# PhyGNNet: Solving spatiotemporal PDEs with Physics-informed Graph Neural Network

arXiv: https://arxiv.org/abs/2208.04319 · HTML: https://mlsanity.com/paper/2208.04319/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 27 references that are in the map.
- First posted on arXiv 7 Aug 2022.

## Builds on (most cited first, 11 of 11)

- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domain](https://mlsanity.com/paper/2004.13145/) (2020)
- [PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs](https://mlsanity.com/paper/2106.14103/) (2021)
- [Physics-informed deep learning for incompressible laminar flows](https://mlsanity.com/paper/2002.10558/) (2020)
- [A Physics-Informed Machine Learning Approach for Solving Heat Transfer Equation in Advanced Manufacturing and Engineering Applications](https://mlsanity.com/paper/2010.02011/) (2020)
- [Differentiable Physics-informed Graph Networks](https://mlsanity.com/paper/1902.02950/) (2019)

## Built on by (most cited first, 5 of 5)

- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (2022)
- [Discovering Physics-Informed Neural Networks Model for Solving Partial Differential Equations through Evolutionary Computation](https://mlsanity.com/paper/2405.11208/) (2024)
- [RBF-MGN:Solving spatiotemporal PDEs with Physics-informed Graph Neural Network](https://mlsanity.com/paper/2212.02861/) (2022)
- [Resolution invariant deep operator network for PDEs with complex geometries](https://mlsanity.com/paper/2402.00825/) (2024)
- [GrINd: Grid Interpolation Network for Scattered Observations](https://mlsanity.com/paper/2403.19570/) (2024)

## Abstract (arXiv)

Solving partial differential equations (PDEs) is an important research means in the fields of physics, biology, and chemistry. As an approximate alternative to numerical methods, PINN has received extensive attention and played an important role in many fields. However, PINN uses a fully connected network as its model, which has limited fitting ability and limited extrapolation ability in both time and space. In this paper, we propose PhyGNNet for solving partial differential equations on the basics of a graph neural network which consists of encoder, processer, and decoder blocks. In particular, we divide the computing area into regular grids, define partial differential operators on the grids, then construct pde loss for the network to optimize to build PhyGNNet model. What's more, we conduct comparative experiments on Burgers equation and heat equation to validate our approach, the results show that our method has better fit ability and extrapolation ability both in time and spatial areas compared with PINN.