MeshODENet: A Graph-Informed Neural Ordinary Differential Equation Neural Network for Simulating Mesh-Based Physical Systems
This work addresses the need for efficient and stable surrogate models for simulating complex structural systems, offering a generalizable approach that could accelerate analysis in applied mechanics.
The paper tackled the problem of error accumulation and instability in long-term predictions of mesh-based physical systems using Graph Neural Networks, by introducing MeshODENet, which combines GNNs with Neural ODEs. The result showed significant outperformance in accuracy and stability over baselines, with substantial computational speed-ups over traditional solvers.
The simulation of complex physical systems using a discretized mesh is a cornerstone of applied mechanics, but traditional numerical solvers are often computationally prohibitive for many-query tasks. While Graph Neural Networks (GNNs) have emerged as powerful surrogate models for mesh-based data, their standard autoregressive application for long-term prediction is often plagued by error accumulation and instability. To address this, we introduce MeshODENet, a general framework that synergizes the spatial reasoning of GNNs with the continuous-time modeling of Neural Ordinary Differential Equations. We demonstrate the framework's effectiveness and versatility on a series of challenging structural mechanics problems, including one- and two-dimensional elastic bodies undergoing large, non-linear deformations. The results demonstrate that our approach significantly outperforms baseline models in long-term predictive accuracy and stability, while achieving substantial computational speed-ups over traditional solvers. This work presents a powerful and generalizable approach for developing data-driven surrogates to accelerate the analysis and modeling of complex structural systems.