MaNGO — Adaptable Graph Network Simulators via Meta-Learning
Authors: Philipp Dahlinger
Tai Hoang
Denis Blessing
Niklas Freymuth
Gerhard Neumann
Venue: NeurIPS 2025 poster ()
Keywords: Graph Network Simulators
Meta Learning
Graph Neural Operators
Conditional Neural Processes
Primary area: machine_learning_for_sciences
TL;DR: We propose a meta-learning approach to enable Graph Network Simulators (GNSs) for fast adaptation to new physical parameters, leveraging conditional neural processes (CNPs) and neural operators to learn shared latent structures.

Abstract: Accurately simulating physics is crucial across scientific domains, with applications spanning from robotics to materials science. While traditional mesh-based simulations are precise, they are often computationally expensive and require knowledge of physical parameters, such as material properties. In contrast, data-driven approaches like Graph Network Simulators (GNSs) offer faster inference but suffer from two key limitations: Firstly, they must be retrained from scratch for even minor variations in physical parameters, and secondly they require labor-intensive data collection for each new parameter setting. This is inefficient, as simulations with varying parameters often share a common underlying latent structure.
    In this work, we address these challenges by learning this shared structure through meta-learning, enabling fast adaptation to new physical parameters without retraining. 
    To this end, we propose a novel architecture that generates a latent representation by encoding graph trajectories using conditional neural processes (CNPs). To mitigate error accumulation over time, we combine CNPs with a novel neural operator architecture. 
    We validate our approach, Meta Neural Graph Operator (MaNGO), on several dynamics prediction tasks with varying material properties, demonstrating superior performance over existing GNS methods. Notably, MaNGO achieves accuracy on unseen material properties close to that of an oracle model.

MaNGO - Adaptable Graph Network Simulators via Meta-Learning
Philipp Dahlinger" Tai Hoang Denis Blessing Niklas Freymuth Gerhard Neumann
Autonomous Learning Robots
Karlsruhe Institute of Technology Karlsruhe
Abstract
Accurately simulating physics is crucial across scientific domains, with applications spanning from robotics to materials science. While traditional mesh-basee simula- tions are precise, they often computationally expensive and require knowledge of physical parameters, such as material properties. In contrast, data-driven ap- proaches like Graph Network Simulators (GNSs) offer faster inference but suffer from two key limitations: Firstly, they must be retrained from scratch for even minor variations in physical parameters, and secondly they require aabor-intensive data collection for each new parameter setting. This is inefficient, as simulations with varying parameters often share common underlying latent structure. In this work, we address these challenges by learning this shared structure through meta- learning, enabling fast adaptation new physical parameters without retraining. To this end, we propose a novel architecture that generates a latent representation by encoding graph trajectories using conditional neural processes (CNPs). To miti- gate error accumulation over time, we combine CNPs with novel neural operator architecture. We validate our approach, Meta Neural Graph Operator (MaNGO), on several dynamics prediction tasks with varying material properties, demonstrating superior performance over existing GNS methods. Notably, MaNGO achieves accuracy unseen material properties close to that of oracle model.
Introduction
The simulation of complex physical systems is of paramount importance in wide variety of engineering disciplines, including structural mechanics [1-3], fluid dynamics [4-6], and electromag- netism [7-9]. In particular, simulating object deformations under external forces is essential for applications such as robotics [10-12). Traditional mesh-based simulations are appealing for such problems due the accuracy of the underlying finite element method [13, 14]. However, these methods are typically slow and require precise knowledge of the simulation parameters, including material properties of objects.
In contrast, data-driven approaches for simulating complex systems have emerged as promising alternative to traditional based simulators [15-17]. Among them, Graph Network Simulators (GNSs) have recently become increasingly popular [18-2] 21, 12, 22]. GNSs encode the simulated system graph of interacting entities whose dynamics are predicted using Graph Neural Networks (GNNs) [23]. These models are often orders of magnitude faster than classical simulators [19] while being fully differentiable, making them highly effective for downstream tasks such as inverse design problems [20, 24]. Moreover, these models do not require knowledge of simulation parameters as they directly learn from the training data. However, they must be retrained from scratch for even
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39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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r1
deey
Tis
enci
Context simulations with shared underlying structure
Initial state of target simulation trial
Predicted simulation using the latent representation of the context
The context set is aggregated to form a latent representation of material properties. Given an unseen initial state, the Graph Network Simulator (GNS) uses this latent representation to generate trials that follow the material laws of the context set, enabling accurate predictions for new conditions. The example prediction aligns perfectly with the ground truth data.
Figure 1:
Our proposed Meta Neural Graph Operator (MaNGO) approach:
minor variations in physical parameters, and require data collection for each new parameter setting that is often either costly and time-consuming or even impossible.
To overcome this, Sanzhez-Gonzalez al. [25] proposed to use the simulation parameter condi- tional information when training the GNS, allowing for generalization to unseen simulation parame- ters. However, such approach only works under two assumptions. Firstly, training data must be labeled with the corresponding simulation parameter, and secondly, the simulation parameter must be available test time for the desired simulation. While the first assumption is mild and often satisfied in simulation settings, the second assumption requires solving the inverse problem of inferring the underlying physical parameters from observed system behavior [26]. Material estimation or system identification can be viewed as a specific instance of this problem [27-32]. However, solving such inverse problems is challenging, as they are typically ill- il-posed and require explicit knowledge the governing partial differential equation (PDE) [30, 27, 28].
To overcome this challenge, we investtiaaee data-driver adaptation of GNS enabling fast and accurate simulations for unknown parameters using only a few simulation trials. Our work builds on the premise that training data from different simulations shares common 'latent' underlying structure. We aim to learn this structure via meta-learning using Conditional Neural Processes (CNPs). ) To that end, we propose novel framework called Meta Neural Graph Operator (MaNGO) that builds on Message Passing Networks (MPNs) and neural operator methods to ensure efficient processing of spatiotemporal data. We validate our approach on several dynamics prediction tasks with varying material properties, demonstrating superior performance over existing GNS methods. Notably, our method achieves accuracy on unseen material properties close that of an oracle model which has access to the simulation parameters at test time. To summarize, we identify our contribution as follows: (i) we successfully use meta-learning with Conditional Neural Processes (CNPs) for graph network simulators allowing for fast and accurate adaptation unseen physical parameters. (ii) we identify shortcomings of existing architectures for handling spatiotemporal data and propose a novel GNS architecture. (iii) we provide set of new benchmark tasks suited for testing the adaptation capability of GNS?.
2 Preliminaries
Graph and Message Passing Neural Networks. Graph Neural Networks (GNNs) are a class of neural networks designed process graph-structured data by iteratively updating node representations through localized message passing. Here, a graph is a defined as G = (V, &, {m "ey, {m3 )eee) with nodes V, edges &, and associated vector-valued node and edge features m and m. Message Passing Network (MPN) [25, 19], a GNN architecture well-suited for graph-based simulations, consists of K message passing steps, which iteratively update the node and edge features based on
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Dataset:

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the graph topology. Each such step is given
++1 +++ m
(m m m with e (v, w), m
(m
m +
(I)
E
where & C & are the edges connected to c. Further, Q denotes permutatioonnnnarian aggregation operation such as the sum, the max, or the mean. The functions fV and f are learned Multilayer Perceptrons (MLPs), usually with residual connection. The network's final output are the node-wise learned representations m that encode local information of the initial node and edge features.
Neural Dynamics Prediction. Our goal is to learn the dynamics a multibody system, i.e., a trajectory of graphs (g')) from the initial condition G We follow Brandstetter group existing approaches into two categories, neural operators and autoregressive methods. Neural operator methods treat the mapping from initial conditions to solutions at time t as an onput-output mapping learnable via supervised learning. Formally, neural operator Pso predicts the graph at any E [0, T from the initial condition, that is, g = FNo (t, g(o)). In contrast, autoregressive methods, learn incrementally update the graph starting from g:0):
[33] and
g(++a)) FARR (At,
Here, L'RR is the temporal update and At E IR=0-
Meta-Learning and Conditional Neural Processes. To formalize the meta-learning problem using conditional neural processes (CNPs) [34], we consider a meta-dataset = Di.L consisting L, typically small, task datasets Dj = {x{, y:) of size St. Each task consists inputs x E Rd. and corresponding evaluations y E Rd unknown functions fi. that is, y! = fi(x)) + e,, where e, denotes (possibly heteroskedastic) noise. Meta-learning hinges the idea that tasks share statistical structure, allowing for fast adaptation to a target function f- based on a small target dataset size S.. To leverage this shared statistical structure, Conditional Neural Processes (CNPs) use the meta-dataset to learn how to generate a latent representation E Idd. from given set of (x, y)piiis.. At test time, this latent representation is generated from the target dataset D. enabling generalization to unlabeled inputs x, from the target task without requiring weight adaptation. Formally, to generate the latent representation for set S {xx, y: ) with arbitrary size S, CNPs use a parameterized encoder with a permutation-inet invariian aggregation method,
D. y y 1i i==1
with T encs(xx)) Yt),
with parameters & and permutation-invariant aggregation method θ The latent representation r is then used to predict the mean and variance Gaussian distribution over y. given new input x,
Po x S) M (x, r), dec (xxr))
using a parameterized decoder with parameters 6. For training, the task datasets are further split into context sets Dj C Dr to train the CNP on different dataset sizes St which are used to minimize the negative task log-likelihood
Li( -1E CD
log p po (vl1 Df)
which implicitly depends on & through the encoding of Dj. Here, the expectation indicates randomly sampled subsets. Thus, meta-learning aims maximize the overall task likelihood while conditioning the model on smaller subsets of the data. The complete loss is obtained as C( 0) = Σ, (o, and is optimized end-to-end using stochastic gradients with respect to & and 6.
