G-PARC: Graph-Physics Aware Recurrent Convolutional Neural Networks for Spatiotemporal Dynamics on Unstructured Meshes

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

doi:10.48550/arxiv.2604.16533

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G-PARC: Graph-Physics Aware Recurrent Convolutional Neural Networks for Spatiotemporal Dynamics on Unstructured Meshes

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G-PARC: Graph-Physics Aware Recurrent Convolutional Neural Networks for Spatiotemporal Dynamics on Unstructured Meshes

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

ArXiv.org

Cornell University

04/16/2026

DOI: 10.48550/arxiv.2604.16533

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Preprint (Author's original) This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

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 2-3x fewer parameters than MeshGraphNet, MeshGraphKAN, and GraphSAGE, replacing the traditional encoder-processor-decoder framework with analytically computed differential operators. 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 PADLbeyond idealized Cartesian grids.

Computer Science - Artificial Intelligence

Computer Science - Learning

Details

Title: Subtitle: G-PARC: Graph-Physics Aware Recurrent Convolutional Neural Networks for Spatiotemporal Dynamics on Unstructured Meshes
Creators: Jack T Beerman
Tyler J Abele
Mehdi Taghizadeh
Andrew Davis
Zoë J Gray
Negin Alemazkoor
Xinfeng Gao
H. S Udaykumar
Stephen S Baek
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2604.16533
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 04/16/2026
Academic Unit: Engineering Administration; Injury Prevention Research Center; Chemical and Biochemical Engineering; Mechanical Engineering
Record Identifier: 9985154892502771

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