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:10.1038/s41598-026-59318-9

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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

Scientific reports

07/02/2026

DOI: 10.1038/s41598-026-59318-9

PMID: 42393116

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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 2-3× 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.

Details

Title: Subtitle: G-PARC: Graph-Physics Aware Recurrent Convolutional neural networks for spatiotemporal dynamics on unstructured meshes
Creators: Jack T Beerman - University of Virginia
Tyler J Abele - University of Virginia
Mehdi Taghizadeh - Engineering Systems (United States)
Andrew Davis - University of Virginia
Zoë J Gray - University of Virginia
Negin Alemazkoor - Engineering Systems (United States)
Xinfeng Gao - University of Virginia
H S Udaykumar - University of Iowa
Stephen S Baek - University of Virginia
Resource Type: Journal article
Publication Details: Scientific reports
DOI: 10.1038/s41598-026-59318-9
PMID: 42393116
ISSN: 2045-2322
eISSN: 2045-2322
Publisher: Springer Nature
Grant note: DE-NA0004269 / National Nuclear Security Administration
Language: English
Electronic publication date: 07/02/2026
Academic Unit: Engineering Administration; Injury Prevention Research Center; Chemical and Biochemical Engineering; Mechanical Engineering
Record Identifier: 9985179097402771

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