MeshODENet: A Graph-Informed Neural Ordinary Differential Equation Neural Network for Simulating Mesh-Based Physical Systems

• URL: http://arxiv.org/abs/2509.18445v1
• Date: Mon, 22 Sep 2025 22:04:01 GMT
• Title: MeshODENet: A Graph-Informed Neural Ordinary Differential Equation Neural Network for Simulating Mesh-Based Physical Systems
• Authors: Kangzheng Liu, Leixin Ma,
• Abstract summary: MeshODENet is a general framework that synergizes the spatial reasoning of GNNs with the continuous-time modeling of Neural Ordinary Differential Equations.<n>We show that our approach significantly outperforms baseline models in long-term predictive accuracy and stability.<n>This work presents a powerful and generalizable approach for developing data-driven surrogates to accelerate the analysis and modeling of complex structural systems.
• Score: 0.8811039895321705
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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