp). If the projection falls inside the face, we store the (Xxp)) pair and set A 1 (otherwise, we set Ag - 0).
Reconstructing the Collision Grid. Since there may be multiple faces in proximity to the same affinity grid node, i.c. {xxg1 5') {i..... l]. we select the one with minimum unsigned point- plane distance:
= arg min (dist(xg: E*)l.
(I....)
and store its normal in ng. the sign of the distance in Tg sign(dist(xx {g) and the unsigned distance in dg.
In summary, for each grid node g, the Collision Grid carries the following properties: Ag. dg. Tg ng.
4.1.2 Transfer Collision Grid Material Particles
The Collision Grid used transfer properties to material particles, ensuring accurate interactions with the boundary and possibly correcting undesired behaviors (c.g., penetration).
Particle affinity. Given the material particle position Xp, we set Ap 1 if at least of the 3x3x3 neighboring grid nodes g E (xp)) has Ag =
Particle distance, tag, and normal. For each material particle x, in affinity with the Collision Grid, we retrieve the collision properties through interpolation over N o
(xx)):
dp
Σ
Wi (g(X, To)
np
Σ
(g(Xg -xp)A
(4)
(EN(
(EN(
where w is a nodal weighting function (c.g., B-spline [31 34
Then, we set T₁ = sign(dp). However, if particle penetrates the boundary, incorrect TT may be reconstructed. Therefore, each particle's tag T, retains its first acquired value until the particle loses affinity, i.c., moves away from the boundary. As result, if a particle penetrates the boundary due simulation errors, it will have an incorrect dp (i.e., wrong sign) while still retaining a correct Tp. This allows penetrations to be fixed: fp dpp.p. where fp is the penalty force to apply to the material particle p and ky is the penalty stiffness parameter.
Particle-grid compatibility. When a material particle approaches the boundary, its tag Tp is compared with the neighboring nodes g E (x,)): p and g are incompatible if TT and T, = -1, or vice versa. In other words, they are two different sides of the boundary. This condition is used during the P2G and G2P (Sec. [.13.) to identify the particles that are about to collide and adjust their velocities in particle-wise manner, rather than applying nodal velocities during the G-OP stage.
4.1.3 P2G and G2P with CPIC
During the P2G stage, material particles transfer velocities only to compatible grid nodes. Conse- quently, no collision handling occurs during the G-OP stage, as nodal velocities receive contributions solely from particles away from the boundary. the G2P stage, however, material particles gather velocities from both compatible and incompatible grid nodes. For each incompatible node, directly reuse the particle's ' current velocity Vp. enabling particle-wise collision handling with the surface. For instance, assuming a slippery surface, the velocity is projected onto the surface as yrroj Vp (Vp n,,) np.
4.2 Representing Rigid Body as 2D Gaussians
As discussed in Sec. 4.1.1 previous work represents the rigid body collider a mesh [10] In contrast, we design generalized interface for our framework, enabling seamless integration of both meshes and 2D Gaussians [1]] colliders. By utilizing the Collision Grid as proxy for transferring collision properties from the rigid body to the material particles, our framework can accommodate any collider represented set of primitives ç with associated normals n,
5

---

We reconstruct the rigid body from multi-view images using 2D Gaussian Splatting [1]] Thus, in this case, the rigid body primitive ç corresponds planar disk (i.e., 2D Gaussian) rather than mesh face. The collider is imported into AS-DifIMPM following the procedure in Sec. 4.1 with minimal adaptation required for identifying the affinity grid nodes (Sec. (.1.1).
Sampling rigid particles. We follow the previously described procedure to sample rigid particles Xyp on the primitives e*
Identifying affinity nodes. The 3x3x3 neighboring grid nodes (xrp) of rigid particle Xrp are projected onto the plane defined by the planar disk ç If the projection falls inside the disk, we store the (xg: (xxp)) and set the affinity flag Ag accordingly.
From this stage onward, the procedure adheres the presented approach for transferring collision properties to material particles and resolving collisions during the P2G and G2P stages.
4.3 System Identification
We integrate our AS-DifIMPM with multiple rendering methods to enable system identification from visual observations.
Voxel-based NeRE We follow 4 to integrate voxel-based NeRF [ with AS- AS-DiffMPM. Both MPM and voxel-based NeRFs rely on a grid view (G) for computation and rendering, respectively. However, while MPM uses Lagrangian view (P) to advect particles representing the continuum material, voxel-based NeRFs lack an equivalent point-based representation. Thus, a mapping between voxels and Lagrangian particles is required to enable dynamic rendering. This process involves: (i) mapping voxel fields F.C to Lagrangian particle fields F/", (ii) advecting particles using MPM and (ii)) mapping the updated particle positions back to voxels for dynamic rendering. The following interconverters for G and P views are used:
p
Σ, FipF Σ p wip
JP ~
Wip FG
FC
(5)
where p and indicate the index the particle and grid node, respectively; and Wip is a weighting function defined on i and evaluated p. As result, this mapping mechanism enable bidirectional transfer between the voxel grid and Lagrangian particles, allowing for gradient- based optimization of physical parameters from visual observations.
naturally integrate with MPM as they both utilize the Lagrangian view (P) for rendering and particle advection. By employing differentiable point-based primitives [T], the gradient of the photometric loss with respect to each rendering primitive is computed and propagated to its corresponding Lagrangian particle, thereby supporting gradient- basedd optimization the physical parameters from visual observations. Formally:
Point-based methods. Point-based rendering methods g
0C 00
dc
0I
Ox,
Ox 00
ΣΣ
(6)
0x,
0x
Rendering
Mapping
MPM
where is the photometric loss comparing the rendered image with the ground truth, x, denotes the location of the rendering primitive r, x indicates the position of the Lagrangian particle associated with primitive and represents the physical parameters (e.g.. stiffness, viscosity). The final gradient is the product of three components: (i) rendering, (ii) primitive-partic mapping, and (iii) differentiable MPM. For simplicity, each Lagrangian particle initialized from-and tied to-a rendering primitive (i.e., x x,), reducing the gradient flow to:
Ac
JL 0T
0xp
Σ
xx,)
08
ar
00
P

---

Figure 3: Qualitative examples of reference frames used in experiments. Note that previous works 4 perform system identification only with a planar surface and do not support such colliders.
5
Experiments
Physical Parameters. Our analysis focuses material types that undergo noticeable deformation upon collision with rigid bodies, specifically Newtonian fluids, non-Newtonian fluids, and granular media. For Newtonian fluids, we estimate fluid viscosity (μ) and bulk modulus (K). For Newtonian fluids, we recover shear modulus (μ)), bulk modulus (ri), yield stress (Ty ) and plasticity viscosity (n)) For granular media, estimate the friction angle (0 Fric). For comprehensive overview physical parameters and constitutive models, we refer to [4]
Dataset. We follow the protocol in 4 and generate ground-truth simulation rollouts using the cross-shaped object from [4] as our continuum material, with the physical parameter values provided in Appendix [ The object undergoes free fall and collides with static rigid body (Box. Bunny, or Armadillo) having sticky surfaces. For each rollout, we collect both the 3D particle trajectories (i.c.. point clouds over time) of the continuum material and the corresponding rendered frames (see Fig. B captured from 11 cameras placed around the scene. These data are used in Sec. 5.1 and Sec. 5.2 for experiments system identification. Following the protocol in 4 generate 10 rollouts per collider for each material type, except for granular media, where videos are generated, resulting in total of 75 rollouts. Each rollout is 16 timesteps long.
Training and Evaluation. Our training setup also adheres 4 including the use of the Adam optimizer [35] and the initial guesses for the physical parameters. Unlike 4 we do not optimize the initial velocity vector during the free-fall phase; instead, we use the ground truth values, as our focus is on system identification during collisions. Finally, report the results of physical parameters estimation using the mean and standard deviation of absolute errors, scaled by a factor of 100.
5.1 System Identification from Particle Trajectories
Training. This experiment evaluates system identification performance by estimating the physical parameters of the continuum material using the 3D particle trajectory supervision. Specifically, compute a particle-wise Mean Squared Error (MSE) loss between the reference trajectory and the one simulated by the MPM using the current parameter estimates. The loss is backpropagated through the differentiable simulator to iteratively optimize the physical parameters. We emphasize that this experiment does involve visual observations rendering models, as the focus is exclusively on evaluating the effectiveness of different collision handling strategies for system identification.
Baselines. As discussed in Sec. 4.1 straightforward approach for collision handling in MPM is during the G-OP stage, where a Signed Distance Function (SDF) is reconstructed from the rigid body collider (7). Assuming sticky surfaces, the nodal velocities for grid nodes inside the collider are set to zero. We refer to this baseline as GOP-DifIMPM. Additionally. following prior works [1 36), the rigid collider can be represented
of rigid particles. We denote this approach RP-DiffMPM.
Results. Tab. compares the performance of AS-DiffMPM with baselines. Notably, no consistent trend is observed across colliders: even geometrically simpler shapes like the Box present
7

---

Material
Collider
Parameters
RP-DiLIMPM
GOP-DiIMPM
AS-DiIIMPM (Ours)
(08)
4.82 + 5.15
2.73 3,95
+ 2.73
Box
11g1
37.97 + 21.8
17.09 19.9
27.81 + 33.49
(14
6.69 + 5.97
01.43 0.3
4.35 + 5.24
Newtonian
Bunny
(1)
35.04 :: 37.35
11.52 15.97
31.37 = 50.02
(1)
5.67 + 3,98
0.83 = 1.14
0.4 0.76
Armadillo
[M]
34.61 + 46.52
13.08 = 10.66
0.22 + 0.24
11)10
42.01 + 32.76
41.11 27.78
23.51 30.07
logio
99.55 + 98.64
136.04 78.32
27.06 + 19.12
Box
1ogio(T))
20.13 + 25.83
5.86 = 3.21
3.75
10)
52.38 + 27.63
53.22 = 42.22
17.7 15.17
(p)
53.02 + 47.05
20.29 = 13.96
21.92 + 36.89
logio
82.83 + 86.55
134.82 75.71
26.77 + 25.09
Non-Newtonian
Bunny
logio
31.86 = 50.01
7.10 2.72
2.48 - 1.87
10g
56.01 = 31.13
53.36 36.15
39.1 36.2
log1o (14)
36.67 + 20.92
36,81 = 34.27
7.14 6.64
logio (x)
192.43 + 76.69
176.31 73.89
56,26 + 76.97
Armadillo
logia (TV)
13.72 + 4.58
12.10 + 5.29
5.07 + 5.79
10g
64.40 + 40.39
54.47 38.32
44.98 + 41.34
Box
Ofric
1.58 + 0.65
1.16 0.84
1.22 0.71
Granular
Bunny
ffri
1.91 + 0,42
0.11 0.15
0.06 + 0.07
Armadillo
Byvs
2.28 + 0.66
0.26 = 0.16
0.51 + 0.96
Table 1: System identification from particle trajectories. We compare AS- AS-DifIMPM with two differentiable baselines for collision handling with arbitrarily shaped rigid bodics. Each method is evaluated based on its ability to recover physical parameters using partiele trajectories supervision. Best (light red) and second best (very light red) results are highlighted.
challenges due to sharp corners, while more complex shapes like the Bunny and Armadillo have intricate surfaces leading complex particle trajectories. Overall, AS-DifiMPM achieves comparable or superior performance, due to its particle-wise collision handling. In contrast, GOP-D ROP-DiffMPM may less accurate with complex geometries, as it assigns a single velocity field to all particles within the same grid cell. Finally, RP-DifMMPM consistently underperforms, suggesting that accurate system identification requires tailored collision resolution strategies.
5.2 System Identification from Visual Observations
Training. We follow the system identification pipeline outlined in 44. Given multi-view video, we first segment the continuum object using video matting techniques [37]. Morcover, since our setting involves interactions with rigid body, import the mesh-based collider into AS-DiffMPM following the procedure described in Sec. 4.2 The static geometry the continuum object is then reconstructed from the multi-view images at the initial timestep. With the setup complete, initialize the physical parameters with an initial guess and start the optimization process.
Rendering Models. To the best of our knowledge, existing system identification methods 4 do not account for scenarios involving continuum materials interacting with arbitrarily shaped rigid bodies. To address this limitation,
integrate AS-DiffMPM with several rendering models and establish a benchmark for this novel setting. Specifically, we combine AS-DifIMPM with the voxel-based NeRF from (5] (DVGO), the point-based 2D Gaussian Splatting method from [II] Dynamic 3D Gaussian Splatting model (MDyn-3DGS) introduced
(2DGS), and the in B. Unlike the first two methods, MDyn-3DGS performs dynamic scene reconstruction prior to optimization. This reconstructed information is then used during physical parameter optimization to constrain particles within the rendered dynamic scene.
Results. The results presented Tab. are summarized as follows:
Newtonian fluid: MDyn-3DGS generally provides more accurate estimates of physical pa- rameters compared to 2DGS ||| and DVGO (5). It also matches exceeds the performance

