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

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Bibliographic Details
Title: MeshODENet: A Graph-Informed Neural Ordinary Differential Equation Neural Network for Simulating Mesh-Based Physical Systems.
Authors: Liu, Kangzheng1 kangzhen@asu.edu, Ma, Leixin1 leixin.ma@asu.edu
Source: Journal of Applied Mechanics. May2026, Vol. 93 Issue 5, p1-10. 10p.
Subjects: Graph neural networks, Continuous time models, Elastic deformation, Prediction models, Computer simulation, Structural mechanics
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 different elastic bodies undergoing large, nonlinear 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. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
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 different elastic bodies undergoing large, nonlinear 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. [ABSTRACT FROM AUTHOR]
ISSN:00218936
DOI:10.1115/1.4071488