Organizations: Academy for Advanced Interdisciplinary Studies, Peking University · School of Computer Science, Peking University · School of Electrical and Computer Science, University of Southampton
Deep learning-based approaches, particularly graph neural networks (GNNs), have gained prominence in simulating flexible deformations and contacts of solids, due to their ability to handle unstructured physical fields and nonlinear regression on graph structures. However, existing GNNs commonly represent meshes with graphs built solely from vertices and edges. These approaches tend to overlook higher-dimensional spatial features, e.g., 2D facets and 3D cells, from the original geometry. As a result, it is challenging to accurately capture boundary representations and volumetric characteristics, though this information is critically important for modeling contact interactions and internal physical quantity propagation, particularly under sparse mesh discretization. In this paper, we introduce MAVEN, a mesh-aware volumetric encoding network for simulating 3D flexible deformation, which explicitly models geometric mesh elements of higher dimension to achieve a more accurate and natural physical simulation. MAVEN establishes learnable mappings among 3D cells, 2D facets, and vertices, enabling flexible mutual transformations. Explicit geometric features are incorporated into the model to alleviate the burden of implicitly learning geometric patterns. Experimental results show that MAVEN consistently achieves state-of-the-art performance across established datasets and a novel metal stretch-bending task featuring large deformations and prolonged contacts.
Figures & tables
Figure 1: The physical state on the continuous material domain is discretized using structured meshes. Node-based methods construct point-edge graphs from the mesh and apply GNNs for computation. However, such abstraction may overlook contact interactions. A more effective approach should incorporate higher-dimensional geometric structures in the mesh, such as 3D cells and 2D facets, which retain accurate geometric information after discretization.
Figure 2: The overall structure of MAVEN. MAVEN follows an encoder–processor–decoder pipeline: it extracts geometric and physical features for vertices, cells, and facets, updates them through position-aware geometric aggregation and refined cell–facet message passing, and finally disaggregates the processed features back to vertices to produce smooth predictions.
Figure 3: Visual description of the dataset.
Model
Rollout
CG
DP
MBD
Pos
Pos
Stress
Pos
Stress
PEEQ
MGN
50
6.38±0.39
14.01±0.087
24,495,364±793,284
686.19±70.51
12508.07±392.56
0.24±0.045
ALL
16.89±0.49
23.65±0.19
30,623,890±457,279
2012.16±299.60
9737.58±287.61
1.45±0.060
GT
50
6.15±0.37
14.72±0.30
24,384,076±915,030
678.87±39.99
10368.29±1737.58
0.41±0.060
ALL
16.69±0.62
26.77±0.52
32,171,330±224,721
1406.61±72.84
14255.72±1203.51
2.07±0.083
HCMT
50
6.14±0.29
14.46±0.47
22,335,358±663,289
851.86±52.23
17940.56±2662.00
0.45±0.010
Table 1: Rollout results( ×103 ) for MAVEN and other baselines, with 50-step rollouts and full-sequence rollouts. Our results are derived by averaging the root mean square error (RMSE) values computed across all intermediate steps and test datasets.
Figure 4: Visualization of error maps. The first and second rows respectively show sample visualizations from cavity grasping and metal bending datasets.
Model
Rollout
CG
MBD
Pos
Pos
Stress
Ours
50
5.21
276.73
4901.56
ALL
15.41
810.42
4776.72
Model A
50
6.26
402.79
5302.67
ALL
17.45
926.71
6683.94
Model B
50
5.41
391.40
6839.26
Table 2: Ablation results on CG and MBD.
Appendix figures & tables9 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 5: Description of Deforming Plate from ( Pfaff et al., 2020 ) .
Figure 6: Description of Cavity Grasping from ( Linkerhägner et al., 2023 )
Figure 7: Description of Metal Bending.
Figure 8: (a) True Stress-Strain Curve of Aluminum Profile. (b) Exemplar Motion Trajectory for Clamp Mechanism.
Deforming Plate
Metal Bending
Cavity Grasping
MGN
HIDDENS
[128, 128]
[128, 128]
[128, 128]
LAYERS
15
15
15
PARAMETERS(M)
3.85M
3.85M
3.85M
HCMT
HIDDENS
[144, 144]
[144, 144]
[144, 144]
LAYERS
12+3
6+9
10 + 5
PARAMETERS(M)
3.24M
3.24M
3.11M
Appendix
Table 3: Key hyperparameters and parameter numbers of models.
