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.

Figures (10)

• 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.
• Figure 4: Visualization of error maps. The first and second rows respectively show sample visualizations from cavity grasping and metal bending datasets.
• Figure 5: Description of Deforming Plate from pfaff2020learning.