ORIGINAL RESEARCH
Aerosp. Res. Commun.
Volume 3 - 2025 | doi: 10.3389/arc.2025.14842
This article is part of the Special IssuePhysics-Informed Machine Learning for Modeling and Design OptimizationView all 5 articles
Spatial-temporal parallel physics-informed neural networks for solving forward and inverse PDE problems via overlapping domain decomposition
- 1Huazhong University of Science and Technology, Wuhan, China
- 2National University of Defense Technology, Changsha, China
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Physics-informed neural networks (PINNs) have emerged as an effective tool for solving both forward and inverse partial differential equation (PDE) problems. However, the expensive computational cost restricted the applications of PINNs in large-scale problems. In this study, we employ an overlapping domain decomposition technique to enable the spatial-temporal parallelism in PINNs to accelerate the training. Moreover, we propose a rescaling approach for the input of PINNs in each subdomain, which is capable of migrating the spectral bias in vanilla PINNs. We justify the accuracy of the PINNs with overlapping domain decomposition (overlapping PINNs) for spatial parallelism using several differential equations: a forward ODE with high-frequency solution, a two-dimensional (2D) forward Helmholtz equation, and a 2D inverse heat conduction problems. In addition, we test the accuracy of overlapping PINNs for spatial-temporal parallelism using two nonstationary PDE problems, i.e. a forward Burger equation and an inverse heat transfer problem. The results demonstrate (1) the effectiveness of overlapping PINNs for spatial-temporal parallelism in solving forward and inverse PDE problems, and (2) the rescaling technique proposed in this work is able to migrate the spectral bias in vanilla PINNs. Finally, we demonstrate that the overlapping PINNs achieve about 90% efficiency up to 8 GPUs using the
Keywords: parallel PINN, domain decomposition, overlapping, multi-GPU, forward and inverse PDEs
Received: 01 May 2025; Accepted: 09 Jul 2025.
Copyright: © 2025 Ye, Xu, Zhou and Meng. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Xuhui Meng, Huazhong University of Science and Technology, Wuhan, China
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