MeshODENet: A Graph-Informed Neural Ordinary Differential Equation Neural Network for Simulating Mesh-Based Physical Systems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915508273545216 |
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| author | Liu, Kangzheng Ma, Leixin |
| author_facet | Liu, Kangzheng Ma, Leixin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18445 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | MeshODENet: A Graph-Informed Neural Ordinary Differential Equation Neural Network for Simulating Mesh-Based Physical Systems Liu, Kangzheng Ma, Leixin Machine Learning Applied Physics 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. |
| title | MeshODENet: A Graph-Informed Neural Ordinary Differential Equation Neural Network for Simulating Mesh-Based Physical Systems |
| topic | Machine Learning Applied Physics |
| url | https://arxiv.org/abs/2509.18445 |