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

arXiv: https://arxiv.org/abs/2604.16533 · HTML: https://mlsanity.com/paper/2604.16533/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 22 references that are in the map.
- First posted on arXiv 16 Apr 2026.

## Builds on (most cited first, 9 of 9)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [PARCv2: Physics-aware Recurrent Convolutional Neural Networks for Spatiotemporal Dynamics Modeling](https://mlsanity.com/paper/2402.12503/) (2024)
- [Reduced Order Modeling of Energetic Materials Using Physics-Aware Recurrent Convolutional Neural Networks in a Latent Space (LatentPARC)](https://mlsanity.com/paper/2509.12401/) (2025)
- [Multi-resolution Physics-Aware Recurrent Convolutional Neural Network for Complex Flows](https://mlsanity.com/paper/2512.06031/) (2025)
- [Size is Not the Solution: Deformable Convolutions for Effective Physics Aware Deep Learning](https://mlsanity.com/paper/2601.11657/) (2026)

## Abstract (arXiv)

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.