Adaptable Graph Network Simulators via Meta-Learning
Having established the foundations, we now explain how meta-learning with Conditional Neural Processes (CNPs) can be used to make graph network simulators adaptable to novel unseen physical parameters. To that end, we start by formalizing setup and introducing the meta-dataset in

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D
(+(,)!)
(3
x+f
x
Figure 2: Meta-dataset representation: This figure illustrates the structure of the meta meta-dataset, consisting of multiple task datasets. Each dataset includes simulations with shared material properties but varying starting conditions. Two example simulations, though starting similarly, produce vastly different results due to their distinct material properties.
Section 3.1. Next, we propose an extension to meta-learning that improves training with additional information that is not available at test-time in Section 3.2. Lastly, we introduce a CNP architecture that is tailored to setup. Specifically, we propose encoder that generates a latent representation from spatiotemporal data in Section 3.3. Furthermore, we introduce a novel decoder that addresses shortcomings of existing methods as outlined in Section 3.4.
3.1 Problem Formalization and Setup
The aim is to learn graph network simulator (GNS) that predicts a sequence of graphs G1.T {Gr) describing, e.g., mesh deformation over time without knowing some simulation or physical parameters, which we refer to as p Rd, For example, o could be stiffness or compression properties of a deformable object in the simulation. To that end, we use meta-learning to extract latent representations from similar data to generalize unseen physical parameters. As outlined in Section 2, in order to perform meta-learning we require meta dataset D containing L task datasets D, E D that in turn consist of multiple input-output pairs (x/, y!) E Dr. In our setting, each output given by
y! (PI.T: virr).
where Pi.r. vi. E Nxxx denote the positions and velocities of a sequence of nodes belonging to (possibly deformable) objects in d-dimensional space. An input x our setting is given by
X = (p' V Po.r Vo.T h'),
Lext Lext
(6)
where Ph. vyg E Nxd the initial node positions and velocities. Here Porr Vo:r [TT+1)x xd are positions and velocities of 'external' objects, that is, objects that we do not wish to simulate, such as a rigid collider that interacts with the object of interest. Lastly, h' (="+N"))xds represents node features that remain constant over time, such the node's 's type (deformable or collider) or whether a force applied to the node. Initial condition x' and simulation result y' together result in a sequence of graphs G with N + Nex nodes. In our work, assume fixed graph structure: the connectivity and the number of nodes in G is constant over time and task datasets D,. An illustration meta dataset D is shown in Figure 2.
Lest 1eett
3.2 Incorporating Simulation Parameters into Meta-Trainiag Training
For training, we could follow the procedure outlined in Section 2 and optimize the loss defined in Equation (4). However, contrary to the setup discussed in Section 2, we additionally assume access to the simulation parameters for each training task, i.e., {p' ] but not for target tasks D rendering them useless in the standard meta-learning formulation. Here, we slightly extend the meta training such that we obtain additional learning signals from p'. To that end, we use an additional parameterized neural network f 1d + 2 with parameters & that aims to predict p' from

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latent representation r'. Using the following definition for the joint likelihood between and p. i...
po, (y. S) y dec (x, r)
dec (x,
9
(r)
we obtain novel per-task loss function as
S1 log pa. (y', ,11x,, DD)
Li 0, = EDD
where the full loss again sums over the task losses, L( with respect to the encoder parameters & are informed by p via fw, As another positive side-effect, we obtain an estimate ý = f (r) which could be used for downstream tasks.
Li 0 1). Intuitively, gradients
3.3 Spatiotemporal Encoder
In Section we treated the encoder and decoder of the CNP architecture as black boxes that are responsible for generating latent representation and a predictive distribution over outputs, respectively. However, since our data consists of non-standard structures, specifically graphs with both spatial and temporal components, we introduce the following novel architectures.
Recall that the encoder of CNP generates latent representation r' Rd- from set of input-output pairs, typically a context set Di C 'D. Then, for each yx), E Df we separately generate a latent representation, i.e., r = enca xx!, y!) which are then aggregated in perruuationninnaaiin fashion to obtain r'. As discussed in Section 3.1, each component. We first aggregate over the temporal dimension and then over the spatial dimension. To that end, we combine the inputs x (see Equation (6)) and y (see Equation (5)) as
pair in our setting has a spatial and temporal
Lext Lext z = (Ph.T: VOLT Po:r
U.T bb.r):
where ht is simply copied for each time step. We ensure translation invariance by subtracting the initial mean position. To remove the temporal component, we apply ID convolutional neural network, i.e., & CNN (z.). Lastly, obtain a mntiallindependent latent representation, we apply a deep set encoder [35] on the node level, that is,
N N+
+ enc (2) = Souter
Σ
Junner (Z)
N + N
where, furrer and finner are neural networks. In this work, choose deep sets spatial aggregation method, as they have demonstrated good performance in graph-level problems similar to ours [36]. Finally, to aggregate whole of input-output pairs, we follow Equation (2) and use permutation invariant aggregation method.
3.4 Meta Neural Graph Operator Decoder
We propose novel MaNGO decoder architecture that combines elements of MeshGraphNet (MGN) [19] and the Equivariant Graph Neural Operator (EGNO) [22]. EGNO predicts graph sequences using equivariant GNN layers and temporal convolutions in Fourier space. While beneficial some settings, these equivariance constraints can limit performance when not required. We discuss this limitation Appendix B, where mathematically show that EGNO struggles on certain tasks. Alternatively, MGN models graph sequences autoregressively using Message Passing Networks (MPNs), which are highly effective for graph-based simulations [19]. However, autoregressive prediction is not ideal when paired with the current meta- veta-lcarning training setup, see Appendix E for further discussions. To address these limitations, MaNGO retains the strengths of neural operator methods by replacing the equivariant GNN layers with MPNs and equivariant convolutions with a 1D CNN (see Figure 3). Formally, we use the MaNGO decoder realize y docø (x, r) (omitting the task index I for readability). Thus, we define single MaNGO block as mapping
(m m m.1.)) + (m++) k+1 E,1:T m,ir),
m
following the notation in Section 2. The initial edge and note features (m 2.:75 m are extracted from rx by copying to every node feature and replicating the initial graph T times. Additionally,
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CNN
xK
Message Passing Step
Repeal
Nodewise Concar
Latent
Representation
Initial State
Simulated Future States y
Figure 3: MaNGO Decoder: Our simulator takes latent representation and an initial state as input. The initial state is combined and iteratively processed to generate a trajectory of graphs. By alternating between pessaag--passing network for spatial processing and 1D CNN for temporal processing, the simulator produces accurate dynamic simulations.
include time embeddings for every time step t and use relative positions edge features. Further details on the feature creation are provided in Appendix C. As first step of the MaNGO block, we leverage the MPN for spatial update, that is, we process the edge and node features according to Equation (1) for each timestep separately to obtain
tuple (m k++ e,1TT g,1TT) The temporal update is subsequently performed using a 1D residual convolutional layer, that is,
k+1 v.I:T
= Conv 9 (m 0,1:7) + m k+1 E.1:T
m
After K MaNGO blocks the final node features m every time-step. Specifically, displacement vector is computed using a parameterized network fo that is, d, f (m to obtain node positions P., P., Pv.0 + d
used for predicting the node positions for
The resulting positions P define the graph sequence over time. this work, we do not predict input-dependent variances, and instead use a fixed dec (x,r)= := to stabilize and simplify the training scheme. variances are required, for example, for uncertainty estimation, they can be easily predicted from the decoder as well. By alternating between spatial message passing and temporal convolution, the MaNGO simulator efficiently models time-series graph data while avoiding the pitfalls of equivariance over-constraints and autoregressive prediction.