---

Material
Collider
Parameters
DVGO 5
2DGS 11
MDyn-3DDGS g
10)10(μ)
6.71 + 4.4
6.68 + 4.55
5.58 1 3.25
Box
(k)
120.94 + 73.37
112.13 + 85.89
40.07 + 39.47
11)
3.55 4.36
7.37 + 5.91
3.29
Newtonian
Bunny
(1)
53.34 64.94
99.16 + 68.65
22.38 + 17.32
(1)
1.99 1.59
5.28 + 2.55
0.97 + 0.86
Armadillo
(k)
32.94 42.24
49.66 1 35.79
14.99 17.13
(p)
23.83 14.77
28.88 - 50.41
67.55 + 128.49
(x)
52.76 51.68
70.78 + 88.13
32.10 49.97
Box
log1o
5.84 4.34
12.77 16.22
8.8 - 2.86
(ng
26.10 19.21
58.02 + 41.46
51.25 + 28.81
(1)
55.38 = 31.85
10.05 7.95
15.91 + 25.49
(k)
68.84 38.11
44.44 + 33.39
23.16 18.29
Non-Newtonian
Bunny
10g10(T))
11.43
3.30 2.15
4.97 +
(og
62.06 - 49.71
46.05 - 27.02
43.37 + 22.43
(1)
79.23 + 82.21
12.34 + 13.32
12.62 + 10.30
(k)
107.90 95.32
33.30 + 20.60
19.75 13.67
Armadillo
log1o Ty)
63.01 = 148.55
2.34 2.41
4.32
log1o(T)
83.60 + 50.2
55.18 + 37.20
39.74 + 23.07
Box
Ofric
4.16 0.76
0.75
3.16 + 1.04
Granular
Bunny
fric
4.02 0.68
0.50 + 0.29
3.33 + 0.62
Armadillo
fric
4.11 1.05
0.36 + 0.13
2.89 + 0.78
Table 2: System identification from visual observations. We evaluate our AS-DifIMPM combined with three rendering methods on the task of physical parameter estimation from multi-view videos. Best (light red) and second best (very light red) results are highlighted.
obtained using particle trajectories as supervision (see Tab. []. demonstrating that visual supervision provides meaningful additional information for system identification 4
Non-Newtonian fluid: Consistent with prior work 44 8), this material presents the greatest challenges, and single rendering method consistently outperforms others across all colliders.
Granular: lower absolute errors are generally observed for this material, indicating rela- tively simpler deformation behavior compared to fluids. Despite underperforming on fluid simulations, the explicit point- representation of 2DGS [T]] achieves superior results for granular media without relying on additional dynamic reconstruction supervision, as required by MDyn-3DGS [
Overall, MDyn-3DGS typically outperforms 2DGS and DVGO (5), highlighting the advan- tages of incorporating dynamic reconstruction into the rendering pipeline. However, the choice of method may ultimately depend on the complexity of the specific material-collider interactions being modeled. Finally, while prior work [4] [] has shown promising results for system identification with planar surfaces, our findings indicate that handling more complex interactions inherently more challenging yet essential for advancing toward models that operate under fewer assumptions.
Real-World Application: Parameter Estimation of a Dough Sample
To further validate the proposed framework, we conduct real-world experiment using dough sample approximately the size of a football. The dough is modeled as non-Nec Non-Newtonian material due to its viscoelastic behavior, which combines solid-like elasticity with fluid-like viscosity.
Experimental Setup. The dough is released in free fall and collides with the edge box, creating non-planar contact scenario. Upon impact, part of the dough adheres to the horizontal surface, while the rest deforms and gradually flows along the vertical edge. The experiment recorded using five cameras placed around the scene, and in each frame the dough is segmented using SAM2 [38]

---

Experiment Pipeline. The procedure consists of three stages:
1. Static geometry reconstruction. We reconstruct the scene without the dough in view using 2DGS M and import into AS-DifIMPM as collider. Then, we reconstruct the initial dough geometry using the nulti-view images of the first timestep. We use isotropic Gaussians to ensure an even distribution along the surface. To avoid structural collapse upon collision during the simulation, apply the intermal infilling strategy from [T] The resulting Gaussians are then fine-tuned, with densification and pruning disabled to preserve their distribution. These adjustments lead more realistic MPM simulations.
2. Initial motion estimation. We estimate the initial velocity and gravity vectors from the free-fall phase and keep them fixed in subsequent stage.
3. System identification. With geometry and motion initialization in place, we optimize the dough's physical parameters over the full sequence.
Results. The estimated physical parameters are: μ = 57, 003.0, K = 139, 650.4, ry = 7,919.1, 17 25.1. We further assess visual reconstruction quality over three seconds after collision. Tab. shows the metrics averaged over 60 frames and five cameras. We observe a degradation in reconstruction quality in the later frames (see also Fig. 4 As the dough undergoes significant deformation, the Gaussians deviate from their original positions, introducing visual artifacts. A potential remedy is to incorporate time-dependent Gaussian attributes, which we leave for future work.
Time after collision
PSNR (1)
SSIM (t)
LPIPS (1)
1 s
33.2 + 4.1
0.994 + 0.004
0.019 0.001
2 s
28.9 + 6.6
0.988 + 0.011
0.024 0.011
3
25.3 + 7.8
0.966 + 0.013
0.035 + 0.012
Table Evaluation of image reconstruction quality for the dough over time.
Reconstruction Reference
Figure 4: Example visualization of the dough experiment.
Conclusion
Limitation. One limitation of our work is the preliminary rigid body reconstruction-and-impee into AS-DifIMPM, prior to start the system identification optimization. This restricts our approach to static colliders. Although the extension to moving rigid bodies is trivial in framework, leave the system identification analysis under such conditions as future work. Indeed, as significant deformation of the continuum material may occur, a carefully designed dynamic reconstruction -imilar to the one proposed in
required to mitigate visual artifacts.
In conclusion, we proposed AS- DiffMPM.. differentiable Material Point Method supporting arbitrar- ily shaped colliders. We validated our method quantitatively and combined it with various rendering models to perform system identification from visual observations, providing extensive results in a novel scenario where the continuum material undergoes deformations against complex colliders rather than planar surfaces.
10

---

References
[1] Tianyi Xie, Zeshun Zong, Yuxing Qiu, Xuan Li, Yutao Feng, Yin Yang, and Chenfanfu Jiang. Physgaussian: Physics-integrated 3d gaussians for generative dynamics. In Proceedings the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4389-4398, 2024.
[2] Bernhard Kerbl, Georgios Kopanas, Thomas Leimkühler, and George Drettakis. 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph., (2(4):139-1, 2023.
[3] Deborah Sulsky, Shi-Jian Zhou, and Howard Schreyer. Application of particle-in-cell method to solid mechanics. Computer Physics Communications, 87(1):236-252, 1995. Particle Simulation Methods.
[4] Xuan Li, Yi-Ling Qiao, Peter Yichen Chen, Krishna Murthy Jatavallabhula, Ming Lin, Chen- fanfu Jiang, and Chuang Gan. Pac-nerf: Physics augmented continuum neural radiance fields for gcometry-agnosee system identification. In International Conference on Learning Repre- sentations (ICLR), 2023.
[5] Cheng Sun, Min Sun, and Hwann-Tzon Chen. Direct voxel grid optimization: Super-fast convergence for radiance fields reconstruction. Proceedings of the IEEE/CVF conference on computer vision and pultern recognition, pages 5459-5469, 2022.
[6] Yuanming Hu, Luke Anderson, Tzu-Mao Li, Qi Sun, Nathan Carr, Jonathan Oogan-Kelley, and Frédo Durand. Difftaichi: Differentiable programming for physical simulation. In International Conference on Learning Representations, 2020.
[7] Takuhiro Kaneko. Improving physics-augmenter continuum neural radiance field-based geometry-agnosic system identification with lagrangian particle optimization. In Proceedings of the IEEE/CVF Conference Computer Vision and Pattern Recognition, pages 5470-5480, 2024.
[8] Junhao Cai, Yuji Yang. Weihao Yuan, HE Yisheng. Zilong Dong. Liefeng Bo, Hui Cheng, and Qifeng Chen. Gic: Gaussian-informed continuum for physical property identification and simulation. In The Thirty-eighth Annual Conference Neural Information Processing Systems, 2024.
[9] Licheng Zhong, Hong-Xing Yu, Jiajun Wu, and Yunzhu Li. Reconstruction and simulation of elastic objects with ppring-mast 3d gaussians. In European Conference on Computer Vision, pages 407-423. Springer, 2024.
[10] Yuanming Hu, Yu Fang, Ziheng Ge, Ziyin Qu, Yixin Zhu, Andre Pradhana, and Chenfanfu Jiang. moving least squares material point method with displacement discontinuity and two-way rigid body coupling. ACM Transactions on Graphics (TOG), 37(4):1-14, 2018.
[11] Binbin Huang, Zehao Yu, Anpei Chen, Andreas Geiger, and Shenghua Gao. 2d gaussian splatting for geometrically accurate radiance fields. In ACM SIGGRAPH 2024 conference papers, pages 1-11, 2024.
[12] Sameer Agarwal, Yasutaka Furukawa, Noah Snavely, Ian Simon, Brian Curless, Steven M Seitz, and Richard Szeliski. Building rome in a day. Communications of the ACM. 54(10):105-112 2011.
[13] Derek Hoiem. Alexei A Efros, and Martial Hebert. Recovering surface layout from an image. International Journal of Computer Vision, 75:151-172, 2007.
[14] Johannes L Schonberger and Jan-Michael Frahm. Structure-from frotimmtioo revisited. In Proceed- ings of the IEEE conference on computer vision and pattern recognition, pages 4104-4113, 2016.
[15] Ben Mildenhall, Pratul P Srinivasan, Matthew Tancik, Jonathan T Barron, Ravi Ramamoorthi, and Ren Ng. Nerf: Representing scenes as neural radiance fields for view synthesis. ECCV, 2020.
11

---

[16] Thomas Müller, Alex Evans, Christoph Schied, and Alexander Keller. Instant neural graphics primitives with multiresolution hash encoding. ACM Transactions on Graphics (ToG), 2022.
[17] Ayaan Haque, Matthew Tancik, Alexei A Efros, Aleksander Holynski, and Angjoo Kanazawa. Instruct-nerf2nerf: Editing 3d scenes with instructions. In ICCV, 2023.
[18] Shuaifeng Zhi, Tristan Laidlow, Stefan Leutenegger, and Andrew J Davison. In-place scene labelling and understanding with implicit scene representation. In ICCV, 2021.
[19] Clément Jambon, Bernhard Kerbl, Georgios Kopanas, Stavros Diolatzis, George Drettakis, and Thomas Leimkühler. Nerfshop: Interactive editing of neural radiance fields. Proceedings of the ACM on Computer Graphics and Interactive Techniques, 2023.
[20] Ri-Zhao Qiu, Ge Yang, Weijia Zeng, and Xiaolong Wang. Language-driven physics-based scene synthesis and editing via feature splatting. In European Conference on Computer Vision, pages 368-383. Springer, 2024.
[21] Yutao Feng. Xiang Feng, Yintong Shang, Ying Jiang, Chang Yu, Zeshun Zong, Tianjia Shao, Hongzhi Wu, Kun Zhou, Chenfanfu Jiang, et al. Gaussian splashing: Dynamic fluid synthesis with gaussian splatting, arXiv e-prints, pages arXiv-2401, 2024.
[22] Ying Jiang, Chang Yu, Tianyi Xie, Xuan Li, Yutao Feng, Huamin Wang, Minchen Li, Henry Lau, Feng Gao, Yin Yang, et al. Vr-gs: A physical dynamics-aware interactive gaussian splatting system in virtual reality. In ACM SIGGRAPH 2024 Conference Papers, pages 1-1, 2024.
[23] Yutao Feng, Yintong Shang, Xuan Li, Tianjia Shao, Chenfanfu Jiang, and Yin Yang. Pic- nerf: Physics-based interactive elastodynamics with nerf. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages
2024.
[24] Vismay Modi, Nicholas Sharp, Or Perel, Shinjiro Sueda, and David IW Levin. Simplicits: Mesh- free, geometry-agnoste elastic simulation. ACM Transactions on Graphics (TOG), 43(4):1-11, 2024.
[25] Piotr Borycki, Weronika Smolak, Joanna Waczyúska, Marcin Mazur, Slawomir Tadeja, and Przemystaw Spurek. Gasp: Gaussian splatting for physic-based simulations. arXiv preprint 2.X.::2409008819, 2024.
[26] Tianyuan Zhang. Hong-Xing Yu, Rundi Wu, Brandon Y Feng, Changxi Zheng, Noah Snavely, Jiajun Wu, and William T Freeman. Physdreamer: Physics-based interaction with 3d objects via video generation. In European Conference on Computer Vision, pages 388-406. Springer, 2024.
[27] Yuchen Lin, Chenguo Lin, Jianjin Xu, and Yadong MU. OmniphysGS: 3d constitutive gaussians for general ahysics-based dynamies generation. The Thirteenth International Conference on Learning Representations, 2025.
(28) Tianyu Huang. Haoze Zhang, Yihan Zeng, Zhilu Zhang, Hui Li, Wangmeng Zuo, and Ryn- son WH Lau. Dreamphysics: Learning physical properties of dynamic 3d gaussians with video diffusion priors. arXiv preprint arXiv:2406.0 01476, 2024.
[29] Fangfu Liu, Hanyang Wang, Shunyu Yao, Shengjun Zhang, Jie Zhou, and Yueqi Duan. Physics3d: Learning physical properties of 3d gaussians via video diffusion. arXiv preprint arXiv:2406.04333 04338, 2024.
[30] Dimitris Metaxas and Demetri Terzopoulos. Shape and nonrigid motion estimation through physics-based synthesis. IEEE Transactions on Pattern Analysis and Machine Intelligence. 15(6):5805555 591, 1993.
[31] Alexey Stomakhin, Craig Schroeder, Lawrence Chai, Joseph Teran, and Andrew Selle. A material point method for snow simulation. ACM Trans. Graph., 32(4), July 2013.
[32] Chenfanfu Jiang, Craig Schroeder, Joseph Teran, Alexey Stomakhin, and Andrew Selle. The material point method for simulating continuum materials. ACM SIGGRAPH 2016 Courses, SIGGRAPH 16, New York, NY, USA, 2016. Association for Computing Machinery.
12

