G-PARC is a physics-aware deep learning framework for forecasting complex spatiotemporal dynamics on unstructured meshes. It combines graph neural networks with numerical methods — Moving Least Squares (MLS) differential operators and explicit time integrators — to learn physical dynamics directly from simulation data.
The framework is validated across three challenging domains: elastoplastic dynamics, planar shock wave flows, and river flood forecasting.
Paper under review.
- MLS differential operators (gradient, Laplacian, strain) computed directly on unstructured meshes
- Temporal conditioning for variable-timestep generalization — a single trained model handles arbitrary Δt at inference
- Numerical time integration (Euler, Heun, RK4) replacing learned integrators for physical consistency
- 604–2,382× throughput advantage over neural operator baselines (GINO/GNO)
Trained model checkpoints, test datasets, and configuration files are hosted on Hugging Face:
🤗 huggingface.co/jacktbeerman/Gparc
The demo notebooks download these artifacts automatically — no manual data setup required.
G-PARC/
├── models/ # Model architectures (G-PARC, G-PARC (w/o MLS), baselines)
├── differentiator/ # MLS differential operators & physics modules
├── integrator/ # Numerical time integration (Euler, Heun, RK4)
├── utilities/ # Feature extractors, SPADE fusion, training utilities
├── data/ # Dataset classes & normalization
├── scripts/ # Training & evaluation scripts per domain
├── demos/ # Demo notebooks with Hugging Face auto-download
├── tests/ # Unit tests for operators and per-domain models
├── visualizations/ # Visualization, metrics, and comparison utilities
├── assets/ # GIFs for README
└── requirements.txt
Side-by-side comparison of ground truth and G-PARC predictions on the PLAID elastoplastic benchmark, showing mesh deformation.
Compressible Euler equation solutions demonstrating stability and accuracy across varying initial pressure ratios and timestep sizes.
Flood inundation forecasting on unstructured HEC-RAS meshes, predicting water surface elevation and depth evolution.
G-PARC (the primary architecture) follows a modular Differentiate → Integrate design:
- Graph Convolution Layers — extract spatial features from unstructured mesh node/edge data using GATConv
- MLS Differential Operators — compute physics-grounded spatial derivatives (gradients, Laplacians, strain rates) via Moving Least Squares on the mesh stencil
- SPADE Fusion — combine learned GNN features with MLS differential quantities through spatially-adaptive normalization
- FiLM Conditioning — modulate learned representations with simulation parameters (pressure ratio, Δt) for variable-condition generalization
- Numerical Integration — advance the state forward in time using Euler, Heun, or RK4 schemes
G-PARC (w/o MLS) uses a learned GNN integrator (IntegralGNN) instead of numerical schemes, serving as an ablation baseline.
git clone https://github.com/JackBeerman/G-PARC.git
cd G-PARC
pip install -r requirements.txtNote: PyTorch and PyTorch Geometric should be installed separately based on your CUDA version. See pytorch.org and PyG installation.
The demo notebooks in demos/ automatically download model weights and test data from Hugging Face:
cd demos/elastoplasto
jupyter notebook plaid_elastoplastic_demo.ipynbpython tests/run_all.pyThis runs operator-level and per-domain integration tests to verify model correctness.
2D elastoplastodynamics from the PLAID benchmark suite — high-velocity impact simulations on steel plates with nonlinear elastoplastic constitutive laws, solved with OpenRadioss on unstructured meshes.
Casenave, F., Roynard, X., Staber, B., Piat, W., et al. "Physics-Learning AI Datamodel (PLAID) datasets: a collection of physics simulations for machine learning." arXiv:2505.02974, 2025. [Paper] [Data (Zenodo)] [HuggingFace]
1D compressible shock tube simulations on 2D domain solving the Euler equations with varying initial pressure and density ratios. Simulation data generated using the high-order finite-volume combustion solver of Gao et al.
Gao, X., Owen, L. D., & Guzik, S. M. "A high-order finite-volume method for combustion." In 54th AIAA Aerospace Sciences Meeting, p. 1808, 2016. [Paper]
White River flood simulation data from HydroGraphNet — 2D shallow water equation solutions on unstructured meshes with varying hydrograph boundary conditions.
Taghizadeh, M., Zandsalimi, Z., Nabian, M.A., Shafiee-Jood, M., & Alemazkoor, N. "Interpretable physics-informed graph neural networks for flood forecasting." Computer-Aided Civil and Infrastructure Engineering, 2025. [Paper]
The repository includes implementations of the following baseline models used for comparison:
- MeshGraphNet — encoder-processor-decoder GNN from NVIDIA PhysicsNeMo (Pfaff et al., 2021; PhysicsNeMo)
- MeshGraphKAN — MeshGraphNet variant with Fourier KAN layers replacing MLPs, reimplemented from NVIDIA PhysicsNeMo
- GraphSAGE — sampling-based GNN baseline (Hamilton et al., 2017)
- G-PARC (w/o MLS) — ablation using learned integration instead of numerical schemes
@article{beerman2026gparc,
title={G-PARC: Graph-Physics Aware Recurrent Convolutional Neural Networks for Spatiotemporal Dynamics on Unstructured Meshes},
author={Beerman, Jack T. and Abele, Tyler J. and Taghizadeh, Mehdi and Davis, Andrew and Gray, Zo{\"e} J. and Alemazkoor, Negin and Gao, Xifeng and Udaykumar, H. S. and Baek, Stephen S.},
journal={Under review},
year={2026}
}This project is licensed under the MIT License. See LICENSE for details.