Related Work
Learning-based forward simulators. Using deep neural networks to learn physical simulations
has become an emerging research direction in scientific machine learning [19, 37, 38]. Deep learning-base based approaches have demonstrated success applications such fluid dynamics [39, 40], aerodynamics [41, 19], and deformable object simulations [12, 42). A popular class of learned neural simulators are Graph Network Simulators (GNSs) [43, 25]. GNSs utilize MPNs, a special type of GNN [44, 23] that representationally encompasses the function class of many classical solvers [33]. GNSs handle physical data by modeling arbitrary entities and their relations as a graph. Notably. all previously mentioned GNSs predict system dynamics iteratively from given state, whereas directly estimate entire trajectories, improving rollout stability and prediction speed. Related to our approach is the Equivariant Graph Neural Operator (EGNO) [22], which also predicts full trajectories using SE(3) equivariance to model 3D dynamics and capture spatial and temporal correlations. In this work, adopt the trajectory prediction framework of EGNOs for decoder (as shown in Figure: 3) but remove the equivariance constraint. We justify this choice in Appendix B.
Material estimation. Determining physical parameters from observational data is challenging and ill-posed problem [26). Machine learning methods have shown success in inferring material properties from videos [27-29] and point clouds [30], but they rely on knowledge of the underlying

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MaNGO (Ours)
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Deformable Plate (Easy)
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Sphere Cloth Coupling
Planar Bending
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Figure 4: Performance comparison of our proposed methods and baselines across four datasets. We report the mean and 95% confidence interval of the Full Rollout MSE over five random seeds. The x-axis indicates the number of context samples used by the meta-learning approaches. We compare (i) meta-learning methods that employ a latent simulation parameter representation, (ii) a two-stage setup that explicitly predicts simulation parameters, and (iii) a baseline model that ignores context and performs direct simulation. The MaNGO (Oracle) variant, which has privileged access to the ground-truth simulation parameters, serves upper performance bound. Overall, MaNGO consistently outperforms both non- men-mee--earning and alternative meta-learning approaches, and achieves results close to the oracle.
PDE. Recently, approaches utilizing pre- pre-trained Graph Network Simulators (GNS) to infer material parameters gained popularity due to their computational efficiency and differentiability [31, 32). By back- poopaaarpagg through the learned simulator, these methods estimate latent material codes directly from observations. While the approach in Zhao et al. [31] and ours share this goal, only aggregate a context set of simulation trials to extract the underlying structure. Furthermore, our method does not require any backward pass and model weight updates, resulting in faster adaptation.
Meta-learning and Neural Processes. Learning models that can quickly adapt to small context datasets at test time is often referred to Meta-Learning, This emerging paradigm has found wide applications in fields such as language models [45] and robotics [46, 47], where it is commonly referred to as In- In-Context Learning. Meta-Lcarning is typically categorized into two approaches: optimization sidaez methods with few-shot examples and context-aggregatinn methods in a zero-shot fashion. A prominent example of the former is Model-Agnostic Meta-Learning (MAML) [48-5] 51], which employs gradient- based updates to adapt the model to new tasks using few examples. In the latter, Neural Processes (NPs) [34, 52-57] aggregate latent features from variable-sized context set to produce a latent task description that can be used directly during inference.
In this paper, we adopt Conditional Neural Processes (CNPs) [34] the core mechanism for aggregating context from different simulation trials to produce a latent description representing the simulation parameters. A GNS is then trained to condition to adapt dynamically to new materials. To the best of our knowledge, this is the first time such a framework has been proposed, combining meta-learning with graph network simulators to quickly adapt to unknown material properties given only few context- exammless without requiring retraining or knowledge of the underlying PDE.
this latent descriptor, enabling it
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MaNGO (Oracle)
MGN (Oracle)
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Figure 5: Left: Comparison of different GNS decoders with oracle information. MaNGO outperforms both MGN and EGNO, with the performance gap being more visible in the Sphere Cloth Coupling task due to its highly complex underlying dynamics. Additionally. EGNO fails to learn in the Planar Bending task, phenomenon further analyzed in Appendix B. Right: Visualization of the 2D latent space for Deformable Plate (Easy), with points color-coded by Poisson's 's ratio. The structured separation (at Poisson value shows that effectively captures the underlying material properties.
5 Experiments
We validate MaNGO on four different simulation datasets derived from three distinct simulation platforms. All tasks are normalized to [0, 1J". The first dataset is 2D Deformable Plate (DP) task [12], which has two variants: Da-easy and DP-hard. In DP-easy, the material property of interest is Poisson's 's ratio [58]. To increase complexity, DP-hard additionally varies Young's 's modulus and the initial velocity across trials within the same task. Next, we introduce a novel Planar Bending (PB) dataset, which simulates the bending of 2D sheet subjected to two external forces perpendicular to the sheet. this task, Young's modulus is the property of interest. The final dataset new Sphere Cloth Coupling (SCC) task, inspired by the Physion++ dataset [59], which involves a coupling system consisting a sphere and a cloth. In this task, spheres of varying sizes are dropped onto cloth. Their density is varied to influence the cloth's 's deformation upon contact.
The length of each simulation trial varies across datasets: 52 time steps for DP. 50 for PB, and 100 time steps for SCC to account for the increased complexity of simulating elastic behaviors. Further details about preprocessing steps and ground-trute simulators can be found in Appendix D.
5.1 Training setup and baselines
In this section, we present all methods evaluated in our experiments. Each model variant, whether meta-learning non-men meta-mmettaannnne has approximately three million trainable parameters, ensuring fair comparison across architectures.
Meta-learning, We first describe the setup used for our meta-learning framework. Each task dataset D, contains different simulation trials, where each trial shares the same material properties p (e.g. Poisson's 's ratio Young's 's modulus) but varies in initial conditions (e.g., collider position and size, or force positionn. During training, we randomly select a subset of St of a size between to to serve as the context dataset. This context is then used to predict random trial using different decoder methods. We compare our proposed MaNGO decoder against the EGNO architecture and a step-based MGN simulator. For testing, split D. into two distinct subsets. The first subset is used as the context dataset, while the second subset provides the initial conditions for predicting the full trajectory. We evaluate various context sizes assess adaptation capability.
Two-Stage Training Setup. Since we assume access to the simulation parameters during training. we compare the meta-learning methods against a two-stage training scheme. In the first stage, we train an encoder to predict simulation parameters given simulation trial. In the second stage, we freeze the encoder and train a decoder that uses the predicted simulation parameters from the encoder as an additional input. Therefore, this baseline predicts an explicit representation rather than a latent representation of the simulation parameters. We refer to this approach as MaNGO/MGN/EGNO (Two-Stage).
We empirically find that predicting random trial per batch instead of all trials improves performance.

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Vanilla GNS. We compare our method against non- non-meta-ledt meta-leariing baselines, including EGNO, and MGN, and our proposed MaNGO decoder without context information. To assess the upper bound, we additionally train an oracle method using the MaNGO decoder which has access to the simulation parameters during training and test time. We refer to it as MaNGO-Oracle, For these baselines, the full training set containing all 16 simulation trials is provided. Additionally, for the MGN baseline, we follow the approach of Pfaff et al. [19], adding noise during training to mitigate error accumulation and stabilize rollouts at inference. We tune the input noise level for each task to maximize MGN's performance. The full experimental protocol, along with computational budget details, is available in Section F.
5.2 Results
Main evaluation. We compare the mean-squared error (MSE) between the ground truth and the predicted simulation averaged over all time steps. Overall, Figure shows that meta-learning approaches consistently outperform non-meta-learning baselines, achieving relatively low MSE close the oracle method, MaNGO-Oracle. The two-stage training scheme is only competitive in the simplest environment, Deformable Plate (Easy), and across all environments it requires larger context size to achieve its best performance. general, within the meta-learning setting, performance improves with larger context sizes. Furthermore, we emphasize that strong performance achieved with as few as 2 to 3 context samples (even under the high-complexity DP-hard dataset), highlighting the ability of our meta- meta-learning approach to adapt quickly with minimal context data. All non-monn meta-learning baselines perform similarly. Interestingly, EGNO struggled to learn in the Planar Bending task, phenomenon we further analyze in Appendix B. Qualitative visualizations of all methods and tasks are provided in Section G.
