Adaptive Neural Network Basis Methods for Partial Differential Equations with Low-Regular Solutions

Exploring foci of: Communications in Computational Physics • Vol 39 • No 2 Adaptive Neural Network Basis Methods for Partial Differential Equations with Low-Regular Solutions November 2025 • Jianguo Huang, Haohao Wu, Tao Zhou This paper aims to devise an adaptive neural network basis method for numerically solving a second-order semi-linear partial differential equation with low-regular solutions in two/three dimensions. The method is obtained by combining basis functions from a class of shallow neural networks and the resulting multi-scale analogues, a residual strategy in adaptive methods and the non-overlapping domain decomposition method. Firstly, based on the solution residual, the domain $\Omega$ is iteratively decomposed and eve… Open Article Page

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