Dataset
Input
Output
rW
rF
noise
Deforming Plate
typei , xit−xit−1 , Sit
xit+1−xit , Sit+1−Sit
0.03
0.01
0.003
Cavity Grasping
typei , xit−xit−1 ,
xit+1−xit
0.1
0.05
0.01
Metal Bending
typei , xit−xit−1 , Sit , Pit
xit+1−xit , Sit+1−Sit , Pit+1−Pit
1
0.3
0.1
Appendix
Table 4: Model input, output and contact detection parameters for dataset. S denotes stress, and P denotes PEEQ.
Dataset
MAVEN
MGN
FIGNet
HCMT
HOOD
GT
CG
25.48
18.37
24.15
55.05
51.37
22.02
DP
48.27
39.73
43.08
64.94
57.28
54.83
MBD
23.57
17.42
17.08
43.68
36.45
22.34
Appendix
Table 5: The inference time per step(ms) for each model on three dataset
Figure 9: Visualization of distance error map on Cavity Grasping.
Figure 10: Visualization of distance error map on Metal Bending dataset. Gray indicates that the error at this location exceeds the given error upper bound.
Graph neural networks (GNNs) have emerged as a versatile and efficient option for modeling the dynamic behavior of deformable materials. While GNNs generalize readily to arbitrary shapes, mesh topologies, and material parameters, existing architectures struggle to correctly predict the temporal evolution of key physical quantities such as linear and angular momentum. In this work, we propose MomentumGNN -- a novel architecture designed to accurately track momentum by construction. Unlike existing GNNs that output unconstrained nodal accelerations, our model predicts per-edge stretching and bending impulses which guarantee the preservation of linear and angular momentum. We train our network in an unsupervised fashion using a physics-based loss, and we show that our method outperforms baselines in a number of common scenarios where momentum plays a pivotal role.
Jiahong Wang, Logan Numerow, Stelian Coros +3
Max Planck Institute for Informatics · ETH Zurich · University of Bonn +1
Finite element analysis (FEA) is essential for structural design but remains computationally expensive, particularly when evaluating multiple design iterations or load scenarios. Machine learning surrogate models offer a promising alternative, yet most approaches struggle with a critical limitation: generalizing across varying geometries. This work presents a mesh graph network (MGN) for predicting von Mises stress fields in 2D structural components with arbitrary hole geometries. Unlike traditional machine learning approaches that use absolute node coordinates as features, the proposed model builds on existing MGN frameworks that encode node types (e.g., fixed boundary, free surface, hole edge), relative edge features (distance between neighbors), and global features (applied load). This architecture is inherently translation- and rotation-invariant, enabling generalization to unseen geometries without retraining. The MGN was trained on 11 plate geometries under 20 load conditions and evaluated on 7 unseen geometries and 3 unseen loads. In the most favorable case, the model achieves R2≥0.97 on an unseen geometry and unseen load, compared to R2≈0.01--0.86 for conventional models (Random Forest, Gradient Boosting , K-Nearest Neighbors) trained on identical data. However, even in less favorable cases, the MGN model still outperforms conventional models. This work extends the mesh-based simulation framework of Pfaff et al. (arXiv:2010.03409) to structural mechanics, demonstrating that graph neural networks can serve as efficient surrogates for finite element analysis across varying geometries.
Josiah D. Kunz, Kamal Choudhary
Illinois College, Jacksonville, IL, USA · Department of Materials Science and Engineering, Whiting School of Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
We present MeshLoom, a feed-forward registration network that directly reconstructs vertex deformations across mesh sequences. Our approach advances non-rigid registration beyond existing models, which are typically constrained by costly per-instance optimization, narrow object categories, pairwise-only inputs, or merely intermediate outputs. The network is simple and efficient, registering multiple meshes within seconds. At its core lies a topology-aware encoder--decoder design. Specifically, we first introduce a topology-aware point representation that encodes the anchor (reference) mesh's topology into its per-vertex features. This representation strengthens the network's understanding of the anchor-mesh geometry and disambiguates points that are Euclidean-close yet geodesically distant. We then propose a multi-modal encoder that fuses this anchor-mesh representation with complementary cues from each frame, such as shape latents and image features. These multi-source signals are compressed into a compact global motion embedding that captures dense inter-frame correspondence. A lightweight decoder then queries this global embedding with the anchor-mesh point representation, retrieving per-vertex deformations at target timestamps. Through extensive experiments across diverse motions and object categories, we show that MeshLoom achieves state-of-the-art results on non-rigid registration. In addition, we find that our global embedding-then-query paradigm naturally enables the network to generate deformations at intermediate timestamps, which extends MeshLoom to motion interpolation and mesh morphing. Project page: https://meshloom.github.io/ .