To directly compare our proposed MaNGO decoder with existing architectures, we evaluate it in the or- acle setting, where material properties are known. As shown in Figure on the left side, MaNGO outperforming other baselines, confirming the effec- tiveness of our approach. We suspect that for MGN, ruto-regressive prediction suffers from accumulated errors,
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an issue particularly evident in the Sphere Cloth Cou- pling dataset, where highly nonlinear contact dynam- ics [60, 59] lead to MSE an order of magnitude higher than MaNGO. As for EGNO, while equivariance re- duces the amount of required training data, it can also overly restrictive, as real-world physics not strictly -e3-eqruvariiant [61, 62]. Various factors, such as friction and gravity, can break this symmetry, leading to suboptimal generalization.
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Figure 6: Robustness analysis of MaNGO on the Deformable Plate task under varying levels of Gaussian noise and node dropout, setup mimicking real-world conditions. The normalized MSE is reported. Our method re- mains stable with up to 10% noise (relative to the width of the mesh) and 10% node dropout.
Latent visualization. To understand how the learned latent representation correlates with simulation pa- rameters P. we visualize the 2D latent space with dim(r) 2 for the Deformable Plate task, color- coded by Poisson's ratio. Figure 5 (right) shows a strong correlation between and Poisson's ratio, with two linear trends emerging: one from to 0.49 and the other from 0.99 to 0. This separation reflects the underlying material behavior plates with positive Poisson's 's ratio expand on contact, while those with negative Poisson's 's ratio contract. The learned representation captures this distinction, indicating that the model encodes meaningful physical properties.
Robustness under sparse and noisy observations. Inspired by the setup in [31], we evaluate the robustness of MaNGO on the Deformable Plate task by introducing Gaussian noise into the observational context data and reducing the number of observed nodes at test time. To this end, we also introduce small noise level of 0.05 for the context split during training to enhance the robustness of the encoder. We report the normalized MSE in the range [0, 1), where the minimum set by MaNGO-Oracle and the maximum by the con--eta--cariinn MaNGO approach (as shown in

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Figure 4). As shown in Figure 6, the lower-left region of the corresponding to 10% noise level and 10% node propout-demoniin
near-optimal performance. Even with 50% of nodes unobserved, the performance drop remains around 15%, highlighting the model's ability to handle sparse and noisy observations. These results confirm that our encoder is robust under such conditions, reflecting real-world scenarios.
Runtime Efficiency and Memory Consumption A key advantage of MaNGO is its ability to predict entire trajectories in a single forward pass, enabling efficient batched inference over time. This design leads to substantial improvements in inference speed compared to traditional autoregressive next-step simulators. On the Sphere-Clos Cloth Coupling benchmark, the CNP encoder requires approximately 6 ms to compute the latent representation, and the MaNGO decoder simulates the full trajectory in only 13 ms. In contrast, the MGN next-step simulator takes about 500 ms, as it predicts one step at a time, making MaNGO over an order of magnitude faster than the already efficient autoregressive neural simulator.
However, the batched inference and training scheme comes with increased memory requirements. GPU memory consumption scales approximately linearly with the number of predicted time steps, since the model retains intermediate activations across the temporal dimension. In our experiments, we observe that
Memory(MaNGO) R Memory(MGN) x Number of predicted steps.
6 Conclusion
In this work, we explored data-driven adaptation of graph network simulators (GNS) via meta- learning. Specifically, we investigated the setting where simulation parameters are unknown at test time which would require retraining or labor-intensive data collection for existing methods. In series of experiments, we demonstrated the potential of meta-learning for GNS, where our approach achieves accuracy on unseen material properties comparable that of an oracle model. We view this work as first stepping-ste stone towards the next generation of data dataenriven simulators, that are fast, differentiable, and capable of adapting to wide variety of simulation settings. A discussion of the broader impact of this work is provided in Section A.
Limitations and Future Work One limitation of our current approach its focus on a single data modality at test time. In practical scenarios, however, test-time data may come in diverse formats, such as point clouds captured by cameras. Our method does not yet support such modalities, which constrains its applicability in real-world settings. Addressing this limitation would require the development of new architectures capable of handling heterogeneous data.
A further limitation is that MaNGO assumes a fixed graph topology and requires substantial GPU memory when predicting full trajectories in a single forward pass. These constraints limit its scalability and applicability to systems with dynamic connectivity. A promising direction for future work adopt a hybrid decoding strategy that predicts shorter temporal segments while dynamically updating the graph structure after each segment. Such an approach could reduce memory demands and enable the modeling of systems with evolving topologies, bridging the gap between efficiency and flexibility.
Acknowledgements
This work is part the DFG AI Resarch Unit 5339 regarding the combination of paysics-based simulation with Al-based methodologies for the fast maturation of manufacturing processes. The financial support by German Research Foundation (DFG, Deutsche Forschunggeemiinccaatt) is gratefully acknowledged. The authors acknowledge support by the state of Baden- Württemberg through bwHPC, as well as the HoreKa supercomputer funded by the Ministry of Science, Research and the Arts Baden-Wiin Württemberg and by the German Federal Ministry of Education and Research. We thank Philipp Becker for suggesting the title acronym used in this work.
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11. Safeguards
Question:
Does the paper describe safeguards that have been put in place for responsible release of data models that have high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Answer: [NA]
Justification: We do not use pretrained language models, image generators or similar high- risk models in our approach, and do not scrape datasets. We still discuss potential cases for miss-use our learned simulator in Appendix A.
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Justification: We adapt the DeformablePlate dataset of Linkerhägner et al. [12], which we cite at the corresponding part of the paper.
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A Braoder Impact Statement
Our proposed Graph Network Simulator, with its ability to adapt to new material properties through a small context set, offers significant advancements across fields that rely computational modeling and simulation. By reducing the need for extensive simulation data and recalibration, it can lower computational costs while maintaining high aceuracy. This adaptability could benefit industries ranging from materials science to robotics, enabling more efficient design and testing of novel materials.
However, this flexibility in simulating a wide range of material properties could also be misused in contexts where precise material behavior is critical, such as in the development of advanced weaponry or other high-risk technologies. While the primary intent to advance scientific and engineering applications, ethical considerations must be taken into account to prevent unintended harmful uses.
B Limitations of the Equivariant Graph Neural Network
In this section, we analyze the limitations of the Equivariant Graph Neural Network (EGNN) [63], which serves as the GNN backbone of the Equivariant Graph Neural Operator (EGNO) baseline [22]. During experiments, observed that EGNO fails to predict any deformation in the Planar Bending task.
In this task, all neural operators receive an initial input configuration Po. representing completely flat plane as the positions of the mesh. Consequently, points in this initial graph lie within a plane E embedded in tbree-dimensional space. In this appendix, we demonstrate that the spatial output of any trained EGNN will also remain confined to a plane. This implies that an EGNN cannot solve the Planar Bending task, as the required deformed state does not lie within a single plane.
We establish this result by first proving that an EGNN maps all points in the specific plane
-=o {(x, v, E 3 z = 0}
back onto the same plane Z To see this, consider any node E with an initial position P = (z,8, 0) E Z=o. Applying a single layer of EGNN to update the node positions, we obtain
p P +C
Σ (p. P= (EN(v)
Examining the z-coordinate, note that the message term (f. (m is scaled by (p. - p.)) Since all P lie in Z their z-coordinates are zero, meaning (p., -P p has no z-component. Consequently, the updated z-coordinate in ph remains zero, ensuring that holds for all subsequent layers, proving that EGNN maps Z onto itself.
Zo By induction, this property
Next, we extend this result to any arbitrary plane E in three-dimensional space. Since E is plane, there exists a transformation T e SE(3) such that
T(E) = Z
By the equivariance property of EGNN, there exists another transformation S SE(() satisfying
EGNN = S(EGNN(G))
CZ
From our previous result, the left-hand side remains confined to Z=g. Thus, applying 5 yields
EGNN(G) c S-1
which is another plane in three- dimeeesiians space. This establishes the key result: an EGNN always maps planar inputs to planar outputs, rendering it incapable of solving the Planar Bending task.
similar argument extends to the full EGNO architecture since its equivariant temporal convolution layer in Fourier space is also equivariant and it preserves the property of mapping Z onto itself. Thus, EGNO, like EGNN, is inherently unable to capture the required deformations in the Planar Bending task.
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C Feature creation for the MaNGO decoder
This appendix provides detailed explanation of the input processing for the MaNGO simulator. First, similar to the Spatiotemporal encoder, we create a sequence of graphs G, over time. However, unlike the encoder, we repeat the initial positions and velocities of all deformable nodes across time, as the future positions-out target variable-are are unknown and need to be estimated. In G. we define the node features for node as the tensor [r, h Vt, TE(()] consisting of the latent system identification r, the node features h the velocity V, and a time embedding of the time step L. Note that the position is not part of the node features. Instead, following [19], we compute for each edge the relative position Pe.t to ensure translation invariance. The complete edge features are given as (ce, P TE(t)] consisting of the (time-independent)) edge features, the relative position and time step embedding.