---

[33] Eduardo WV Chaves. Notes on continuum mechanics. Springer Science & Business Media, 2013.
[34] Michael Steffen, Robert M Kirby, and Martin Berzins, Analysis and reduction of quadrature errors in the material point method (mpm). International journal for numerical methods in engineering, 76(6):222 948, 2008
[35] Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In Interna- fional Conference Learning Representations (ICLR), 2015.
[36] Pingchuan Ma, Peter Yichen Chen. Bolei Deng, Joshua B Tenenbaum, Tao Du, Chuang Gan, and Wojciech Matusik. Learning neural constitutive laws from motion observations for generalizable pde dynamics. In International Conference on Machine Learning, pages 23279-23300. PMLR, 2023.
[37] Shanchuan Lin, Andrey Ryabtsev, Soumyadip Sengupta, Brian I. Curless, Steven M Seitz, and Ira Saattmacchh--Shizermmaa Real-time high-resolution background matting. In Proceedings of the IEEE/CVF Conference Computer Vision and Pattern Recognition, pages 8762-8771, 2021.
[38] Nikhila Ravi, Valentin Gabeur, Yuan- Ting Hu, Ronghang Hu, Chaitanya Ryali, Tengyu Ma, Haitham Khedr, Roman Rädle, Chloe Rolland, Laura Gustafson, et al. Sam 2: Segment anything in images and videos. In International Conference on Learning Representations (ICLR), 2025.
13

---

NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: The main claims made in the abstract and and introduction reflect the paper's contributions and objectives.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or
NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
is fine to include aspirational goals as motivation as long as is clear that these goals are not attained by the paper.
2. Limitations
Question: Does the paper discuss the limitations the work performed by the authors?
Answer: [Yes]
Justification:
The paper presents Conclusion section where limitations are discussed.
Guidelines:
The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create a separate "Limitations" section their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g.. independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect on the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution is low images are taken in low lighting. Or speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.
While the authors might fear that complete honesty about limitations might used by reviewers as grounds for rejection, worse outcome might be that reviewers discover limitations that aren't 't acknowledged judgment and recognize that individual actions in favor of transparency play impor- tant role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
the paper. The authors should use their best
3. Theory assumptions and proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
Answer: [NA]
14

---

Justification:
The paper does not contain theoretical results
Guidelines:
The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced the statement of any theorems.
The proofs can either appear the main paper or the supplemental material, but they appear in the supplemental material, the authors are encouraged to provide short proof sketch to provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix supplemental material.
Theorems and Lemmas that the proof relies upon should be properly referenced.
4. Experimental result reproducibility
Does the paper fully disclose all the information needed to reproduce the main ex- perimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
Question:
Answer: [Yes]
Justification: We did our best to include the details for reproducibility. Moreover, we will release the code of our framework.
Guidelines:
The answer NA means that the paper does not include experiments.
If the paper includes experiments, No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is novel architecture, describing the architecture fully might suffice, or if the contribution is a specific model and empirical evaluation, it may be necessary to either make possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data is often one good way accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g.. in the case of large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
While NeurIPS does not require releasing code, the conference does require all submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) If the contribution is primarily a new algorithm, the paper should make it clear how reproduce that algorithm. (b) If the contribution is primarily
model architecture, the paper should describe the architecture clearly and fully.
(c) If the contribution is a new model (e.g., a large language model), then there should either be way to access this model for reproducing the results or way to reproduce the model (e.g., with an open-source dataset instructions for how to construct the dataset).
(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome deseribe the particular way they provide for reproducibility, In the case of closed-source models, it may be that access to the model is limited in some way (e.g., registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results.
5. Open access to data and code
Question: Does the paper provide open access to the data and code, with sufficient instruc- tions to faithfully reproduce the main experimental results, as described in supplemental material?
15

---

Answer: [No]
Instructions on how to download the data and run scripts are not included in the paper, however, we will rely on a project page (linked to our paper) to provide instructions for reproducibility. We well release ready-to-use data and scripts (e.g., no data prepprocessing required).
Justification:
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurIPS code and data submission guidelines (https://nips.cr co/
for more details.
While we encourage the release of code and data, we understand that this might be possible, so "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for new open-source benchmark).
The instructions should contain the exact command and environment needed to run reproduce the results. See the NeurIPS code and data submission guidelines (https /CodeSubmeei "piips.c/ppulli//guu Socie///ggiddeeeeeouSuuubbbbbii ssionPolicy) for more details.
The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only subset of experiments are reproducible, they should state which ones are omitted from the script and why.
At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).
Providing as much information as possible supplemental material (appended the paper) is recommended, but including URLs to data and code is permitted.
6. Experimental setting/details
Question: Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Answer: [Yes]
Justification: We both described our training/test details (in the Experiments section) and referred to priors works 4 when the settings are unchanged.
Guidelines:
The answer NA means that the paper does include experiments.
The experimental setting should be presented in the core the paper to a level of detail that is necessary appreciate the results and make sense of them.
The full details can be provided either with the code, appendix, or as supplemental material.
7. Experiment statistical significance
Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Answer:
[Yes]
Justification:
We reported tables for quantitative analysis in the Experiments section
Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results are accompanied by error bars, confi- dence intervals, statistical significance tests, least for the experiments that support the main claims of the paper.
The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall with given experimental conditions).
16

---

The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)
The assumptions made should be given (e.g.. Normally distributed errors).
should be clear whether the error bar is the standard deviation or the standard error of the mean.
It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of errors is not verified.
For asymmetric distributions, the authors should be careful not to show in tables figures symmetric error bars that would yield results that are out of range (c.g. negative emror rates).
If error bars reported in tables plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables the text.
8. Experiments compute resources
For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed reproduce the experiments?
Question:
Answer: [Yes)
Justification:
We described this in the supplementary material.
Guidelines:
The answer NA means that the paper does not include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, cloud provider, including relevant memory and storage.
The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't 't make it into the paper).
9. Code ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of
Answer: [Yes]
Justification: This work conform with the NeurIPS Code of Ethics.
Guidelines:
The answer NA means that the authors have reviewed the NeurIPS Code of Ethics.
If the authors answer No, they should explain the special cireumstances that require deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g., if there is special consid- eration due to laws or regulations in their jurisdiction).
10. Broader impacts
Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: [NA]
Justification: There is no socictal impact of the work performed.
Guidelines:
The answer NA means that there is no societal impact of the work performed.
If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact.
Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
17

---

The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.
If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition attacks, mechanisms for monitoring misuse, mechanisms to monitor how system learns from feedback over time, improving the efficiency and accessibility ML).
11. Safeguards
Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, scraped datasets)?
Question:
Answer: [NA]
Justification: This paper poses no such risks
Guidelines:
The answer NA means that the paper poses no such risks.
Released models that have high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make best faith effort.
12. Licenses for existing assets
Question: Are the creators or original owners of assets (e.g.. code, data, models), used in the paper. properly credited and are the license and terms of use explicitly mentioned and properly respected?
Answer: [Yes]
Justification: The used assets are properly cited throughout the paper and more specifically in the Experiments section.
Guidelines:
The answer NA means that the paper does not use existing assets.
The authors should cite the original paper that produced the code package dataset.
The authors should state which version of the asset is used and, if possible, include URL.
The name of the license (c.g., CC-BY 4.0) should be included for each asset.
For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided.
If assets are released, the license, copyright information, and terms of use in the Datasets.papersstt paperswi thcode. cww/ datasets package should be provided. For popular datasets,
has curated licenses for some datasets. Their licensing guide can help determine the license of dataset.
For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.
18

---

If this information is not available online, the authors are encouraged to reach out to the asset's creators.
13. New assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [NA]
Justification: This paper does not release new assets
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details of the dataset/code/mmoel as part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent obtained from people whose asset is used.
At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
14. Crowdsoureing and research with human subjects
Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well details about compensation (if any)?
Answer: [NA]
Justification: This paper does not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Including this information in the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then as much detail as possible should be included the main paper.
According the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional review board (IRB) approvals or equivalent for research with human subjects
Question:
Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?
Answer: [NA]
Justification: This paper does not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Depending the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and expect authors to adhere to the NeurlPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if applicable), such the institution conducting the review.
16. Declaration of LLM usage
19

---

Question: Does the paper describe the usage of LLMs if it is important, original, or non-standard component of the core methods this research? Note that if the LLM used only for writing, editing, or formatting purposes and does not impact the core methodology. scientific rigorousness, or originality of the research, declaration is not required.
Answer: [NA]
Justification: The core methodology and contributions of this paper do not involve LLM
Guidelines:
The answer NA means that the core method development in this research does not involve LLMs any important, original, non-standard components.
Please refer to our LLM policy fattps://neurda: //t.a/rrpp...co/ooffeeerr//////s for what should or should not be described.
20

---

Appendix
This supplementary material provides additional results that both complement the main paper and preliminarily explore more scenarios. We invite the reader to also refer to the supplementary media attached this paper and the project page for additional visualizations.
A Additional Results on System Identification
This section complements the results in Tab. 1 and Tab, 2 qualitative visualizations.
with additional quantitative metrics and
A.1
System Identification from Particle Trajectories
A.1.1 Quantitative Results on Geometric Error
Beyond the results reported in Tab. 1 we quantify the geometric accuracy of the simulated particle trajectories (after convergence of the physical parameter optimization) by comparing them against the reference trajectory used for supervision. Following [ 9). report the Chamfer Distance (CD) and Earth Mover's Distance (EMD). The Chamfer Distance is computed using the squared distance and is expressed in units of 10x mm? Each metric is averaged over all timesteps across the dataset. Results are presented in Tab.
Material
Collider
Metries
RP-DifIMPM
GOP-DiAMPP
AS-DiNMPM (Ours)
CD 1
3.903 + 2.603
3.879
2.625
3.925 + 2.590 0.066 0.019
Box
EMD |
0.066 0.018
0.066
0.019
CD 1
2.948 + 2.060
2.946
2.059
2.955 2.059
Newtonian
Bunny
EMD
0.059 + 0.017
0.059 = 0.017
0.059 + 0.017
CD L
2.977 2.515
2.964 2.512
2.960 2.521
Armadillo
EMD 1
0.064 + 0.025
0.064 = 0.025
0.064 0.024
CD 1
16.566 + 6.847
16.492 = 6.854
16.558 6.868
Box
EMD 1
0.108 0.023
0.107 0.023
0.107
CD 1
12.858 + 5.323
12.822 + 5.308
12.826 = 5.353
Non-Newtonian
Bunny
EMD
0.098 + 0.023
0.098 0.023
0.098 0.023
CD |
15.576 10.921
15.571 = 10.909
15.519 10.936
Armadillo
EMD +
0.121 + 0.045
0.121 = 0.045
0.121 + 0.045
3.478
3,485 1.090
3.448 1.043
Box
EMD 1
0.064 + 0.005
0.064 = 0.006
0.063 0.005
CD |
3.084 + 0.820
3.067 0.847
3.055 0.851
Granular
Bunny
EMD 1
0.058 0.006
0.0558 0.005
0.058 0.005
CD | EMD
2.896 + 0.857
2.860 = 0.845
2.858 +: 0.902
Armadillo
0.056 + 0.006
0.056 0.006
0.056 0.006
Table 4: Evaluation of geometric error using CD and EMD for different materials and colliders.
21

