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math.NA2023
Solving Poisson Problems in Polygonal Domains with Singularity Enriched Physics Informed Neural Networks
Tianhao Hu, Bangti Jin, Zhi Zhou
Physics-Informed Neural Networks (PINNs) are a powerful class of numerical solvers for partial differential equations, employing deep neural networks with successful applications a…
math.NA2022
Solving Elliptic Problems with Singular Sources using Singularity Splitting Deep Ritz Method
Tianhao Hu, Bangti Jin, Zhi Zhou
In this work, we develop an efficient solver based on neural networks for second-order elliptic equations with variable coefficients and singular sources. This class of problems co…