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

2026-04-06

AI Summary

Existing graph neural network–based methods for deformable simulation typically model only vertices and edges, neglecting higher-dimensional geometric entities such as faces and volumes, which limits their ability to accurately capture boundary and volumetric properties—particularly on sparse meshes. This work proposes a novel neural architecture that explicitly integrates vertex, face, and volume elements, introducing for the first time in deep learning–based deformation simulation a joint representation of 2D faces and 3D volumes. By establishing learnable mappings and flexible inter-element transformation mechanisms across multidimensional mesh components, and combining mesh-aware voxel encoding with graph neural networks, the method significantly enhances modeling of contact interactions and internal physical quantity propagation. It achieves state-of-the-art performance across multiple benchmarks and a newly introduced large-deformation metal simulation task, demonstrating exceptional robustness under sparse discretizations and prolonged contact scenarios.

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.

Problem

• flexible deformation
• mesh representation
• volumetric features
• boundary representation
• contact simulation

Innovation

• mesh-aware
• volumetric encoding
• higher-dimensional geometric elements
• 3D flexible deformation
• learnable mappings