---

A.1.2 Qualitative Visualizations
We provide example visualizations of the 3D particle trajectories used in our experiments (see Fig. 5 Please refer the supplementary material attached this paper for more videos.
Figure 5: Particle trajectories of a Newtonian material colliding with the Armadillo rigid body.
A.2
System Identification from Visual Observations
A.2.1
Quantitative Results Image Reconstruction
In addition the results shown in Tab. we assess the image reconstruction quality of all models after convergence of the physical parameter optimization. We report in Tab. the standard metrics used radiance field evaluation: Peak Signal-to-Noie Ratio (PSNR), Structural Similarity Index Measure (SSIM), and Learned Perceptual Image Patch Similarity (LPIPS). Each metric is averaged over all views and timesteps across the dataset.
Material
Collider
Metries
DVGO
2DGS
MDyn-3DGS X
PSNR f
35.318 + 4.901
35.669 + 6.779
41.300 2.130
SSIM
0.985
0.010
0.978 0.022
0.997 + 0.002
LPIPS 1
0.023
0.016
0.022 0.019
0.017 + 0.007
PSNR f
36.491 1 4.217
36.949 1 6.083
41.537 T 1.856
Newtonian
Bunny
SSIM
0.987 0.009
0.981 0.019
0.998 = 0.001
LPIPS
0.021 = 0.014
0.019 0.017
0.015 = 0.006
PSNR
36.905 + 3.409
37.484 5.310
41.888 1.395
Armadillo
SSIM
0.987 0.008
0.017
0.998 + 0.001
LPIPS
0.021 = 0.012
0.019 + 0.015
0.015 = 0.005
PSNR f
28,331 + 5.462
29.468 6.658
48,521 2.291
Box
SSIM
0.973 0.014
0.980 0.015
0.998 + 0.001
LPIPS L
0.037 0.014
0.023 + 0.015
0.011 + 0.003
PSNR f
28.871 1 5.077
31.718 5.184
48.659 2.278
Non-Newtonian
Bunny
SSIM
0.975 = 0.012
0.986 + 0.011
0.998 = 0.001
LPIPS
0.035 0.012
0.018 + 0.011
0.010 = 0.003
PSNR f
27.196 5.573
32.176 1.459
48.762 1.814
Armadillo
SSIM
0.971
0.013
0.986 + 0.009
0.998 + 0.001
LPIPS
0.038 0.014
0.018 1 0.010
0.010 = 0.002
PSNR f
31.338 + 5.558
31.055 + 7.419
40.527 1 3,951
Box
SSIM
0.967 0.023
0.957 + 0.040
0.992 + 0.006
LPIPS 1
0.046 0.028
0.035 + 0.029
0.022 - 0.009
PSNR f
32.487 1 4.841
32.063 6.870
42.522 1 2.127
Granular
Bunny
SSIM
0.972 0.018
0.963 + 0.034
0.994 = 0.003
LPIPS
0.042 0.024
0.031 + 0.026
0.018 = 0.007
PSNR 1
32.204 + 4.577
31.361 + 6.936
41,900 + 2. 121
Armadillo
SSTM
0.970 0.018
0.959 + 0.035
0.993 + 0.003
LPIPS
0.044 0.024
0.034 0.027
0.021 = 0.008
Table 5: Evaluation of image reconstruction using PSNR, SSIM, and LPIPS for different materials and colliders.
22

---

A.2.2 Qualitative Visualizations
We provide example visualizations of the models convergence (see Fig. and Fig. 7 We remind that, prior to the physical parameters optimization, the rigid collider is imported into AS-DitIMPM for collision handling and the continuum material is segmented out from the ground truth views. During physical parameters optimization, the visual observations containing the segmented-out continuum object are used for supervision. Please refer the supplementary material attached this paper for videos, along with the reconstruction metrics and estimated physical parameters.
Ground
2DGS
MDуп- 3DGS
DVGO
Figure 6: Non-Newtonian material colliding with the Bunny rigid body.
Ground tnith
2DGS
MDул- 3DGS
DVGO
Figure 7: Sand material colliding with the Box rigid body.
23

---

B Mesh vs. 2DGS as Rigid Body Collider
In contrast the experiments presented in the main paper (Sec 5). where the collider imported into AS-DifIMPM is represented mesh, in this analysis we segment and reconstruct the collider using 2DGS[1,, and import it into AS-DiffMPP, as described in Sec. [4.2 We then perform the same system identification experiment based on particle trajectories to evaluate the impact of using mesh compared to 2DGS as rigid body collider representation. Results are presented in Tab. and colliders obtains lower accuracy. This is due to the reconstructed
Tab. 7 Gaussians not being as precise as a mesh, which introduce noise into the Collision grid (Sec. I.1.T) and result in less accurate collision handling. However, remark that AS-DifiMPM is versatile enough to support both mesh and 2DGS- colliders. This flexibility is particularly valuable for real-world scenarios, where colliders may need to be reconstructed on-the-fly using 2DGS to enable simulation.
As expected, 2DGS-basse
Material
Collider
Parameters
AS-DifiMPM WDGS
AS-DifiMPM w/ Mesh
10)10(p)
4.36 + 2.66
5.08 + 2.73
Box
36.26 + 24.63
27.81 = 33.49
log (p)
7.03 + 4.09
4.35 + 5.24
Newtonian
Bunny
1og1o (k)
81.30 + 31.53
31.37 = 50.02
log (n)
8.75 + 6.17
0.4 + 0.76
Armadillo
1o (R)
+: +
0.22 + 0.24
log10 (p)
55.51 + 42.28
23,51 + 30.07
log (R)
126.10 + 99.60
27.06 + 19.12
Box
log10 Tyy
11.18
7.28 = 3.75
log1o(1)
+6.71:35..8
17.7 = 15.17
log
1:.12:444
21.92 + 36.89
logio (K)
110.70 73.58
26.77 + 25.09
Non-Newtonian
Bunny
logio (TY)
16.40 + 5.74
2.48 + 1.87
lo)1o(1))
56.57 + 35.17
39.1 + 36.2
log (n)
25.22 + 24.02
7.14 + 6.64
log
124.88 + 75.89
56.26 + 76.97
Armadillo
log1o (TY)
(TY)
28.43 + 19.45
5.07 + 5.79
log1o(n)
51.76 + 30.75
44.98 + 41.34
Box
ffric
1.86 + 1.14
1.22 + 0.71
Granular
Bunny
i frric
0.91 + 1.15
0.06 + 0.07
Armadillo
Ofric
1.38 + 1.08
0.51 + 0.96
Table 6: System identification from particle trajectories. Evaluation (reported absolute error) of physical parameter estimation when using mesh and 2DGS [1]] as collider.
24

---

Material
Collider
Metrics
AS-DifIMPM w/ 2DGS
AS-DifIMPM w/ Mesh
CD +
3,893 + 2.586
3,925 + 2.590 0.066 + 0.019
Box
EMD +
0.066 = 0.018
CD 4
2.955 = 2.049
2.937 + 2.059
Newtonian
Bunny
EMD
0.059 1 0.017
0.059 1 0.017
CD
2.962 = 2.515
2.960 + 2.521
Armadillo
EMD
0.064 + 0.024
0.064 + 0.024
CD |
16.629 + 6.882
16.558 + 6.868
Box
EMD
0.108 = 0.023
0.107 = 0.022
CD 4
12.867 + 5.355
12.826 = 5.353
Non-Newtonian
Bunny
EMD 4
0.098 1 0.023
0.098 1 0.023
CD
15.538 = 10.854
15.519 + 10.936
Armadillo
EMD +
0.121 + 0.045
0.121 + 0.045
CD |
3.468 + 1.042
3.448 + 1.043
Box
EMD +
0.064 + 0.005
0.063 + 0.005
CD +
3.094 = 0.867
3.055 = 0.851
Granular
Bunny
EMD
0.057 1 0.005
0.058 1: 0.005
CD +
2.872 + 0.886 0.056 + 0.006
2.858 + 0.902 0.056 + 0.006
Armadillo
FMD
Table 7: System identificatinn from particle trajectories. Evaluation of geometric error when using
mesh or 2DGS as collider.
C Exploring More Conditions for System Identification
We further benchmark AS-DiffMPM framework under more conditions, both in terms of colliders and materials. This section is not intended to provide an in-depth analysis for each condition, but rather to explore wide range of possibilities, aiming possibly identify which ones deserve more thorough analysis in future work. All experiments are conducted using the pipeline described in Sec. 5.1 for system identification from particle trajectories.
C.1
Same Colliders in Different Conditions
We use the three colliders (Box, Bunny and Armadillo) of our analysis in the main paper but changing characteristics. For each case, results are reported per material type, averaging over the colliders (see Tab.
The collider is moved the side (instead of being underneath the object) such that the continuum material first impacts the ground and then interacts with the collider as spreads. We perform nine experiments experiments-comprriiigg three material types and three colliders.
Condition
Condition 2. Each collider tested at two scales (0.5 and 1.5), for all material types and colliders, resulting in 18 experiments.
Condition 3. We combine all the colliders at once, placing them side by side, that the material interacts with all of them upon collision. This results in three experiments, one per material type
Overall, Condition appears to be the one with more significant challenges in physical parameter estimation, likely due this foound-frs--colldder-eey complex interactions between the material and the collider.
25

---

Material
Parameter
Cond.
Cond. 2
Cond.
log1o
10.31 12.09
5.21 + 7.02
6.85
Newtonian
log10
39.82 + 9.65
26.88 = 25.91
47.34
log1o (a)
23.02 10.31
22.17 12.81
3.41
log10 (k)
50.34 +: 7.78
23.15 + 15.64
41.98
Non-Newtonian
log10 TY)
9.56 + 5.90
5.34 + 4.26
7.59
log
34.41 + 12.74
21.03 7.98
32.02
Granular
fric
4.02 + 1.70
1.09 = 0.93
3.04
Table 8: System identification errors across three conditions.
Material
Parameter
S-MPM
RP-DiffMPM
GOP-DifMMPM
AS-DifIMPM (Ours)
(0)
7.51
8.03
7.63
7.98
Newtonian
10g10
31.98
35.21
32.45
33.21
(1)
24.09
24.57
24.91
24.03
log (k)
19.01
21.12
20.19
19.03
Non-Newtonian
log10 TV
4.91
5.12
4.78
4.54
10 (n)
30.53
32.10
31.05
31.21
Granular
fric
0.15
0.56
0.22
0.12
Table 9: System identification errors for planar collider.
C.2 More Colliders and Material Types
In this section, we focus both on different colliders and material types, comparing our AS-DifIMPM framework with baselines. For the former, first explore a comparison using the condition adopted in previous works 7 8 2 i.c., a planar collider, and then with bowl-shaped collider. Instead, for the latter, explore both further material types and shapes.
Planar Collider. We conduct experiments comparing our AS-DiAfMPM with both the baselines used in our main paper (GOP-DiffMii and RP- DiffMMPPM and the Standard MPM (S-MPM) collision strategy adopted by previous works 4 7 9. S-MPM, collisions are resolved at the Grid Operations stage 3.1): for planar surface defined by point x,, and normal n,. the nodal velocity Vg is set to zero for all grid nodes Xg such that (x, - xx,) ny S O. contrast, AS-DiffMPM represents the same planar collider as mesh surface positioned at Xs, and applies particle- wise collision handling during both P2G and G2P steps. We performed three experiments, one per material type (see Tab. 9.. The S-MPM achieves slightly lower errors for some parameters, likely due to its use of analytically defined boundary conditions, which may offer improved numerical stability in simple geometries.
We import a bowl-shaped collider into our framework and place it such that the falling material impacts its open cerfface-causing some particles to enter the bowl while others fall outside. conducted three experiments, one per material type (see Tab. T0P. The general trend observed in the main paper appears to be consistent here, with our method outperforming the baselines.
Bowl Collider.
More material types. While the main focus of our work on Newtonian, non-Newtonian and granular materials, we explore here also with clastic and plasticine materials, For clastic material, we consider Young's modulus (E) and Poisson's ration (v)) while for plasticine material, consider also yield stress (ry). We refer the reader to 4 for the constitutive models. Each method was evaluated on six experiments: two material types and with three colliders. The results are presented in Tab. II] averaged over the colliders. Interestingly, all methods generally perform well on the elastic material. This may due the simpler nature Silider--sine the material tends to bounce away upon contact, the particle-wise collision handling mechanism of AS-DiffMPM has less impact. Indeed, in these scenarios, no fin-ngrained interaction (c.g., material flowing around sharp corners) occurs.
interaction between the elastic material and
26

