Symmetry group based domain decomposition to enhance physics-informed neural networks for solving partial differential equations

no code implementations • 29 Apr 2024 • Ye Liu, Jie-Ying Li, Li-Sheng Zhang, Lei-Lei Guo, Zhi-Yong Zhang

Specifically, for the forward problem, we first deploy the symmetry group to generate the dividing-lines having known solution information which can be adjusted flexibly and are used to divide the whole training domain into a finite number of non-overlapping sub-domains, then utilize the PINN and the symmetry-enhanced PINN methods to learn the solutions in each sub-domain and finally stitch them to the overall solution of PDEs.

Enforcing continuous symmetries in physics-informed neural network for solving forward and inverse problems of partial differential equations

no code implementations • 19 Jun 2022 • Zhi-Yong Zhang, HUI ZHANG, Li-Sheng Zhang, Lei-Lei Guo

As a typical application of deep learning, physics-informed neural network (PINN) {has been} successfully used to find numerical solutions of partial differential equations (PDEs), but how to improve the limited accuracy is still a great challenge for PINN.