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

2026-04-16

AI Summary

Existing physics-informed deep learning approaches struggle to efficiently and accurately model highly nonlinear spatiotemporal dynamics on unstructured meshes, particularly when dealing with moving meshes and complex geometric domains. This work proposes a novel architecture that, for the first time, explicitly embeds analytical differential operators from partial differential equations into a graph neural network via moving least squares (MLS) kernels, departing from the conventional encoder-processor-decoder paradigm to construct a physics-embedded recurrent graph convolutional framework. The method generalizes across non-uniform spatiotemporal discretizations and accommodates mesh deformation scenarios. Evaluated on nonlinear benchmark problems—including river hydrodynamics, planar shock waves, and elastoplastic dynamics—it significantly outperforms state-of-the-art methods such as MeshGraphNet, achieving higher accuracy with 2–3 times fewer parameters.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Computer Vision: Low Level & Physics-based Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

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.

Problem

• spatiotemporal dynamics
• unstructured meshes
• nonlinear regimes
• physics-aware deep learning
• graph neural networks

Innovation

• Graph Neural Networks
• Physics-Aware Deep Learning
• Moving Least Squares
• Unstructured Meshes
• Spatiotemporal Dynamics