---

Material
Parameter
RP-DiffMPM
GOP-DifIMPM
AS-DifiMPM (Ours)
(1)
7.84
7.29
6.01
Newtonian
30.12
28.45
25.67
(0)
19.31
20.05
15.03
logi0 [k]
38.22
35.79
29.84
Non-Newtonian
log1a (TY)
7.31
6.98
5.15
log (7)
26.78
28.45
20.94
Granular
Ofiic
3.01
1.17
1.41
Table 10: System identification errors for bowl collider.
Material
Parameter
RP-DiffMPM
GOP-DiffMPM
AS-DifIMPM (Ours)
log (ao(() FE)
2.01 + 0.45
2.87 + 1.18
1.91 + 0.96
Flastic
0.36 0.43
1.23 0.32
0.49 0.12
logio( (o((E) E))
28.45 3.12
16.88 1.84
12.07 2.21
Plasticine
9.29 + 5.04
10.24 + 3.03
8.21 + 1.02
login(Ty) (Ty)
9.44 + 2.05
8.76 = 1.88
6.23 + 1.47
Table 11: System identification errors for elastic and plasticine material types.
Shape
Material
Parameter
RP-DifIMPM
GOP-DiAMPM
AS-DiЛМPM (Ours)
(p)
7.81 1: 3.52
6.94 4.41
5.87 1 3.37
Droplet
Newtonian
logio
32.33 + 3.25
21.91 + 8.13
24.50 + 3.98
10g
8.12 1 3.49
7.22 1. 2.38
6.05 1 1.35
Letter
Newtonian
logio
31.01 1 5.40
23.12 1: 2.17
22.36 1 6.04
(p)
19.42 + 7.61
18.67 + 2.53
14.73 + 5.12
logio (k)
46.50 + 12.09
44.12 + 3.88
38.08 4.65
Cream
Non-Newtonian
logio (TY)
6.92 = 0.58
6.58 0.47
4.97 + 0.34
lo)1
54.88 + 12.72
46.41 + 5.85
40.01 7.43
log (w)
20.05 5.45
19.18 +
15.30 1.06
1og
44.44 + 4.33
44,99 + 3.04
39.72 + 3.89
Toothpaste
Non-Newtonian
log
7.35 + 1.61
6.97 + 0.52
5.12 + 0.38
log (n)
62.19 + 19.06
47.55 + 21.95
41.17 + 9.01
log (E)
1.85 + 0.83
2.87 + 0.75
2.69 1 0.62
Torus
Blastic
0.22 1 0.02
0.25 1: 0.02
0.19 1 0.01
log ( (E)
2.31 + 0.90
2.94 + 0.81
2.51 + 0.69
Bird
Elastic
0.22 + 0.02
0.26 0.02
0.21 + 0.01
log
17.38 + 1.14
15.89 1 1.03
11.62 0.89
Playdoh
Plasticine
8.31 1 3.03
9.27 2.02
6.22 1: 2.01
log1o (TY)
9.91 + 1.46
8.70 = 0.62
6.74 + 0.51
login(
18.11 + 1.20
16.32 + 1.05
12.01 0.95
Cat
Plasticine
8.30 + 2.71
8.28 + 1.02
6.23 + 1.98
lognu(Ty) (TY)
10.02 + 0.84
9.14 + 0.71
7.20 + 0.57
Trophy
Granular
Onte
2.19 + 0.15
1.95 + 0.12
1.24 + 0.09
Table 12: System identification errors for different material shapes.
27

---

More material shapes. We use the 9 shapes and their associated material types introduced in [ Each method is tested on all 9 shapes, with each shape colliding against the three colliders, resulting in 27 experiments per method. The results are presented in Tab. 12 averaged over the colliders.
D Extensions of AS-DiffMPM
Due to our collision handling mechanism integrated into the P2G and G2P stages, the AS-DiIIMPM framework can accommodate additional physical constraints. the following, we present two illustrative examples.
D.1 Material Cutting
We consider thin surface intersecting with a continuum material. We implement a separating surface behavior where adjust the velocity of the particle v, based on its relative position to the surface. Concretely, during the G2P stage, for each incompatible particle (Sec. (41.2), we compute the signed particle normal n ppFpp and update the velocity according to the particle's 's motion
relative to the surface. If the particle is moving away from the boundary (i.e., Vp np > 0), its velocity
remains unchanged. Otherwise, we project the velocity along the surface: vproj Vp (vp -p)) up.
Figure 8: thin surface cutting an elastic object.
D.2 Collider-to-Continum Coupling
We present a scenario where moving collider can interact with the continuum material. During the G2P stage, for each incompatible particle, we correct the velocity as V Vp + Vr, where v, the rigid body velocity at position Xp.
Figure 9: A ball colliding with sand object.
E Values of Physical Parameters for Ground-truth Rollouts
For fair comparison, we generate ground-truth simulation rollouts using the same physical parameter values in [4, listed in Tab. [3 for convenience. Each ground- -truth rollout is executed three times, one for each collider, totaling 75 rollouts. We remark that for each rollout a separate training run of system identification is performed, where an initial guess of the physical parameters is optimized by comparing the current rollout against the reference (either the form of particle trajectories or visual observations). For each material type, use the same initial guess across all training runs.
28

---

Newtonian (Iniial Guess: 10, 104)
Parameter
6
8
19.46
436.62
155.83
121.76 257356.08
49.09
38.44
64.16
228.71
552 98
106.93
193525.59
13772.52
358237.13
16789.77
Non- Newtoiatn (Initil Guess: μ 100,
10', TV
10, 1)
Parameter
3
7
8
24
13209
65351 .08
43757.04
36027.61
19593.71
20522.72
51519.45
121865.90
241579.97
33764.59
2015666599
171054.03
2496.39.00 94
134751.55
121836.33
14494,30
370317.66
32859.59
30124.90 98
122896. 10
Ty
7491.00
3964.94
5061.12
4153.38
3303.67
1192.76
1251.29
4689.16
6.68
26.09
23.27
22.31
38.83
27.24
20.43
10.27
10.62
22.89
Granular (Initial Guess Prio 10)
Purameter
Pre
3066777
32,3751
26 8816
29. 19.3458
42.2861
Table 13: Values of physical parameters for ground-truth simulation rollouts.
F
Implementation Details
implemented our framework using Python and Taichi for differentiable programming and parallel computation. AS-DifiMPM is built upon the open source DiftMPM implementation in 4 and
subsequent works 7 []. We run the experiments on NVIDIA RTX 3080 and 4090 graphics cards.
29