D Datasets and Preprocessing information
In this section, we provide detailed information about the datasets used in our experiments. Table 1 summarizes the key characteristics of each dataset, including the dataset splits, simulation length, and the number of nodes used for prediction.
For brevity, we use the following abbreviations throughout the paper:
PB: Planar Bending.
DP: Deformable Plate, with two variants: DP-easy and DP-hard.
SCC: Sphere Cloth Coupling.
Table 2 further details the training setup for each dataset, specifying the material properties considered and the variations initial conditions. These variations influence dynamics of each task, ensuring diverse training scenarios that test the generalization capabilities of our method.
Table 1:
Dataset descriptions
Name
Train/Val/Test Splits
Number of Steps
Number of Nodes for Prediction
PB
460/50/50
50
225
Da-easy
600/100/100
52
DP-hard
600/100/100
52
81
SCC
600/100/100
100
400 (cloth) 98 (sphere)
Table 2: Training setup for each dataset
Name
Material Properties
Initial Condition Variations
PB
Young's modulus
Two forces: (a., v) position. {-1, 1] direction, constant magnitude
DP-easy
Poisson's 's ratio
Collider's x position, size, constant initial velocity
DP-hard
Young's 's modulus, Poisson's 's ratio Sphere's density
Collider's æ position, size. varied initial velocity
SCC
Sphere's size, same initial position
Planar Bending, We uniformly select Young's modulus from 10 to 500, from very deformable to an almost stiff sheet. The boundary nodes of the sheet are kept in place.
Deformable Plate. The original task was introduced in [12], generated using Simulation Open Framework Architecture (SOFA) [64]. We extended meta-learning setting by sampling Poisson's 's ratios between -0.9 to 0.49, under different trapezoidal meshes. We further increase the difficulty of this dataset by also randomizing the Young's modulus within range from 500 to 10000 using Log-Uni Ungforni distribution.
Sphere Cloth Coupling. Each trajectory in this dataset is generated by selecting sphere radius from the range 00.2. 0.8). The material property interest is the sphere's density, which varies between [2.0, 100.0]. The cloth is initialized in a stable state, remaining consistent across all tasks and trials. This dataset is created using NVIDIA Isaac Sim [65], which leverages Phys 5.0 [66] to simulate position-base based dynamics (PBD) particle interactions.
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Table 3: Left: Training setup for each dataset.
Right: Noise-scale per task for Auto-regressive
methods
Parameter
Value
Node feature dimension
128
Latent representation dimension
128
Decoder hidden dimension
128
Message passing blocks
15
Task
Value
GNN Aggregation function
Mean
GNN Activation function
Leaky ReLU
PB
5.0 x 10 -
Learning rate regso-regressive methods)
5.0 10-4
DP-easy
7.0 10 10-4
Learning rate
1.0 x 10
DP-hard
7.0 x 10
Optimizer
AdamW W [67]
SCC
1.0 x 10-3
Min Context Size (Training)
1
Max Context Size (Training)
8
MaNGO-CNN Decoder Kernel size
7
CNN-Deepset Encoder Kernel size
3
Latent representation aggregation
Maximum
For meta-learning setup, we assume set S, containing 16 different simulation trials, where each trial shares the same material properties (e.g.. density, Poisson's ratio, Young's modulus) but varies in initial conditions (e.g., sphere size, force positions, and magnitudes).
MGN Decoder for Conditional Neural Processes
In step-based prediction tasks, batches typically shuffled include different simulations and time steps. However, when using a Conditional Neural Process (CNP), only data from the same task can be used for each batch, which tested a modified version of the MGN where we reduced batch shuffling to mimic the CNP approach. This modification resulted in poorer performance compared the standard MGN, This difference in performance may partially explain why Meta-MGN underperforms relative to MaNGO.
impact performance. During hyper parameter optimization,
F Experimental Protocol
In order to promote reproducibility, we provide details of our experimental methodology. Table presents the hyperparameters used in our experiments. For a comprehensive description of the creation of all datasets, please refer to Appendix D.
The training took place on an NVIDIA A100 GPU, with each method given the same computation budget of 48 hours. Consequently, the number of epochs varied, the batching differed significantly between the meta-learning methods and the hep-based MeshGraphNet (MGN). In total, generating the results presented in this paper required approximately 8,500 GPU hours.
We conducted a multi-staged grid- based hyperparameter search for the learning rate, input noise, and other hyperparameters residual connections and layer but tuned all hyperparameters on a separate validation split. This split was also used to determine the best epoch checkpoint to mitigate any overfitting effects. Hyperparameter tuning required an additional computational budget of approximately 6,000 GPU hours.
We did not the test data for this,
For MGN, included velocity features of the current step.
G Visualizations
In this section, we present qualitative results for all tasks and methods discussed in the main paper.
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=
t 11
f 16
f 21
t 31
t 41
t 51
Figure 7: Simulation over time of an exemplary test trajectory from the DP-easy task. The figure compares predictions from MaNGO, MGN, and EGNO, The last row, MaNGO-Oracle, is separated by horizontal line and represents predictions using oracle information. The context set size is set to 4. All visualizations show the colored predicted mesh, with a wireframe representing the ground-truth simulation. MaNGO accurately predicts the correct material properties, leading to highly accurate simulation.
t=1
== 6
t= 11
t= 16
t t= 21
t 31
t 41
t t= 51
Figure 8: Simulation over time of an exemplary test trajectory from the DP-hard task. The figure compares predictions from MaNGO, MGN, and EGNO. The last row, MaNGO-Oracle, is separated by horizontal line and represents predictions using oracle information. The context set size is set to 4. All visualizations show the colored predicted mesh with a wireframe representing the ground-truth simulation. MaNGO accurately predicts the correct material properties, leading to highly accurate simulation.
26

---

t=
16
21
31
41
50
Figure 9: Simulation time of exemplary test trajectory from the PB-easy task. The figure compares predictions from MaNGO, MGN, and EGNO. The last row, MaNGO-Oracle, is separated by horizontal line and represents predictions using oracle information. The context set size is set to 4. All visualizations show the colored predicted mesh, with a wireframe representing the ground-truth simulation. MaNGO accurately predicts the correct material properties, leading highly accurate simulation.
t=1
t
11
t= 21
t= 31
== 41
== 61
81
t= 100
Figure 10: Simulation over time of an exemplary test trajectory from the Sphere Cloth Coupling task. The figure compares predictions from MaNGO, MGN, and EGNO. The last row, MaNGO-Orrcka is separated by horizontal line and represents predictions using oracle information. The context set size is set to 4. All visualizations show the colored predicted mesh, with a wireframe representing the ground-truth simulation. MaNGO accurately predicts the correct material properties, leading to highly accurate simulation.
