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arXiv · 2407.00442

A Review of Neural Network Solvers for Second-order Boundary Value Problems

Ramesh Chandra Sau·Luowei Yin
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Abstract

Deep learning-based partial differential equation(PDE) solvers have received much attention in the past few years. Methods of this category can solve a wide range of PDEs with high accuracy, typically by transforming the problems into highly nonlinear optimization problems of neural network parameters. This work reviews several deep learning solvers proposed a few years ago, including PINN, WAN, DRM, and VPINN. Numerical results are provided to make comparisons amongst them and address the importance of loss formulation and the optimization method. A rigorous error analysis for PINN is also presented. Finally, we discuss the current limitations and bottlenecks of these methods.

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Ramesh Chandra Sau, Luowei Yin. 2024-06-29. A Review of Neural Network Solvers for Second-order Boundary Value Problems. https://arxiv.org/abs/2407.00442

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