Reviews:
[{"review_id": "7s83RaW4LS", "reviewer": "Reviewer_dazL", "summary": "The authors propose a method to recover physical properties from video for fluid or granular media. The approach combines existing MP methods for physics simulation with differrentiable rendering. Different to prior work, arbitrary colliders (beyond planes) are supported. The contributions are on how to relate these colliders with the grid&point representations in MPM. Notably the reconstruction is done jointly with 3D reconstruction of the shape through differentiable rendering, without an intermediate step to track visual features.", "questions": "- how important are tne #of sequences used, when does it degrade?\n- are there other limitations, have other material types been tested? Would certain shapes be problematic? \n- why is the collider shape imported and not reconstructed from multi-view?", "limitations": "- See questions above, I find the current limitation section a little shallow as it adresses only once conceptual issue but leavs out other.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- the implementation and experiments are extensive, including both Voxel-based NeRF and Gaussian Splatting as point-based methods.\n- experiments are on established benchmarks and i comparison to existing methods\n\n- the addition of arbitrary colliders appears as rather a technical detail yet there are a few considerations to be made and the evaluation is decent, so there is still value for the community.\n\nWeaknesses:\n- experiments are only on synthetic sequences, would you think it generalizes to real scenes? Should be included in limitation section.\n- It would be better to up-front explain that the focus is on Newtonian fluids, non-Newtonian fluids, and granular media. From the intro I was more expecting deformable solid objects to be tackled, as it was very general.\n- in the eperiment section authors refer largely to prior work. To be self contained, it would be beneficial to know how close the initial parameter guesses are to the GT etc.", "was_revised": true, "final_justification": "Authors clarified my concerns, I stick to recommending acceptance.", "rebuttal": "We thank the reviewer for their thoughtful and constructive feedback. We appreciate the recognition of our paper’s quality, clarity, technical soundness and experimental evaluation. Below, we address each of the reviewer’s points in detail. \n\n***In summary, this rebuttal clarifies the limitations and open challenges that need to be addresses to extend our approach to real world scenarios, and provides additional experiments on novel material types and object shapes.***\n\nPlease let us know if there is anything we can clarify further.\n\n> [W1]. experiments are only on synthetic sequences, would you think it generalizes to real scenes? Should be included in limitation section.\n\nWe agree that the limitations section should discuss this point. Specifically, a key difficulty lies in the nature of the materials we target — Newtonian, non-Newtonian, and granular — which lack a **fixed rest shape**. This differs from previous work on deformable solids [1], where shape reconstruction and parameter estimation can be decoupled—for example, by first reconstructing the **object's rest shape** and then estimating physical parameters based on **observed deformations**. Instead, when dealing with fluid or granular materials in real-world settings, these tasks must be addressed simultaneously, as the object's shape evolves continuously during interaction. For example, estimating the viscosity of a fluid being poured requires reasoning jointly over its **shape** and **dynamics**. \n\nOur proposed AS-DiffMPM supports such scenarios (e.g., pouring into complex containers; see supplementary video at `supp/SecC2/glass_newtonian.mp4`), and we believe it represents a step forward toward system identification in uncostrained environments (i.e., involving complex colliders). However, to fully achieve system identification of fluid or granular materials in the real world, **joint reconstruction and identification** from real world video is required—an open challenge that lies beyond the scope of this work. We acknowledge that this limitation was not stated in the original manuscript and we will update the limitations section to reflect this point.\n\n> [W2]. It would be better to up-front explain that the focus is on Newtonian fluids, non-Newtonian fluids, and granular media. From the intro I was more expecting deformable solid objects to be tackled, as it was very general.\n\nWe thank the reviewer for pointing this out. We acknowledge that the introduction frames the work around the general challenge of system identification, without clearly stating our specific focus on fluid and granular materials. We will revise the introduction to explicitly clarify this scope.\n\n> [W3]. in the eperiment section authors refer largely to prior work. To be self contained, it would be beneficial to know how close the initial parameter guesses are to the GT etc.\n\nFor a fair analysis, we generated data and ground truth values using the same procedure as in previous work [2]. Therefore, the conditions (i.e., cameras, initial guess, ground truth values) are the same as in [2]. For completeness, for each material, **we show below the initial guess and the different ground truth physical parameters for each sequence**. We remind that there are 25 different sequences and 3 colliders, totaling 75 sequences for our experiments. We will revise the experiments section to clarify this point.\n\n### Newtonian (initial guess: µ=10, κ=10000)\n| Parameter | 1        | 2         | 3         | 4         | 5         | 6        | 7         | 8        | 9        | 10        |\n| --------- | -------- | --------- | --------- | --------- | --------- | -------- | --------- | -------- | -------- | --------- |\n| µ         | 19.46    | 436.62    | 155.83    | 121.76    | 49.09     | 38.44    | 64.16     | 228.71   | 552.98   | 106.93    |\n| κ         | 56075.55 | 152696.25 | 193525.59 | 257356.05 | 518012.47 | 13772.52 | 358237.13 | 11041.06 | 16789.77 | 112569.73 |\n\n### Non-Newtonian (initial guess: µ=100, κ=100000, τY=10, η=1)\n| Parameter | 1         | 2         | 3         | 4         | 5         | 6        | 7         | 8         | 9         | 10        |\n| --------- | --------- | --------- | --------- | --------- | --------- | -------- | --------- | --------- | --------- | --------- |\n| µ         | 13209.25  | 65351.08  | 43757.04  | 36027.61  | 19593.71  | 20522.72 | 51549.45  | 121865.90 | 241579.97 | 33764.59  |\n| κ         | 201566.59 | 171054.03 | 249639.94 | 134751.55 | 121836.33 | 14494.30 | 370317.66 | 32859.59  | 30324.98  | 122896.10 |\n| τY        | 1151.42   | 7491.70   | 3964.94   | 5061.12   | 1462.78   | 4153.38  | 3203.67   | 1192.76   | 1251.29   | 4689.16   |\n| η         | 6.68      | 26.69     | 23.27     | 22.31     | 38.83     | 27.24    | 20.43     | 10.27     | 10.62     | 22.89     |\n\n### Granular (initial guess: θ_fric=10)\n| Parameter | 1       | 2       | 3       | 4       | 5       |\n| --------- | ------- | ------- | ------- | ------- | ------- |\n| θ_fric    | 30.6577 | 32.3751 | 26.8816 | 29.3458 | 42.2861 |\n\n> [Q1]. how important are tne #of sequences used, when does it degrade?\n\nWe would kindly ask the reviewer to clarify what is meant by “number of sequences used”. As described in Sec. 5 \"Datasets\" and \"Physical Parameters\", our dataset follows the protocol of [2]: we use 10 sequences each for Newtonian and Non-Newtonian materials, and 5 for Granular, repeated across 3 colliders, totaling 75 sequences. Each sequence is a multi-view video recorded from 11 cameras, and the optimization is performed independently per sequence.\nIf the question refers to how performance scales with fewer camera views, we agree this is a relevant research direction. However, this analysis is beyond the scope of our current work. We kindly refer the reviewer to [3] for such analysis.\n\n> [Q2]. are there other limitations, have other material types been tested? Would certain shapes be problematic?\n\nPlease refer to our answers to reviewer **CpqV** for additional experiments in this direction. Specifically, we address **material shape variation** and further **material types** in answers to points **Q1** and **Q2** of reviewer **CpqV**.\n\n> [Q3]. why is the collider shape imported and not reconstructed from multi-view?\n\nWe thank the reviewer for raising this concern. Sec. 5.1 and 5.2 aims to quantitatively assess the system capabilities in recovering physical parameters. For a fair analysis, all other sources are set at their ideal condition. Thus, we import the collider shape instead of reconstructing it from multiple views since the reconstructed collider might be imprecise, this affects the particle trajectories and thus the estimation of physical parameters. We invite the reviewer to check Sec. B in the supplementary PDF, as we believe it addressess the concern raised here (i.e., it analyzes *the performance drop when using the reconstructed collider instead of the imported one*). We are open to further clarification if needed.\n\n\n[1] Licheng Zhong, Hong-Xing Yu, Jiajun Wu and Yunzhu Li. Reconstruction and Simulation of Elastic Objects with Spring-Mass 3D Gaussians. In European Conference on Computer Vision (ECCV) 2024.\n\n[2] Xuan Li, Yi-Ling Qiao, Peter Yichen Chen, Krishna Murthy Jatavallabhula, Ming Lin, Chenfanfu Jiang and Chuang Gan. PAC-NeRF: Physics Augmented Continuum Neural Radiance Fields for Geometry-Agnostic System Identification. In International Conference on Learning Representations (ICLR) 2023.\n\n[3] Takuhiro Kaneko. Improving Physics-Augmented Continuum Neural Radiance Field-Based Geometry-Agnostic System Identification with Lagrangian Particle Optimization. In Computer Vision and Pattern Recognition (CVPR) 2024."}, {"review_id": "m7Lrgcr1It", "reviewer": "Reviewer_rXMc", "summary": "This paper introduces AS-DiffMPM, a differentiable Material Point Method (MPM) framework that supports system identification in scenes involving interactions between deformable objects and arbitrarily shaped rigid body colliders. The authors extend differentiable MPM techniques with a particle-wise collision handling mechanism inspired by CPIC, enabling gradient-based physical parameter estimation in the presence of non-planar, complex rigid bodies. AS-DiffMPM is evaluated in combination with various rendering pipelines (voxel-based NeRF, 2DGS, MDyn-3DGS), and both qualitative and quantitative results demonstrate its effectiveness across multiple material types and collider", "questions": "1. In Table 1 (System Identification from Particle Trajectories), AS-DiffMPM appears to outperform the baselines predominantly in the case of Non-Newtonian materials, whereas for Newtonian and Granular materials, the baseline methods achieve lower errors in many settings. Could the authors elaborate on the underlying reasons for this discrepancy? What characteristics of Non-Newtonian materials make AS-DiffMPM particularly effective?\n2. In Table 3 (Geometric Error Evaluation), AS-DiffMPM only outperforms baselines in the case of Granular materials, which does not fully align with the trends observed in Table 1 for System Identification. Could the authors provide a deeper analysis of under what conditions (material type, collider complexity, or metric) AS-DiffMPM provides superior performance compared to GOP-DiffMPM or RP-DiffMPM?\n3. The proposed method is titled Any-Shape Differentiable Material Point Method, yet no experimental results are reported for interactions with planar colliders—scenarios where prior works (e.g., PAC-NeRF, GIC) are typically evaluated. Could the authors clarify whether AS-DiffMPM maintains competitive performance in this condition?\n4. The method is evaluated in conjunction with several rendering pipelines (DVGO, 2DGS, and MDyn-3DGS), which differ substantially in complexity and representation. Could the authors quantify the differences in training time and rendering latency among these models in the context of the system identification task? A breakdown of computational efficiency would be helpful for practitioners deciding between rendering backends.", "limitations": "Yes. The paper explicitly addresses its limitations, most notably the assumption of static rigid bodies and the absence of real-world evaluations. The authors also mention that their approach could be extended to moving colliders but defer such experimentation to future work. This upfront discussion is appreciated.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n1. [Exploration of non-planar colliders] The paper addresses a previously underexplored problem—system identification with non-planar rigid body colliders—by extending differentiable MPM to handle complex geometry interactions. This is a novel and necessary advancement over prior works like PAC-NeRF and GIC. By supporting arbitrarily shaped colliders, AS-DiffMPM enables more realistic physics-based analysis and simulation. This has clear value for downstream applications in robotics, graphics, and 3D perception.\n2. [Good compatibility] AS-DiffMPM is designed to be compatible with multiple rendering pipelines, increasing its adaptability and potential for broad adoption.\n3. [Technical novelty of Integrating CPIC] The proposed method integrate CPIP to project the rigid body onto a grid-based distance field so that it can handle collisions in a particle-wise manner and apply velocity corrections on particles in local neighborhood. \n4. [Extensive experimental evaluation] The authors conduct extensive evaluations on both particle-trajectory-based and vision-based system identification tasks across diverse material types and collider geometries, showing superior or competitive performance.\n\n\nWeaknesses\n1. [No comparison with existing method on planar colliders] Although the paper emphasizes AS-DiffMPM’s capability to handle interactions with arbitrarily shaped rigid bodies, it does not report results on planar colliders—a standard experimental setting used in prior work such as PAC-NeRF. This omission makes it difficult to assess whether the proposed method remains competitive in the regimes where earlier methods perform well, and prevents a direct comparison under identical conditions.\n2. [Lack of qualitative comparison with other methods] The qualitative visualizations provided do not include side-by-side comparisons between AS-DiffMPM, baseline methods (e.g., GOP-DiffMPM), and ground truth. Such comparisons are critical for visually assessing the fidelity of simulated trajectories and would significantly strengthen the empirical claims of the paper.", "was_revised": true, "final_justification": "The authors clarify the effectiveness of the proposed method for non-Newtonian materials, the trend difference between Table 1 and Table 3, and the training times, addressing my concerns. \n\nI keep my rate \"borderline accept\" after the rebuttal and discussion.", "rebuttal": "We thank the reviewer for the detailed reading of our paper and constructing suggestions. Specifically, we appreciated the recognition of the impact of the proposed method for handling complex colliders and the extensive evaluation. \n\n***Briefly, in this rebuttal, we provide additional experiments in the planar setting, clarify the distinct challenges posed by non-Newtonian versus Newtonian and granular materials, and present a computational efficiency analysis of different rendering backends.***\n\nWe hope our responses below adequately address your concerns and we are open to further clarification.\n\n> [W1]. [No comparison with existing method on planar colliders] [...]\n\nPlease see Q3.\n\n> [W2]. [Lack of qualitative comparison with other methods] [...]\n\nWe thank the reviewer for the suggestion and agree that qualitative side-by-side comparisons would further support our claims. As per NeurIPS rebuttal guidelines, we cannot include additional media at this stage, but we plan to add such visualizations to the supplementary material.\n\n> [Q1]. In Table 1 (System Identification from Particle Trajectories), AS-DiffMPM appears to [...]. What characteristics of Non-Newtonian materials make AS-DiffMPM particularly effective?