27


Reviews:
[{"review_id": "d1z9K5XK2n", "reviewer": "Reviewer_maMF", "summary": "The paper introduces a meta-learning framework that enables Graph Network Simulators to easily adapt to unseen physical parameters without requiring retraining or explicit parameter input at test time. By leveraging Conditional Neural Processes, the proposed method encodes a small set of observed simulations into a latent representation that captures the underlying material behavior. MaNGO outperforms existing GNS baselines across several physics simulation benchmarks, achieving performance close to models with access to simulation parameters.", "questions": "- Could the authors provide some insights and comparisons regarding the number of parameters and runtimes?", "limitations": "Yes.", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 4, "originality": 3, "strengths_and_weaknesses": "## Strengths\n\n- Well written paper that provides detailed theoretical analysis of the task and the method. The figures were also very helpful.\n\n- The authors propose a novel method for critical scenarios where simulation parameters are unknown or unavailable at test time.\n\n\n- The experimental section is quite rich, demonstrating consistently great results and clearly proving  architectural improvements.\n\n- The method showcases strong generalization to unseen parameters, achieving near-oracle accuracy.\n\n\n## Weaknesses\n\n- Compared to autoregressive methods, neural operator methods might be more memory-intensive.", "was_revised": true, "final_justification": "The authors provided an adequate rebuttal, addressing most of the concerns raised by all the reviewers. I maintain my original score.", "rebuttal": "We thank the reviewer for the positive feedback and their interest in our work. The reviewer asked about the **parameter count** and **runtime efficiency**, which we are happy to clarify below.\n\n- **Parameter Counts**: All models use the same Graph Neural Network (GNN) backbone to ensure a fair architectural comparison. The full network comprises approximately **3 million parameters**.\n- **Runtime Efficiency**: A key advantage of MaNGO is its ability to predict **entire trajectories in a single forward pass**, enabling **efficient batched inference** over time. This results in significant inference-time speed-ups compared to traditional **autoregressive next-step simulators**.\n    \n    On the **Sphere-Cloth Coupling** benchmark:\n    \n    - The **CNP encoder** takes approximately **6 ms** to compute the latent representation.\n    - The **MaNGO decoder** simulates the full trajectory in just **13 ms**.\n    - In contrast, the **MGN next-step simulator** requires approximately **500 ms**, as it predicts one step at a time.\n\nAll models were trained with the **same computing resources**  to ensure a fair comparison.\n\nThese results demonstrate that, although neural operator approaches like MaNGO incur a higher memory footprint (due to storing temporal activations), they offer **substantial improvements in inference speed**, making them highly suitable for **applications requiring fast rollout generation**.\n\nOnce again, we thank the reviewer for their time and are happy to provide further clarifications if needed."}, {"review_id": "ositaNejgF", "reviewer": "Reviewer_nqEU", "summary": "The paper introduces Meta Neural Graph Operator (MaNGO), a meta-learned graph–network simulator that i) encodes a set of short \"context\" roll-outs with a spatio-temporal Conditional Neural Process (CNP) encoder, producing a latent code $r$ that captures hidden physical parameters, and ii) decodes an entire future trajectory in a single shot via a new neural-operator-style architecture that alternates spatial message passing and 1-D temporal convolutions. Experiments on four synthetic dynamics datasets show that with as few as 2-3 context simulations MaNGO achieves rollout MSE close to an oracle that knows the ground-truth material constants at test time.", "questions": "1) Could you report concrete numbers for MaNGO’s inference‐time GPU memory, and wall-clock latency on the Sphere Cloth Coupling (SCC) benchmark, and compare it with MGN?\n2) Do you have preliminary results on larger (>10 k node) or variable-topology meshes, e.g., fracture or contact-break scenarios? What modifications, if any, would MaNGO require in those settings?\n3) What is the quantitative error (e.g., RMSE) of the regressor $f_\\psi(r)$ when recovering hidden material parameters such as Young’s modulus and Poisson’s ratio on held-out tasks?", "limitations": "Yes.", "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\n- **Thorough Experiments (Quality and Significance):** The authors compare against non-meta and oracle baselines, vary the number of context runs, test robustness to noise and drop-out, and explain why ENGO, a strong equivariant baseline, fails on the Planar Bending dataset. This makes the empirical case convincing.\n\n- **Clarity:** The paper is well-written and easy to follow. \n\n- **Well-motivated Problem (Significance):** The paper tackles an important problem: how to make learned simulators handle new material or boundary settings without retraining (which can be computationally very costly).\n\n- **Fresh Meta-learning Angle (Originality):** Treating the task as a Conditional Neural Process (CNP) lets the model learn from just a handful of \"context” simulations, and even predict the hidden physical parameters at the same time.\n\n- **Practical Decoder Design (Originality):** The new decoder removes the heavy SE(3)-equivariant layers equivariant layers, and replaces them with message passing networks and equivariant convolutions with a 1D CNN. It still predicts the entire trajectory in one shot and consistently outperforms the previous baselines on the reported benchmarks.\n\n\n**Weaknesses**\n\n- **Clarity:** This is minor but I believe \"Figure 5\" in line 290 should actually be \"Figure 6\". \n\n- **All synthetic data (Quality, Significance):** Every benchmark comes from a simulator, uses a fixed graph, and has at most $\\approx$ 500 nodes. There is no evidence the method works on larger meshes, changing topologies, or real sensor measurements.\n\n- **High Training Cost (Significance):** Roughly 8,500 GPU-hours for training plus 6,000 GPU-hours for hyper-parameter search is heavy for four mid-scale tasks, and there is no comparison to optimization-based meta-learners like MAML.\n\n- **Fixed Edge Set Assumption (Significance):** The model requires the same graph connectivity across time and tasks, limiting use in problems with fracture, contact loss, or remeshing.", "was_revised": true, "final_justification": "Despite some practical limitations (notably the high training budget), this submission makes a clear and useful contribution: a well-motivated meta-learning formulation for graph simulators and a novel decoder.\n\nI therefore maintain my original positive score, and support acceptance of this paper.", "rebuttal": "We thank the reviewer for their thoughtful and constructive feedback. We address the raised points below:\n\n**Clarity: \"Figure 5\" in line 290 should actually be \"Figure 6\"**\n\nThank you for pointing this out. You are correct about this typo, and we will correct it in the camera-ready version.\n\n**Synthetic Data and Limited Graph Scale**\n\nWe appreciate the reviewer’s concern regarding the use of synthetic datasets and relatively small, fixed-topology graphs (≤500 nodes). This was a deliberate design choice to **systematically assess MaNGO’s meta-learning capabilities** in controlled environments where:\n\n- Ground-truth simulation parameters are available,\n- Noise levels can be precisely controlled,\n- Comparisons to oracle and ablation baselines are reproducible.\n\nWe agree that **scaling to real-world data and variable topology** is an important next step. While we have not yet conducted experiments on meshes with >10k nodes or on scenarios involving fracture, contact-breaking, or remeshing, we note the following:\n\n- MaNGO’s architecture  is computationally scalable and can, in principle, be applied to significantly larger graphs. The primary challenge is the **memory footprint** incurred when predicting full trajectories in a single forward pass. To address this, a promising extension is a **hybrid decoding strategy**, where instead of predicting all remaining time steps at once, the model predicts **smaller temporal windows** (e.g., 10–20 steps) sequentially. This would reduce peak memory usage by limiting the temporal span of each prediction and retain the advantages of batched inference. Alternatively, a more engineering-focused solution using multi-GPU parallelism is also a viable direction to handle large-scale setups efficiently.\n- To support **dynamic topologies**, MaNGO could be extended to **rebuild the graph connectivity at each time window**, using dynamic neighborhood graphs (e.g., k-NN or radius-based methods). While promising, this introduces additional design challenges such as temporal consistency and remeshing dynamics, which we consider **outside the scope of the current work**, but worth exploring in future research.\n\n**Training resources**\n\nWe appreciate the reviewer’s concern regarding the computational resources used in our experiments.\n\nWe agree that the total training and hyperparameter tuning cost—approximately **8,500 GPU-hours** for training and **6,000 GPU-hours** for search—is considerable. Upon reviewing our pipeline, we observed that **data loading and preprocessing** could still be optimized. The GPU usage logs indicate that improving these components could further **reduce idle time and accelerate training**.\n\nThat said, it's important to highlight that **Graph Network Simulators (GNS)** are generally **resource-intensive to train**, especially on mid-scale physics environments with complex interactions. This characteristic applies equally to the **baseline models**, which are also non-trivial to train.\n\nImportantly, we trained all models under **identical hardware and time constraints**, ensuring a fair comparison in terms of real-world training cost. Within those constraints, MaNGO consistently achieved **strong generalization and fast inference**, which we believe justifies the computational investment.\n\n**Inference-Time GPU Memory and Runtime on SCC Benchmark**\n\n- **Runtime efficiency:** One of MaNGO’s key advantages is its ability to predict **entire trajectories in a single forward pass**, enabling effective batched inference over time. This leads to a significant **speed-up at inference time** compared to traditional **autoregressive next-step simulators**.\n    \n    On the **Sphere-Cloth Coupling** benchmark:\n    \n    - The **CNP encoder** takes approximately **6 ms** to compute the latent representation $r$,\n    - The **MaNGO neural operator decoder** simulates the full trajectory in just **13 ms**,\n    - In contrast, the **MGN next-step simulator** requires **approximately 500 ms**, as it predicts step-by-step over time.