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<p>Physics-aware recurrent convolutional networks (PARC) have demonstrated strong performance in predicting nonlinear spatiotemporal dynamics by embedding differential operators directly into the computational graph of a neural network. However, pixel-based convolutions are restricted to static, uniform Cartesian grids, making them ill-suited to following evolving localized structures in an efficient manner. Graph neural networks (GNNs) naturally handle irregular spatial discretizations, but existing graph-based physics-aware deep learning (PADL) methods have difficulty handling extreme nonlinear regimes. To address these limitations, we propose Graph PARC (G-PARC), which uses moving least squares (MLS) kernels to approximate spatial derivatives on unstructured graphs, and embeds the derivatives of governing partial differential equations into the network’s computational graph. G-PARC achieves better accuracy with 2–3<InlineEquation ID="IEq1"><EquationSource Format="TEX">\(\times\)</EquationSource></InlineEquation> fewer parameters than MeshGraphNet, MeshGraphKAN, and GraphSAGE, replacing the traditional encoder-processor-decoder framework with analytically computed differential operators. We further benchmark against Transolver, a transformer-based neural operator, under a direct multi-step prediction strategy at matched parameter budget, characterizing when recurrent integration is preferable to direct prediction across rollout horizons. We demonstrate that G-PARC (1) generalizes across nonuniform spatial and temporal discretizations; (2) handles moving meshes required for structural deformation; and (3) outperforms existing graph-based PADL methods on nonlinear benchmarks including fluvial hydrology, planar shock waves, and elastoplastic dynamics. By embedding explicit physical operators within the flexibility of GNNs, G-PARC enables accurate modeling of extreme nonlinear phenomena on complex computational domains, moving PADL beyond idealized Cartesian grids.</p>

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G-PARC: Graph-Physics Aware Recurrent Convolutional neural networks for spatiotemporal dynamics on unstructured meshes

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月2日

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  • Jack T. Beerman,
  • Tyler J. Abele,
  • Mehdi Taghizadeh,
  • Andrew Davis,
  • Zoë J. Gray,
  • Negin Alemazkoor,
  • Xinfeng Gao,
  • H. S. Udaykumar,
  • Stephen S. Baek

摘要

Physics-aware recurrent convolutional networks (PARC) have demonstrated strong performance in predicting nonlinear spatiotemporal dynamics by embedding differential operators directly into the computational graph of a neural network. However, pixel-based convolutions are restricted to static, uniform Cartesian grids, making them ill-suited to following evolving localized structures in an efficient manner. Graph neural networks (GNNs) naturally handle irregular spatial discretizations, but existing graph-based physics-aware deep learning (PADL) methods have difficulty handling extreme nonlinear regimes. To address these limitations, we propose Graph PARC (G-PARC), which uses moving least squares (MLS) kernels to approximate spatial derivatives on unstructured graphs, and embeds the derivatives of governing partial differential equations into the network’s computational graph. G-PARC achieves better accuracy with 2–3\(\times\) fewer parameters than MeshGraphNet, MeshGraphKAN, and GraphSAGE, replacing the traditional encoder-processor-decoder framework with analytically computed differential operators. We further benchmark against Transolver, a transformer-based neural operator, under a direct multi-step prediction strategy at matched parameter budget, characterizing when recurrent integration is preferable to direct prediction across rollout horizons. We demonstrate that G-PARC (1) generalizes across nonuniform spatial and temporal discretizations; (2) handles moving meshes required for structural deformation; and (3) outperforms existing graph-based PADL methods on nonlinear benchmarks including fluvial hydrology, planar shock waves, and elastoplastic dynamics. By embedding explicit physical operators within the flexibility of GNNs, G-PARC enables accurate modeling of extreme nonlinear phenomena on complex computational domains, moving PADL beyond idealized Cartesian grids.