MeshODENet: A Graph-Informed Neural Ordinary Differential Equation Neural Network for Simulating Mesh-Based Physical Systems
cs.LG, physics.app-ph
Submitted: 2025-09-22
Updated: 2025-09-22
Comments: 9 pages, 7 figures
Journal ref: Journal of Applied Mechanics, 93(5), 051005 (2026)
DOI: 10.1115/1.4071488
Code: https://github.com/leixinma/MeshODENet
License: http://creativecommons.org/licenses/by/4.0/
The gist: 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.
Terminology
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.
Sources
- Relational inductive biases, deep learning, and graph networks
- Graph Neural Ordinary Differential Equations
- Combining Post-Circular and Pad'e approximations to compute Fourier domain templates for eccentric inspirals
- A Posteriori Evaluation of a Physics-Constrained Neural Ordinary Differential Equations Approach Coupled with CFD Solver for Modeling Stiff Chemical Kinetics
- Generalizing Graph ODE for Learning Complex System Dynamics across Environments
- Graph-based Multi-ODE Neural Networks for Spatio-Temporal Traffic Forecasting
- Epidemiology-Aware Neural ODE with Continuous Disease Transmission Graph
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