\n- **GPU Memory**: Memory usage scales **linearly with the number of predicted time steps**, as the model retains intermediate activations across the temporal dimension. In our experiments: Memory(MaNGO)≈Memory(MGN)×Number of predicted steps\n    \n    While this can become a bottleneck for long sequences or large meshes, the **hybrid decoding strategy** discussed above offers a clear path forward, without requiring major architectural changes.\n\nOnce again, we sincerely thank the reviewer for their thoughtful and encouraging feedback. We appreciate the opportunity to clarify key aspects of our work and are glad that the contributions of MaNGO were well recognized."}, {"review_id": "fpKmQlrAi1", "reviewer": "Reviewer_wdos", "summary": "This paper introduces MaNGO, a meta-learning framework for graph-based physics simulators. The goal is to enable fast adaptation to new, unseen physical parameters (e.g., material properties) without retraining. MaNGO uses Conditional Neural Processes (CNPs) to infer a latent representation of these parameters from a few \"context\" examples. This representation then conditions a novel, non-autoregressive decoder—which combines Message Passing Networks (MPNs) for spatial dynamics and a 1D CNN for temporal dynamics—to predict the full simulation trajectory.", "questions": "1.The paper notes that the neural operator framework is more memory-intensive than autoregressive methods. Could you elaborate on the memory complexity and scalability of the non-autoregressive MaNGO decoder, particularly when dealing with long time-series and large-scale graphs ?\n2.Is there a practical limit or \"tipping point\" where MaNGO's memory consumption becomes a significant drawback compared to autoregressive models?\n3.The Deep Set encoder aggregate features from samples into a latent representation. Have you explored alternative, potentially more expressive, aggregation mechanisms?  Was there a comparative study to justify the choice of Deep Sets?\n4.Could you please elaborate on the experimental setup for data partitioning? Specifically, how were the tasks divided into meta-training and meta-test sets? Whether to test samples that have never been seen before during the test？", "limitations": "no,I think some comparative experiments should be added.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strength\n1.Important Problem: The paper tackles the critical and practical problem of simulator adaptation, which is a major bottleneck in data-driven science and engineering.\n2.Innovative Decoder Design: The non-autoregressive decoder, blending the strengths of MPNs and 1D CNNs, is a smart solution that effectively avoids common issues like error accumulation (from autoregression) and over-constraining (from strict equivariance).\n3.Clarity and Organization: The paper is well-written and logically structured. The motivation, methodology are presented clearly, making the paper easy to follow. \nWeakness\n1.Missing Comparison with Autoregressive Models: The paper claims its non-autoregressive decoder is more memory-intensive but faster than autoregressive ones. However, it lacks a direct experimental comparison with an autoregressive baseline (like a meta-learning version of MGN) to substantiate this trade-off..\n2.Limited Meta-Learning Baselines: The superiority of the proposed CNP-based framework is not fully established, as it is not compared against other prominent meta-learning approaches, such as optimization-based methods like MAML.\n3.The encoder uses a Deep Set to aggregate context features. This might be an oversimplified approach, and the paper does not explore or justify this choice over potentially more sophisticated aggregation methods.", "was_revised": true, "final_justification": "I thank the authors for their detailed and thoughtful rebuttal. While the rebuttal provided valuable clarifications and addressed several specific points, I am maintaining my original \"Borderline Accept\" (Rating 4) recommendation for the reasons outlined below.\nKey Issues Resolved (and how):\nAutoregressive Comparison (Weakness 1): The authors clarified that Meta-MGN is indeed included in the comparisons (e.g., Figure 4), and the provided quantitative runtime analysis (MaNGO Decoder ~13ms vs. Meta-MGN ~500ms) strongly supports the efficiency claims. This issue is now sufficiently clarified.\nEncoder Choice (Weakness 3 / Question 3): The authors provided a reasonable justification for selecting the Deep Set encoder, citing their own experimentation and hypothesizing that its global aggregation is sufficient for inferring global material parameters.\nMemory Complexity & Scalability (Questions 1 & 2): My questions regarding MaNGO's memory complexity, scalability, and practical limits were clearly addressed. The explanation of linear memory scaling and the proposal of a hybrid decoding strategy for long trajectories are helpful and provide a path forward for large-scale applications.\nExperimental Setup & Data Partitioning (Question 4): The detailed clarification of the meta-learning data partitioning protocol is highly appreciated and confirms the rigor of the experimental setup, ensuring no data leakage from meta-training to meta-testing.\nKey Issues Remaining Unresolved (and why they are weighted):\nLimited Meta-Learning Baselines (Weakness 2): This crucial concern was not addressed in the rebuttal. The paper lacks a comparison with other prominent meta-learning approaches, such as optimization-based methods like MAML. This omission is significant as it prevents a comprehensive understanding of MaNGO's performance and superiority within the broader meta-learning landscape. Without this, the claims about the proposed CNP-based framework's overall superiority in the meta-learning context are not fully substantiated.\nWeight Assigned:\nWhile I acknowledge and appreciate the authors' thorough responses to the majority of my questions and weaknesses, the absence of a comparison with other major meta-learning paradigms (Weakness 2) remains a substantial gap. This particular limitation directly impacts the paper's claimed generalizability and its positioning within the meta-learning field. The strengths of the paper (important problem, innovative decoder, clarity) are notable, and the resolved issues certainly clarify aspects of the proposed method. However, the unaddressed methodological comparison prevents a stronger endorsement beyond a borderline acceptance, as it limits the scope of the empirical validation.\nRecommendation: Borderline Accept.", "rebuttal": "We thank the reviewer for their detailed and thoughtful feedback. Below, we address each of the raised points:\n\n### **Missing Comparison with Autoregressive Models**\n\nWe would like to clarify that we **do include a direct comparison with a meta-learning version of MGN (Meta-MGN)** in our experiments. This baseline is shown in **orange** in the plots (e.g., **Figure 4**), and is discussed throughout the experimental section.\n\n- MaNGO consistently **outperforms Meta-MGN both quantitatively and qualitatively** across all benchmark tasks. Visual comparisons can also be found in the **appendix visualizations**.\n- In terms of **runtime**, MaNGO demonstrates significant efficiency due to its non-autoregressive architecture. Comparing on the Sphere Cloth Coupling task, we get:\n    - **CNP Encoder**: ~6 ms\n    - **MaNGO Decoder** (full trajectory): ~13 ms\n    - **Meta-MGN (autoregressive)**: ~500 ms\n        \n        All models were trained for the same number of steps to ensure a **fair comparison**.\n        \n\nThese results support our claim that MaNGO offers a favorable trade-off: **higher memory usage**, but significantly **faster inference** and **better accuracy**.\n\n### **Choice of Deep Set Aggregation in the Encoder**\n\nWe fully agree with the reviewer that a message-passing-based encoder may appear more expressive. In fact, we **experimented with message-passing architectures** during development. However, we found that they offered **no significant advantage** over the **simpler and more efficient Deep Set encoder**.\n\nWe hypothesize that this is due to the **global nature** of the latent variable being inferred (material parameters like Young’s modulus and Poisson’s ratio are **global properties)**. Deep Sets, especially when provided with **node coordinates and features**, appear sufficient for capturing these latent structures. In contrast, message passing typically excels at modeling **localized spatial interactions**, which may be unnecessary for globally inferred variables.\n\n### **Memory Complexity and Scalability of MaNGO**\n\nMaNGO’s memory consumption scales **linearly with the number of predicted future time steps**, due to the retention of intermediate activations:\n\nMemory(MaNGO)≈Memory(MGN)×Number of predicted steps\n\nWhile this can increase GPU memory usage relative to step-by-step models, it allows for **highly parallelized inference**, offering substantial gains in runtime performance.\n\n### **Practical Memory Limitations**\n\nThere is no sharp \"tipping point\" in MaNGO’s memory profile. The practical limit depends on the **available computing resources** and the **length of the trajectory** to be predicted. In high-resolution or long-horizon simulations, the memory cost may become non-negligible.\n\nTo address this, a **hybrid decoding strategy** can be adopted: instead of predicting the entire trajectory at once, the model predicts **shorter temporal windows** (e.g., 10–20 steps) in sequence. This reduces memory consumption without reverting to fully autoregressive decoding and is a promising direction for future extensions.\n\n### **Experimental Setup and Data Partitioning**\n\nWe thank the reviewer for this important question and are happy to clarify our meta-learning protocol:\n\n- We **randomly sample material parameters** (e.g., Young’s modulus, Poisson’s ratio) from a predefined distribution to define each task.\n- For each material setting, we generate **16 simulation trials** with diverse **initial conditions** (e.g., varying object positions or velocities).\n- We apply a **random split over material parameters** to form the **meta-training and meta-testing sets**. Thus, **material properties in the test set are never seen during training**.\n- During meta-testing:\n    - We select **1 to 8 trials** from a test task to serve as the **context set**.\n    - We evaluate the model on the remaining **8 unseen trials**, ensuring a clean separation between **training**, **context**, and **evaluation**.\n\nThis setup ensures **no data leakage** and measures the model's ability to **adapt to entirely new material parameters** with minimal supervision.\n\nPlease let us know if additional clarification or detail would be helpful. We greatly appreciate the reviewer’s engagement and insights."}, {"review_id": "OD320tqxYK", "reviewer": "Reviewer_EtEt", "summary": "__I have reviewed this paper for ICML. As far as I can tell, the only change to the paper is the title. I will hence re-post my review from ICML.