MAVEN: A Mesh-Aware Volumetric Encoding Network for Simulating 3D Flexible Deformation

Abstract: 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.

• The paper introduces a mesh-aware network that explicitly models vertices, facets, and cells to capture 3D flexible deformation with improved physical fidelity.
• The methodology employs a geometric aggregator and dual-stage message passing to integrate volumetric and boundary data, yielding 3–18% lower error over state-of-the-art methods.
• Empirical results demonstrate significant inference speedups and enhanced contact modeling, positioning MAVEN as a viable alternative to traditional FEM solvers in sparse mesh scenarios.

MAVEN: Mesh-Aware Volumetric Encoding for 3D Flexible Deformation Simulation

Motivation and Problem Formulation

The simulation of 3D flexible deformation and solid contact interactions is fundamental for diverse applications in scientific computing and engineering, where both geometric fidelity and physical accuracy under mesh constraints are crucial. While GNN-based methods have achieved success in simulating solid dynamics, they almost universally frame the physical mesh as a vertex-edge graph, ignoring 2D and 3D mesh entities. This oversimplification discards boundary and volumetric details, severely limiting contact modeling and internal field propagation—errors that are exacerbated on coarse meshes, which are often used for computational efficiency.

MAVEN addresses these deficits by explicitly incorporating volumetric cells and boundary facets as learnable components in the network architecture. This design integrates topological and geometric information latent in the mesh, enabling accurate geometric modeling of both local interactions and boundary-driven phenomena, especially under challenging discretization regimes.

MAVEN Architecture

MAVEN is structured as an encoder-processor-decoder pipeline, where mesh elements (vertices, facets, cells) are all treated as first-class entities:

• Encoder: Vertex nodes encode standard physical quantities; cells and facets encode geometric invariants (volume, surface area, perimeter, etc.), capturing intra- and inter-element properties. Face-to-face contact information is built by detecting interactions between facets via a BVH-based spatial search.
• Geometric Aggregator: Rather than simple averaging, MAVEN uses learnable MLPs to compute geometry-aware aggregation coefficients for mapping vertex features to higher-dimensional entities, leveraging cell/facet local coordinates, which maintain permutation invariance and respect geometric structure.
• Cell-Facet Graph and Message Passing: MAVEN constructs a bipartite graph among facets and cells, with two-stage message passing. Propagation occurs from vertices to facets to cells and back, with boundary-sensitive updates. This explicitly models both internal (volumetric) and boundary (facets/contact) interactions.
• Decoder and Updater: Updated vertex features are decoded to predict the next physical state, with the framework trained via one-step MSE on autoregressive rollout trajectories.

Physical Simulation and Geometric Fidelity

MAVEN’s primary innovation is its cell-facet aggregation mechanism, which provides several advantages:

• Boundary-aware Contact Modeling: By messaging on facet-facet graphs, MAVEN robustly captures contact dynamics, which are missed or smeared by vertex-based methods—particularly when contacts do not align with mesh vertices.
• Volumetric Field Propagation: Cell-based updates allow the network to encode volume changes and propagate physical fields using high-dimensional mesh information, avoiding the degeneracy of vertex-only samplings on coarse meshes.
• Geometric Feature Integration: Explicit inclusion of geometric quantities (e.g., surface areas, cell volume) reduces the learning burden and stabilizes physical inference tasks, mirroring integral-based discretizations in classical physical solvers.

Empirical Results

MAVEN achieved consistently lower error against multiple state-of-the-art baselines (MGN, Graph Transformer, HCMT, HOOD, FIGNet) on standard elasticity datasets (Deforming Plate, Cavity Grasping) and an industrially-relevant, highly challenging Metal Bending elastoplastic sequence. Quantitatively, MAVEN outperforms competing methods by 3–18% (depending on mesh sparsity) when predicting both displacement and internal variables (stress, PEEQ).

• Rollout Error Reduction: Numerical experiments demonstrate that improvements grow as mesh coarseness increases—explicit geometric modeling offsets topological sparsification losses.
• Ablations: Removal of geometry-aware aggregation or explicit cell/facet nodes leads to substantial degradation; simply augmenting vertex nodes with geometric features does not recover full performance—high-dimensional topology modeling is necessary.
• Visualization: Error maps highlight that MAVEN yields globally smoother predictions and more accurate contact handling, especially in regions remote from direct deformation input.

Theoretical and Practical Implications

The explicit, mesh-aware design in MAVEN aligns learned physics simulators more closely with FEM/FVM methodologies, in effect blending geometric discretization theory with GNN expressivity. The approach enables:

• Accurate simulation even with severely under-resolved meshes.
• Direct extension to finite volume and shape-function-inspired computations within DL frameworks.
• Flexible incorporation of boundary conditions and external forces at the facet level, supporting tasks with complex contact and motion programs.

Practically, MAVEN achieves significant speedups over traditional FEM/ABAQUS baselines (e.g., >2900% in inference speed on the Metal Bending dataset), while maintaining improved accuracy. This positions MAVEN as a competitive surrogate for real-time or rapid turn-around physical simulation in engineering applications.

Limitations and Future Directions

While substantially advancing state-of-the-art simulation on sparse meshes, MAVEN’s reliance on explicit mesh topology renders its performance sensitive to mesh quality. Further, as a locality-focused operator, MAVEN does not natively capture long-range (nonlocal) interactions—a common requirement in multiscale physics. Extending MAVEN via geometry-aware hierarchical pooling or global message operators represents a promising research direction.

Adapting the architecture to thin-shell, surface-based, and Eulerian systems (where facet and cell topology must be reinterpreted or reconstructed) will require additional research, potentially involving dynamic mesh representations or meshless hybridizations.

Conclusion

MAVEN presents a principled, mesh-aware approach to neural physical simulation for 3D deformable solids, offering strong improvements in geometric fidelity and predictive stability, especially under sparse discretization regimes. By explicitly encoding mesh topology and geometry at the cell and facet level—and designing custom aggregation and messaging operators across these structures—MAVEN sets a new direction for geometric deep learning in physical simulation. Several open challenges remain, notably in mesh-independence, long-range modeling, and generalization beyond volumetric Lagrangian settings, which form crucial avenues for future work.

Reference: "MAVEN: A Mesh-Aware Volumetric Encoding Network for Simulating 3D Flexible Deformation" (2604.04474)