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  4. Vol 10, Issue 1, 2025

Physics-Informed GNN Coupled with ESN for Solving Forward Problems of Spatiotemporal Partial Differential Equations

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DOI: 10.23977/jnca.2025.100111 | Downloads: 3 | Views: 107

Author(s)

Yushen Tang 1, Jin Su 1

Affiliation(s)

1 School of Science, Xi'an Polytechnic University, Xi'an, Shaanxi, China

Corresponding Author

Jin Su

ABSTRACT

Partial Differential Equations (PDEs) are the foundation of modeling and simulation in numerous scientific and engineering fields. In recent years, breakthrough advancements in deep learning, particularly the rise of Physics-Informed Neural Networks (PINNs), have opened up a data-driven new paradigm for PDE solving and demonstrated enormous potential. However, PINN is essentially a global fitting method based on fully connected networks, and its core drawback is that the global fitting characteristics lead to a large amount of redundancy in high-order derivative calculations and insufficient modeling of spatiotemporal correlations. To address this, we propose the Physics-Informed E-GNN method, which modeling spatiotemporal features separately under a discrete learning framework to improve the accuracy of spatiotemporal prediction. Our method first discretizes the initial values of the PDE into a graph structure as input, feeds it into a Graph Neural Networks (GNN) to update the spatial features, and then inputs the updated feature vectors into an Echo State Networks (ESN) autoregressive module in the form of a time series to capture sequence correlations. We conducted comparative experiments on two classic partial differential equations (the 2D Burgers' equation and the 2D Convection-Diffusion equation) in irregular domains. The experimental results show that our proposed method achieves significant improvements in both solution accuracy and generality, and can effectively capture the complex patterns of changes in the PDE system.

KEYWORDS

Partial differential equations, Graph neural network, Echo state network, Physics-informed neural networks

CITE THIS PAPER

Yushen Tang, Jin Su, Physics-Informed GNN Coupled with ESN for Solving Forward Problems of Spatiotemporal Partial Differential Equations. Journal of Network Computing and Applications (2025) Vol. 10: 96-106. DOI: http://dx.doi.org/10.23977/jnca.2025.100111.

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