__\n\nThe paper introduces a new GNN-based method for learning physical dynamics. It specifically focusses on latent parameter estimation. Given a set of reference simulations, an encoder create a latent embedding r, which contains an estimate of hidden simulation parameters. A GNN decoder can then use r to perform inference with those material parameters.", "questions": "(my questions were already answered in the last review process)", "limitations": "yes, except for what is mentioned above.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "The paper claims better performance on physical simulation by a) a new GNN architecture and b) meta-learned latent parameters (CNP). The claims are supported by experiments, although experimental validation could be improved.\n\nThe method is quite complex, with many choice different to previous work, and it's not immediately obvious to me if they are actually needed or effective.\n- A lot of the complexity comes from CNP, i.e. inferring a latent representation of the hidden material parameters. But then, 3.2. introduces a direct regression loss against the true latent parameters. But if rho has to be assumed known in training, there are much simpler options which need to be tested. The most obvious is training an encoder from D_L -> rho, and conditioning the decoder on rho instead of r. This is much simpler: no Gaussian distribution needed, no potential issues with irrelevant information contaminating the latent. Plus encoder and decoder can be trained separately, severely reducing memory and training time. I would imagine this would actually perform quite well for the datasets investigated in this paper, given the strong performance of the oracle models. (there may be some downsides for ambiguous real-world data, but that's not studied here)\n- The architecture of the encoder is also a bit surprising to me. For (traditional) estimation of material parameters, you'd need spatial and temporal derivatives. Deep sets without any neighborhood information will struggle computing spatial gradients; something like 1 or 2 message passing steps with a short temporal window, and then aggressive spatiotemporal pooling seems like a more obvious choice.\n- EGNO works because the temporal convolution is in Fourier space, i.e. a global operation. Replacing this with a 1D CNN means information will only travel locally, which will likely limit the ability to model long sequences or sequences with complex dynamics (all examples are quite short and contain simple motion).\n\nThere are a lot of novel surprising choices in the model. These need to be properly ablated, and compared to simpler choices (see e.g. the points mentioned under Methods And Evaluation Criteria). I feel the paper tries to do too much, without spending the time to properly evaluate all of its contributions, and we don't end up learned all that much in the end.\n\nFor example, there's actually an interesting point in the core GNN architecture of MGN vs MGNO vs EGNO. EGNO isn't quite made for the type of system studied here, but there may be advantages of this style of approach compared to autoregressive MGN. But this needs to be properly studied, with detailed analysis on pros and cons (e.g. ingesting entire trajectories quite obviously comes with much higher memory footprint, and it's probably not a coincidence that the systems studied here are extremely low-dimensional), ablations to figure out the best configuration for different system types and sizes, etc. There might be good tradeoffs to be had, but this really needs to be its own paper.\n\nSimilarly, material parameter estimation is an important topic for using learned simulator in real-world settings. For this topic, the focus really should be on how to best design an encoder, how to deal with uncertainty (and when that is/isn't important), latent vs. explicit parameter estimation, etc. And most importantly, parameter estimation is fundamentally about real world data (for simulations we can just assume parameters are available). So studying real-world data, or at least a good proxy (where training and testing material model/parameters have a gap) is probably a good idea.", "was_revised": true, "final_justification": "This is a borderline paper-- There's something there, and the method is interesting, but to be really impactful the paper would need more realistic experiments (ideally real-world data or at least a complex material model to really justify the method) and better ablations of the method.\nThat said, adding the two-stage experiment to the paper is already a good step. I revised my score from 'borderline reject' to 'borderline accept'.", "rebuttal": "We thank the reviewer for their time and for re-engaging with our submission. We appreciate the opportunity to respond to the points raised and provide clarification where needed. While we understand that parts of the submission may be familiar, we respectfully acknowledge that each venue offers a fresh review process, and we are grateful for the paper being considered within the context of NeurIPS.\n\n### **On End-to-End Latent Inference vs. Two-Stage Regression**\n\nThe primary motivation behind our approach is the **joint shaping of the latent representation** through **end-to-end training**. While we acknowledge that a two-stage pipeline (e.g., directly regressing material parameters and conditioning on them) may work well on simpler problems, we argue that our method promotes a more **expressive and integrated latent space**. This space captures not only the identity of the physical parameters but also their **functional impact on the system’s dynamics**.\n\nThis is exemplified in **Figure 5b**, where the learned latent representations exhibit a clear and meaningful separation—for example, between **positive and negative Poisson’s ratios**, corresponding to expanding and contracting materials. This reflects the latent’s ability to encode **task-relevant structure**, rather than merely regressing known quantities.\n\n### **On the Use of Deep Sets Instead of Message Passing in the Encoder**\n\nWe appreciate the reviewer’s suggestion and agree that message passing is an intuitive choice for many graph-based problems. In fact, we implemented and tested a **message-passing-based encoder** early in development. However, we found **no significant improvement** over the simpler and more efficient **Deep Sets-based encoder**.\n\nWe hypothesize that this is due to the **global nature** of the material parameters being inferred. Since the encoder has access to **node positions**, Deep Sets can effectively represent the necessary global characteristics. In contrast, message passing is particularly suited for modeling **localized interactions**, which are less relevant when estimating global latent variables such as material properties.\n\n### **On the Finite Receptive Field of Temporal Convolutions**\n\nWe acknowledge the concern regarding the **limited receptive field** of 1D CNNs, especially compared to EGNO's use of global Fourier-based convolutions. However, our design intentionally leverages **local temporal modeling**, which we find more effective for capturing **short-horizon dynamics**, particularly in the presence of **contact interactions** and **localized temporal events**.\n\nUnlike EGNO, our model operates directly in the **time domain**, enabling it to learn **localized temporal dependencies** without assuming global periodic structure. In all experiments, we ensure that the CNN’s **receptive field fully covers the sequence length** used for training and evaluation, mitigating the risk of incomplete temporal context.\n\n### **On Memory Usage and Trajectory Length**\n\nWe agree that ingesting full trajectories introduces a higher **memory footprint**, which is a known trade-off of non-autoregressive models. In MaNGO, memory usage scales **linearly with the number of predicted time steps**, as the network retains activations across the full temporal sequence:\n\nMemory(MaNGO)≈Memory(MGN)×Number of predicted steps\n\nThat said, this design enables **significant inference speed-ups** by eliminating the need for sequential rollout.\n\nOn the **Sphere-Cloth Coupling** benchmark:\n\n- The **CNP encoder** takes approximately **6 ms** to compute the latent representation rrr,\n- The **MaNGO decoder** predicts the full trajectory in **~13 ms**,\n- By comparison, the **autoregressive MGN** requires **~500 ms**, as it generates one step at a time.\n\nTo address the memory challenge, we propose a **hybrid decoding strategy** as a promising extension. Instead of predicting the full sequence at once, the model could generate **smaller temporal windows** (e.g., 10–20 steps) in sequence. This would substantially reduce peak memory usage while maintaining the benefits of batched inference.\n\nWe appreciate the reviewer’s insights and believe the above clarifications help explain the reasoning and trade-offs behind our architectural choices. We hope this response provides useful context for evaluating the submission."}]

Author rebuttal:

Meta-review: This paper proposes a meta-learned graph simulator that infers (a latent representation of) hidden physical parameters from a few context rollouts. It predicts full future trajectories in a single pass using a non-autoregressive neural-operator decoder that interleaves message passing and one-dimensional temporal convolutions. Reviewer maMF praised the clarity, strong generalization to unseen parameters, and near-oracle accuracy, and asked about efficiency; the authors provided concrete comparisons and a clear account of model size and latency. Reviewer nqEU highlighted the thorough evaluation and practical decoder design, while noting limits: synthetic fixed-topology graphs, substantial training budget, and the fixed edge set; these concerns are reasonable but do not undercut the central contribution, and the authors outlined a windowed decoding path for scaling and discussed dynamic neighborhoods. Reviewer wdos emphasized the importance of the problem and requested broader meta-learning baselines (e.g., Model-Agnostic Meta-Learning, MAML) and memory scaling details; the latter were addressed convincingly, though a MAML comparison remains to be added. Reviewer EtEt asked for a simple two-stage parameter-regression baseline and more ablations; the authors report running this finding that MaNGO still work better (and argue, convincingly, that it is simpler). I think that this paper contains several interesting ideas likely to be of considerable interest to the NeurIPS community working on neural operators and simulation surrogates. Execution could be improved, in particular with more realistic problems (and problem sizes)—on the other hand, already the current setup took a significant amount of compute to get all the results for all baselines, with some error bars. For the final version, please do include the two-stage baseline and, if feasible, an optimization-based meta-learner, and briefly expand the prose discussion of efficiency, memory/trajectory trade-offs, and handling changing graph topology.
Decision: Accept (poster)