\n\nWe agree with the reviewer that this analysis requires further clarification. Firstly, we remind that GOP-DiffMPM operates at the grid level during the Grid Operations (G-OP) stage. It applies a single, **averaged** velocity correction to all particles within a grid cell that is detected to be inside a collider. This is a coarse approximation that may overlook fine-grained interactions between the material and the complex collider. \n\nIn contrast, our AS-DiffMPM performs **particle-wise** collision handling during the Particle-to-Grid (P2G) and Grid-to-Particle (G2P) stages. It identifies individual particles near a boundary and applies **particle-wise** velocity corrections based on their specific relationship with the collider surface. These differing collision strategies have practical implications for system identification, particularly depending on the material behavior. \n\nFor **fluid-like materials** (e.g., Newtonian fluids or granular materials), where particles tend to slide along the surface or flow away upon impact, the smoothing effect of GOP-DiffMPM’s grid-based velocity correction is often sufficient. Although it may introduce minor inaccuracies at sharp corners (e.g., slight particle penetration), the approximation can contribute to smoother gradients and potentially help stabilize the optimization process. This may partially explain why GOP-DiffMPM performs competitively—or even slightly better—in some Newtonian and granular settings. However, for **non-Newtonian materials** with higher yield stress (τY) [1], which exhibit **solid-like behavior**, this averaging becomes problematic. In such cases, particles are more prone to adhere to surfaces or accumulate near sharp corners. GOP-DiffMPM’s **grid-level smoothing** tends to blur these interactions, causing the simulated material to partially \"bleed\" into the collider geometry. This results in reduced accuracy when estimating physical parameters. In contrast, AS-DiffMPM’s **particle-wise** correction accurately resolves per-particle contact behavior, particularly around complex or high-curvature boundaries, resulting in better system identification results. \n\nWe acknowledge that such nuances were not mentioned in the original manuscript and we will revise it accordingly. \n\n> [Q2]. In Table 3 (Geometric Error Evaluation), AS-DiffMPM only outperforms baselines in the case of Granular materials, which does not fully align with the trends observed in Table 1 for System Identification [...]\n\nWe understand the reviewer's concern and acknowledge that this analysis was not throughly discussed. \n\nThere is a conceptual distinction between the metrics used in Table 3 (geometric error) and those in Table 1 (parameter estimation error), which explains why they can lead to seemingly different conclusions.\n\nThe Chamfer Distance (CD) and Earth Mover’s Distance (EMD) in Table 3 measure the geometric similarity between predicted and ground-truth particle configurations. These metrics compute spatial correspondences between particles in one point cloud and particles in the other point cloud, and quantify how closely the predicted point cloud matches the reference one. However, a low geometric error does not necessarily imply that the correct physical parameters were identified. Two simulations may produce geometrically similar shapes despite being governed by different underlying physics. Specifically, there can be similar shapes but with different particle trajectories. Therefore, upon convergence of the physical parameters estimation, the model might have different particle trajectories but similar shape with respect to the reference, thus better geometric similarity but worse parameters estimation. \n\nWe acknowledge that the results and analysis in Table 3 are not properly discussed and we will revise this in our manuscript.\n\n> [Q3]. The proposed method is titled Any-Shape Differentiable Material Point Method [...]\n\nWe thank the reviewer for this observation and agree that evaluating AS-DiffMPM under planar collider conditions provides valuable insight into its performance in standard benchmarks. To this end, we conducted additional experiments comparing our AS-DiffMPM with both the baselines used in our paper and the **Standard MPM (S-MPM)** collision strategy adopted by prior works [2, 3, 4]. In S-MPM, collisions are resolved at the **Grid Operations** stage (Sec. 3.1): for a planar surface defined by point **x_b** and normal **n_b**, the nodal velocity **v_g** is set to zero for all grid nodes **x_g** such that **(x_g - x_b) · n_b ≤ 0**. In contrast, AS-DiffMPM represents the same planar collider as a mesh surface positioned at **x_b**, and applies **particle-wise collision handling** during both P2G and G2P steps. We performed three system identification experiments using particle trajectory supervision under planar collider conditions. The results are summarized in the following table, reporting the absolute error in physical parameter estimation.\n\n| Material       | Parameter | S-MPM | RP-DiffMPM | GOP-DiffMPM | AS-DiffMPM (Ours) |\n|----------------|-----------|--------|--------------|-------------|-------------|\n| Newtonian      | µ         | **7.51**    | 8.03          | 7.63         | 7.98         |\n|                | κ         | **31.98**    | 35.21          | 32.45         | 33.21         |\n| Non-Newtonian  | µ         | 24.09    | 24.57          | 24.91         | **24.03**         |\n|                | κ         | **19.01**   | 21.12          | 20.19         |  19.03         |\n|                | τY       | 4.91    | 5.12          | 4.78         | **4.54**         |\n|                | η         | **30.53**    | 32.1          | 31.05         | 31.21         |\n| Granular       | θ_fric    | 0.15    | 0.56          |    0.22      |    **0.12**      |\n\nThe S-MPM achieves slightly lower errors for some parameters, likely due to its use of analytically defined boundary conditions, which may offer improved numerical stability in simple geometries. However, a more systematic analysis would be required.\n\n> [Q4]. The method is evaluated in conjunction with several rendering pipelines (DVGO, 2DGS, and MDyn-3DGS) [...]\n\nWe report the average time for the following components, measured on an NVIDIA RTX 3080 GPU: (1) full training, (2) a forward pass (i.e., particle advection using MPM followed by rendering), and (3) a backward pass. Full training consists of 150 optimization steps. At each step, we perform a forward and backward pass over all 16 frames in the video, followed by an update of the physical parameters (gradient optimization step).\n\n| Rendering Backend | Full Training (h) | Forward Pass (s) | Backward Pass (s) |\n|-------------------|-------------------|------------------------------|-------------------------------|\n| DVGO              | **2.50**              | **12**                           | **48**                            |\n| 2DGS              | 3.21              | 14                           | 63                            |\n| MDyn-3DGS         | 8.88              | 33                           | 180                           |\n\n\nWhile MDyn-3DGS has generally demonstrated higher performance than the other methods (see Tab. 2 in our manuscript), it comes at a significantly higher computational cost. This is primarily due to its particle infilling strategy, which increases the number of particles in the MPM simulation, and the use of a loss function that combines both image reconstruction error (between rendered and ground truth masks) and geometric error on the particles. Additionally, the reported timing for MDyn-3DGS does not include the preliminary dynamic scene reconstruction stage required before physical parameter optimization. This preprocessing step is briefly discussed in lines 297–299 of our manuscript; for further details, we kindly refer to [4].\n\n\n[1] Yonghao Yue et al. Continuum foam: A material point method for shear-dependent flows. In ACM Transactions on Graphics (TOG) 2015.\n\n[2] Xuan Li et al. PAC-NeRF: Physics Augmented Continuum Neural Radiance Fields for Geometry-Agnostic System Identification. In International Conference on Learning Representations (ICLR) 2023.\n\n[3] Takuhiro Kaneko. Improving Physics-Augmented Continuum Neural Radiance Field-Based Geometry-Agnostic System Identification with Lagrangian Particle Optimization. In Computer Vision and Pattern Recognition (CVPR) 2024.\n\n[4] Junhao Cai et al. GIC: Gaussian-Informed Continuum for Physical Property Identification and Simulation. In Advances in neural information processing systems (NeurIPS) 2024"}, {"review_id": "XgGO2CFWds", "reviewer": "Reviewer_gepN", "summary": "This paper introduces AS-DiffMPM, a differentiable Material Point Method framework that supports system identification of continuum objects colliding with arbitrarily shaped rigid bodies. Unlike prior works that only handle planar boundaries, AS-DiffMPM incorporates a particle-wise collision handling mechanism—based on Compatible Particle-in-Cell (CPIC)—to resolve interactions with complex meshes or 2D Gaussian splat primitives. The method is integrated with both voxel-based NeRF and point-based Gaussian splatting renderers to optimize physical parameters from multi-view videos. Extensive experiments demonstrate its effectiveness on Newtonian, non-Newtonian, and granular materials, using both ground-truth particle trajectories and visual observations for supervision", "questions": "See Weakness.", "limitations": "See Weakness.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n\n1.Extends differentiable MPM to arbitrary collider geometries via CPIC, enabling accurate, particle-wise velocity corrections during P2G and G2P stages.\n\n2.Provides seamless interfaces to voxel-grid NeRFs and 2D Gaussian Splatting methods, supporting end-to-end gradient flow from photometric losses to physical parameters .\n\n3.Benchmarks across three material types (Newtonian, non-Newtonian, granular) and three colliders (Box, Bunny, Armadillo), reporting both trajectory-based and vision-based identification results, with clear error statistics and comparisons against two baselines (GOP-DiffMPM, RP-DiffMPM) and multiple rendering backends.\n\n4.Authors plan to release code, facilitating reproducibility and further research in differentiable physics and system identification.\n\n\nWeaknesses\n1. MPM is fundamentally a Galerkin-based method—yet the paper does not analyze whether the differentiable formulation preserves energy conservation, admits closed-form solutions, or under what conditions it remains stable.\n\n2. All P2G/G2P and collision computations occur on the background grid; the results are therefore highly dependent on grid resolution, with coarser grids potentially introducing aliasing or inaccuracy.\n\n3. The paper positions CPIC-based collision handling as a more efficient alternative to hard-clamp methods, compensating for approximation errors with speed. However, it never quantifies whether the computational effort saved by avoiding per-particle constraints is fully realized once the overhead of scatter/gather operations and backpropagation through the grid is accounted for. This raises the question of whether any real efficiency advantage survives in practical, high-resolution scenarios.\n\n4. There is no discussion of the method’s numerical properties: e.g., under what time step or grid refinement regimes the optimization converges, whether the gradient signals remain well-conditioned, or if any spurious oscillations arise during backpropagation.", "was_revised": true, "final_justification": "Most of concerns are to some extent addressed.", "rebuttal": "We thank the reviewer for the insightful feedbacks on our work. We are happy to know that you recognize the contribution for handling complex geometries within the MPM framework and the results on system identification from both particle trajectories and visual observations.\n\n***In this rebuttal, we address concerns about the theoretical properties and computational efficiency of AS-DiffMPM. We clarify the distinction between particle-wise and grid-level collision handling, present timing benchmarks across methods, and include a convergence analysis of gradients of physical parameters during optimization.***\n\nWe address below every point raised by the reviewer, and we welcome any follow-up question. \n\n> [W1]. MPM is fundamentally a Galerkin-based method—yet the paper does not analyze whether the differentiable formulation preserves energy conservation, admits closed-form solutions, or under what conditions it remains stable.\n\nWe thank the reviewer for raising this important point regarding the theoretical properties of our differentiable MPM framework. We have observed empirically stable behavior across all evaluated material types (Newtonian, non-Newtonian, and granular) and collider geometries (Box, Bunny, and Armadillo).\n\nOur implementation builds upon PAC-NeRF [1] and the DiffTaichi framework [2], inheriting their default simulation settings: a timestep of Δt = 0.0002 and a grid spacing of Δx = 0.02. Our code explicitly monitors numerical stability after every simulation step by checking for the **Courant–Friedrichs–Lewy (CFL) condition**: `v_max × Δt ≤ Δx`, where `v_max` is the maximum particle velocity detected at the current timestep. This condition checks if a particle travels more than one grid cell per timestep. If violated, the common approach is to halve the timestep Δt and retry the simulation step. \n\n> [W2]. All P2G/G2P and collision computations occur on the background grid; the results are therefore highly dependent on grid resolution, with coarser grids potentially introducing aliasing or inaccuracy.\n\nWe apologize for the confusion. In our paper, collision computations (both **collision check** and **velocity corrections** upon collision) occur entirely on the background grid for the GOP-DiffMPM baseline and in scenarios where the collider has a simple, analytically defined shape (e.g., a plane, as described in lines 122–126 in our manuscript and adopted in previous work [1]). These approaches are highly dependent on grid resolution. In practice, when a collider surface intersects a grid cell, all particles within that cell receive the same velocity update—regardless of their position relative to the surface—which can lead to artifacts such as penetration. These artifacts tend to worsen as the grid resolution decreases.\n\nIn contrast, our AS-DiffMPM framework can partially mitigate these issues through **particle-wise** collision handling. Although we still use a background grid to determine which nodes are inside or outside a collider (i.e., **collision check** using the Collision Grid), **velocity corrections** are applied at the **particle** level during the G2P stage, rather than during the GOP stage. This enables control over each particle's interaction with the collider, allowing us finer control such as resolving penetration artifacts (see lines 183–185 in our manuscript). Because these corrections happen on a per-particle basis, AS-DiffMPM is less sensitive to grid resolution compared to grid-level methods.\n\nWe hope this response addresses the reviewer's concern. If further clarification is needed, we would be happy to provide it. We will also clarify this point in the revised manuscript.\n\n> [W3]. The paper positions CPIC-based collision handling as a more efficient alternative to hard-clamp methods, compensating for approximation errors with speed. However, it never quantifies whether the computational effort saved by avoiding per-particle constraints is fully realized once the overhead of scatter/gather operations and backpropagation through the grid is accounted for. This raises the question of whether any real efficiency advantage survives in practical, high-resolution scenarios.\n\nWe thank the reviewer for raising this important point on computational efficiency, which we acknowledge was not sufficiently analyzed in the original submission.\n\nTo address this, we provide below a performance comparison of the collision-handling strategies used in our work: GOP-DiffMPM (**grid-level** collision handling), RP-DiffMPM (collider represented as **rigid particles**), and AS-DiffMPM (our **particle-wise** CPIC-based strategy). Timings are measured per simulation step using a 64x64x64 background grid, 25K particles and during collisions with the Box collider.\n\n### Timing comparison\n| Method      | Time (ms) |\n| ----------- | --------- |\n| RP-DiffMPM  | 1812    |    \n| GOP-DiffMPM | 2192    |    \n| AS-DiffMPM  | 2537    |\n\nMoreover, we remind that our AS-DiffMPM extend the MPM by (1) constructing a Collision Grid (Sec. 4.1.1), (2) transfering the Collision Grid to material particles (Sec. 4.1.2), (3) adding compatibility checks during P2G and (4) particle-wise velocity corrections during G2P (Sec. 4.1.3). We report below the time required for these operations.\n\n### Overhead Breakdown for AS-DiffMPM\n| Component                                                        | Time (ms) |\n| ---------------------------------------------------------------- | --------- |\n| Collision grid construction                                      | 779        |\n| Collision grid to material particles                             | 403        |\n| P2G with compatibility checks                                    | 478        |\n| G2P with particle-wise velocity correction                       | 541        |\n\nAlthough AS-DiffMPM introduces a modest overhead compared to the baselines, it obtains superior physical accuracy for system identification with complex colliders (see Table 1 in our manuscript), due to its fine-grained collision handling mechanism.\n\nRegarding the mention of “hard-clamp methods”: we clarify that our work does not compare against true hard constraints, but rather grid-level collision correction (as in GOP-DiffMPM), which may lead to simulation artifacts (e.g., penetration) in high-curvature scenarios. Our contribution is not focused on raw speed improvements, but rather on enabling a more accurate collision handling through particle-wise velocity corrections.