An Operator-Consistent Graph Neural Network for Learning Diffusion Dynamics on Irregular Meshes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914199626579968 |
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| author | Li, Yuelian Hands, Andrew Rushing |
| author_facet | Li, Yuelian Hands, Andrew Rushing |
| contents | Classical numerical methods solve partial differential equations (PDEs) efficiently on regular meshes, but many of them become unstable on irregular domains. In practice, multiphysics interactions such as diffusion, damage, and healing often take place on irregular meshes. We develop an operator-consistent graph neural network (OCGNN-PINN) that approximates PDE evolution under physics-informed constraints. It couples node-edge message passing with a consistency loss enforcing the gradient-divergence relation through the graph incidence matrix, ensuring that discrete node and edge dynamics remain structurally coupled during temporal rollout. We evaluate the model on diffusion processes over physically driven evolving meshes and real-world scanned surfaces. The results show improved temporal stability and prediction accuracy compared with graph convolutional and multilayer perceptron baselines, approaching the performance of Crank-Nicolson solvers on unstructured domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11860 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Operator-Consistent Graph Neural Network for Learning Diffusion Dynamics on Irregular Meshes Li, Yuelian Hands, Andrew Rushing Machine Learning Artificial Intelligence Classical numerical methods solve partial differential equations (PDEs) efficiently on regular meshes, but many of them become unstable on irregular domains. In practice, multiphysics interactions such as diffusion, damage, and healing often take place on irregular meshes. We develop an operator-consistent graph neural network (OCGNN-PINN) that approximates PDE evolution under physics-informed constraints. It couples node-edge message passing with a consistency loss enforcing the gradient-divergence relation through the graph incidence matrix, ensuring that discrete node and edge dynamics remain structurally coupled during temporal rollout. We evaluate the model on diffusion processes over physically driven evolving meshes and real-world scanned surfaces. The results show improved temporal stability and prediction accuracy compared with graph convolutional and multilayer perceptron baselines, approaching the performance of Crank-Nicolson solvers on unstructured domains. |
| title | An Operator-Consistent Graph Neural Network for Learning Diffusion Dynamics on Irregular Meshes |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2512.11860 |