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SDC-GON: Singular Decomposition and Consistency-Regularized Green's Operator Networks for Solving Partial Differential Equations

arXiv · AI, language, vision and robotics · article · Sep 19, 2026 · UTC

Green's function based operator approximation offers an efficient route for solving linear partial differential equations under varying boundary conditions and source terms. Once the Green's function is learned, solutions for new configurations are obtained through integration rather than by solving the differential equation again. Existing Green's function learning methods face two structural challenges. The first is the singular behavior of the Green's function near the source point, which places a difficult approximation burden on neural networks. The second is the absence of explicit consi

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