\n\n\n> [W4]. There is no discussion of the method’s numerical properties: e.g., under what time step or grid refinement regimes the optimization converges, whether the gradient signals remain well-conditioned, or if any spurious oscillations arise during backpropagation.\n\nWe acknowledge that our original submission did not include an analysis on optimization convergence, and we agree that such analysis would strengthen the empirical evaluation of AS-DiffMPM.\n\nBelow, we provide an analysis of the gradient of physical parameters over 150 steps (a subset of steps is visualized) during system identification using AS-DiffMPM. Specifically, we report results from 3 representative experiments, one per material, colliding against a Box shape.\n\n### Newtonian material\n| Step  | 1   | 5   | 10  | 20  | 40  | 60  | 90  | 120 | 150 |\n| ----- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| **μ** | -0.02 | 0.005 | 0.01 | -0.02 | 0.001 | -0.001 | -0.0001 | -2.9e-05 | -2.4e-06 |\n| **κ** | -0.002 | -0.0008 | 0.0001 | -0.0001 | -0.0002 | -0.0001 | -0.0001 | 4.4e-05 | 5.8e-06 |\n\n### Non-Newtonian material\n| Step  | 1   | 5   | 10  | 20  | 40  | 60  | 90  | 120 | 150 |\n| ----- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| **μ** | -0.004 | -0.004 | -0.004 | 5.1e-05 | -0.0004 | 0.0002 | -3.7e-05 | -1.5e-05 | -1.5e-05 |\n| **κ** | -0.0005 | -0.01 | -0.02 | 0.003 | 0.0004 | 0.002 | 0.0004 | 0.0002 | 0.0002 |\n| **τY** | -0.002 | -0.01 | -0.02 | 0.004 | -0.009 | 0.005 | -0.001 | -0.0003 | -0.0002 |\n| **η** | -0.008 | -0.01 | -0.02 | -0.003 | 0.001 | -0.0002 | 0.0001 | -7.5e-05 | -7.7e-05 |\n\n\n### Granular material\n| Step  | 1   | 5   | 10  | 20  | 40  | 60  | 90  | 120 | 150 |\n| ----- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| **θ_fric** | -0.004 | -0.003 | -0.002 | -0.0006 | 9.7e-05 | 9.1e-05 | 5.8e-05 | 1.6e-05 | -3.3e-06 |\n\n\nThe tables above illustrate how the gradients of the physical parameters consistently decrease in magnitude during optimization, suggesting that no problematic oscillations arise to prevent smooth training. While we acknowledge that a more in-depth numerical analysis would be beneficial, we did not observe any stability issues during our empirical evaluations. We therefore leave this study to future work.\n\n\n[1] Xuan Li et al. PAC-NeRF: Physics Augmented Continuum Neural Radiance Fields for Geometry-Agnostic System Identification. In International Conference on Learning Representations (ICLR) 2023.\n\n[2] Yuanming Hu et al. DiffTaichi: Differentiable Programming for Physical Simulation. In International Conference on Learning Representations (ICLR) 2020."}, {"review_id": "eGtDXAZiHG", "reviewer": "Reviewer_CpqV", "summary": "This paper addresses the challenge of system identification using arbitrarily shaped colliders. To achieve this, it enhances an existing differentiable Material Point Method (MPM) by incorporating a differentiable collision handling mechanism. This addition enables the estimation of physical properties using differentiable renderers and simulators. Experiments conducted on several synthetic benchmarks demonstrated the effectiveness of the proposed approach.", "questions": "1.\tPer Weakness 1, could the authors present more results, including but not limited to the following scenarios: (1) move the collider to a corner of the floor instead of directly below the object, (2) make the size of the collider (i.e., the bounding-box size) much greater than that of the object, (3) use an open-surface collider, e.g., a bowl-shaped mesh or a cylinder open at the ends, and (4) place multiple colliders side by side?\n\n2.\tPer Weakness 2, could the authors present results of system identification on elastic and plastic objects?\n\n3.\tPer Weakness 3, could the authors conduct at least one real-world experiment to verify its practical usefulness?\n\n4.\tHow long does it take (on average) to finish an identification task for the proposed method and the baseline approaches?", "limitations": "The authors list several limitations in the paper, including the requirement for rigid-body reconstruction and the use of static colliders. \n\nThe objects considered in the paper appear to have only one shape (i.e., the cross shape) and uniform material properties. It would be interesting to have some results on objects with other shapes and heterogeneous material compositions.\n\nAnother interesting experiment would be to replace the colliders of rigid objects with those of deformable objects.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "**Strengths**:\n\n1. The paper is well written and easy to follow.\n\n2. It extends the existing differentiable MPM simulator with support for a differentiable collision handling strategy that accommodates arbitrarily shaped colliders.\n\n3. The proposed collision handling strategy is generalized to primitives with associated normals, e.g., 2D Gaussian disks.\n\n**Weaknesses**:\n\n1. The proposed method aims to address system identification with complex colliders. While it did present results of non-planar colliders, it still lacks *variety* and *complexity* regarding the (a) location, (b) size, (c) shape, and (d) number of colliders in the considered scenarios. \n\n2. The experiments only show results of a limited range of material types, i.e., only consider fluids and granular media. However, previous work [1] also considers elastic and plastic materials for experiments. This observation may indicate *a lack of generality* of the proposed framework.\n\n3. The method claims that an ad hoc solution for system identification with complex colliders is necessary, yet it only presents results based on synthetic data. In a synthetic environment, we can actually estimate the material properties of objects by using a planar collider to collect simulation trajectories (since we have full control of the simulation). Consequently, a more practical application of the proposed method should involve using multi-view videos captured from *real-world environments*, which show objects colliding with complex colliders. However, the method lacks results that reflect this practical scenario.", "was_revised": true, "final_justification": "The authors' response addressed my initial concerns about the limited evaluation and lack of real-world experiments. The additional results enhance the paper's completeness and demonstrate the potential practicality of the proposed method. Therefore, I decided to revise my rating to 4.", "rebuttal": "We thank the reviewer for their valuable feedback. Specifically, we appreciated the comments on quality, clarity and recognizing the value of handling different primitives (i.e., mesh and 2D Gaussians) in our framework.\n\n***In this rebuttal, we provide additional experiments on various aspect of the colliders, evaluate our method on additional material types and shapes, and provide additional details on the training time.***\n\nBelow, we address every point raised by the reviewer.\n\n> [Q1]. Per Weakness 1, could the authors present more results [...]\n\n## (1) Move collider to the side\nWe conducted additional experiments in which the collider is moved to the side, so that the material **first impacts the ground** and **then interacts with the collider** as it spreads along the surface. We evaluated our AS-DiffMPM across nine experiments—comprising three material types and three colliders. For brevity, we report the results per material type, averaged over the three colliders (Box, Bunny and Armadillo)\n\nThis configuration appears to introduce significant challenges in physical parameter estimation, likely due to this *ground-first-collider-next* complex interactions between the material and the collider. However, a more extensive evaluation would be needed to draw definitive conclusions.\n\n### Newtonian  \n| Parameter | Error |\n| --------- | ----- |\n| μ     |  10.51  ± 12.09   |\n| κ  | 39.82  ± 9.65   |\n\n\n### Non-Newtonian  \n| Parameter              | Error |\n| ---------------------- | ----- |\n| μ                  | 23.02  ±   10.31   |\n| κ               | 50.34  ± 7.78  |\n|  τY | 9.56  ± 5.90   |\n| η                 | 34.41  ±  12.74  |\n\n\n### Granular  \n| Parameter                         | Error |\n| --------------------------------- | ----- |\n| θ_fric | 4.02  ±  1.7  |\n\n\n## (2) Colliders of different size\nFor this analysis, we used AS-DiffMPM and ran 18 experiments: three material types with three colliders, each tested at two scales (0.5 and 1.5), resulting in 3 × 3 × 2 = 18 experiments. The results are averaged over the colliders.\n\nNo significant differences were observed compared to the results in Table 1 of our manuscript, although a more extensive evaluation would be needed to confirm this observation.\n\n### Newtonian  \n| Parameter | Error |\n| --------- | ----- |\n| μ     |  \t5.21 ± 7.02   |\n| κ  | 26.88 ± 25.91  |\n\n\n### Non-Newtonian  \n| Parameter              | Error |\n| ---------------------- | ----- |\n| μ                  | 22.17 ± 12.81   |\n| κ               | 23.15 ± 15.64  |\n|  τY | \t5.34 ± 4.26   |\n| η                 | 21.03 ± 7.98  |\n\n\n### Granular  \n| Parameter                         | Error |\n| --------------------------------- | ----- |\n| θ_fric | 1.09 ± 0.93 |\n\n\n## (3) Bowl collider\nWe imported a bowl-shaped collider into our framework and conducted a comparative study of our AS-DiffMPM method against the baselines. The bowl was positioned such that the falling material impacts its open surface—causing some particles to enter the bowl while others fall outside of it. We conducted three experiments, one for each material type. The results are reported below.\n\n| Material      | Parameter        | RP-DiffMPM | GOP-DiffMPM | AS-DiffMPM  |\n| ------------- | ---------------- | ---------- | ----------- | ----------------- |\n| Newtonian     | μ                | 7.84       | 7.29        | **6.01**              |\n|               | κ                | 30.12      | 28.45       | **25.67**             |\n| Non-Newtonian | μ                | 19.31      | 20.05       | **15.03**             |\n|               | κ                | 38.22      | 35.79       | **29.84**             |\n|               | τY    | 7.31       | 6.98        | **5.15**              |\n|               | η                | 26.78      | 28.45       | **20.94**             |\n| Granular      | θ_fric | 3.01       | **1.17**        | 1.41              |\n\n\n## (4) Multiple colliders\n\nWe conduct three experiments—one for each material type—in scenes containing multiple colliders. Specifically, we place the Box, Bunny, and Armadillo colliders side by side and below the falling material, so that it interacts with all three as it spreads. These experiments are performed using our AS-DiffMPM method. The results are presented below.\n\n| Material          | Parameter        | Error        |\n| ----------------- | ---------------- | ------------ |\n| **Newtonian**     | μ                | 6.85   |\n|                   | κ                | 47.34  |\n| **Non-Newtonian** | μ                | 3.41 |\n|                   | κ                | 41.98 |\n|                   | τY               | 7.59  |\n|                   | η                | 32.02 |\n| **Granular**      | θ_fric            | 3.04         |\n\n\n\n## (5) More material shapes\nWe thank the reviewer for the constructive feedback in the limitations section. We agree that evaluating system identification on a wider variety of material shapes would strengthen our empirical analysis. To this end, we use 9 shapes and their associated material types from previous work [1]. We evaluate our AS-DiffMPM method and the baselines. Each method is tested on all 9 shapes, with each shape colliding against the three colliders, resulting in 27 experiments per method. The results, averaged over the colliders, are presented below.\n\n| Shape      | Material      | Parameter        | RP-DiffMPM  | GOP-DiffMPM  | AS-DiffMPM  |\n| ---------- | ------------- | ---------------- | --------------- | ---------------- | ---------------------- |\n| Droplet    | Newtonian     | μ                | 7.81 ± 3.52     | 6.94 ± 4.41      | **5.87 ± 3.37**        |\n|            |               | κ                | 32.33 ± 3.25    | **21.91 ± 8.13**     | 24.50 ± 3.98       |\n| Letter     | Newtonian     | μ                | 8.12 ± 3.49     | 7.22 ± 2.38      | **6.05 ± 1.35**        |\n|            |               | κ                | 31.01 ± 5.40    | 23.12 ± 2.17     | **22.36 ± 6.04**       |\n| Cream      | Non-Newtonian | μ                | 19.42 ± 7.61    | 18.67 ± 2.53     | **14.73 ± 5.12**       |\n|            |               | κ                | 46.50 ± 12.09    | 44.12 ± 3.88     | **38.08 ± 4.65**       |\n|            |               | τY               | 6.92 ± 0.58     | 6.58 ± 0.47      | **4.97 ± 0.34**        |\n|            |               | η                | 54.88 ± 12.72    | 46.41 ± 5.85     | **40.01 ± 7.43**       |\n| Toothpaste | Non-Newtonian | μ                | 20.05 ± 5.45    | 19.18 ± 1.29     | **15.30 ± 1.06**       |\n|            |               | κ                | 44.44 ± 4.33    | 44.99 ± 3.04     | **39.72 ± 3.89**       |\n|            |               | τY               | 7.35 ± 1.61     | 6.97 ± 0.52      | **5.12 ± 0.38**        |\n|            |               | η                | 62.19 ± 19.06    | 47.55 ± 21.95     | **41.17 ± 9.01**       |\n| Torus      | Elastic       | E                | **1.85 ± 0.83**    | 2.87 ± 0.75     | 2.69 ± 0.62        |\n|            |               | ν                | 0.22 ± 0.02     | 0.25 ± 0.02      | **0.19 ± 0.01**        |\n| Bird       | Elastic       | E                | **2.31 ± 0.90**    | 2.94 ± 0.81     | 2.51 ± 0.69        |\n|            |               | ν                | 0.22 ± 0.02     | 0.26 ± 0.02      | **0.21 ± 0.01**        |\n| Playdoh    | Plasticine    | E                | 17.38 ± 1.14    | 15.89 ± 1.03     | **11.62 ± 0.89**       |\n|            |               | ν                | 8.31 ± 3.03     | 9.27 ± 2.02      | **6.22 ± 2.01**        |\n|            |               | τY               | 9.91 ± 1.46     | 8.70 ± 0.62      | **6.74 ± 0.51**        |\n| Cat        | Plasticine    | E                | 18.11 ± 1.20    | 16.32 ± 1.05     | **12.01 ± 0.95**       |\n|            |               | ν                | 8.30 ± 2.71     | 8.28 ± 1.02      | **6.23 ± 1.98**        |\n|            |               | τY               | 10.02 ± 0.84    | 9.14 ± 0.71      | **7.20 ± 0.57**        |\n| Trophy     | Granular      | θ_fric            | 2.19 ± 0.15     | 1.95 ± 0.12      | **1.24 ± 0.09**        |\n\n## (6) Further experiments\n\nMoreover, please refer to answer to point **Q3** of reviewer **rXMc** for results on planar colliders.\n\n> [Q2]. Per Weakness 2, could the authors present results of system identification on elastic and plastic objects?\n\nWe present below the results for elastic and plasticine materials using our AS-DiffMPM method and the baselines. Each method was evaluated on six experiments: two material types and with three colliders. Results are averaged over the colliders. Interestingly, all methods generally perform well on the elastic material. This may be due to the simpler nature of the interaction between the elastic material and the collider—since the material tends to bounce away upon contact, the particle-wise collision handling mechanism of AS-DiffMPM has less impact. Indeed, in these scenarios, no fine-grained interaction (e.g., material flowing around sharp corners) occurs.\n\n| Material       | Parameter     | RP-DiffMPM   | GOP-DiffMPM  | AS-DiffMPM  |\n| -------------- | ------------- | ------------ | ------------ | ----------------- |\n| **Elastic**    | E             | 2.01 ± 0.45 | 2.87 ± 1.18 | **1.91 ± 0.96**   |\n|                | ν             | **0.36 ± 0.43**  | 1.23 ± 0.32  | 0.49 ± 0.12   |\n| **Plasticine** | E             | 28.45 ± 3.12 | 16.88 ± 1.84 | **12.07 ± 2.21**  |\n|                | ν             | 9.29 ± 5.04  | 10.24 ± 3.03  | **8.21 ± 1.02**   |\n|                | τY            | 9.44 ± 2.05  | 8.76 ± 1.88  | **6.23 ± 1.47**   |\n\n> [Q3]. Per Weakness 3, [...]\n\nPlease see answer to point **W1** of reviewer **dazL**.\n\n> [Q4].How long does it take (on average) to finish [...]\n\nPlease see answer to point **Q4** of reviewer **rXMc**.\n\n\n[1] Xuan Li et al. PAC-NeRF: Physics Augmented Continuum Neural Radiance Fields for Geometry-Agnostic System Identification. In International Conference on Learning Representations (ICLR) 2023."}]

Author rebuttal:

Meta-review: The paper received 4 reviews. The authors-reviewers discussion clarified most points raised in the initial reviews. A consensus that the paper brings a valuable contribution with sufficient validation was reached; the paper can be revised to meet the requirements for publication based on the authors-reviewers discussion. The scores were revised accordingly. The paper could be accepted as poster.
Decision: Accept (poster)