SPFNO: spectral operator learning for PDEs with Dirichlet and Neumann boundary conditions
Keywords: neural operator, deep learning-based PDE solver, AI for science, scientific machine learning, spectral method
Abstract: Neural operator has been validated as a promising deep surrogate model for solving partial differential equations (PDEs). Based on the spectral operator learning (SOL) architecture, an enhanced orthogonal polynomial neural operator we have developed significantly improved the method’s accuracy by precisely satisfying the boundary conditions (BCs), but is associated with Gauss-type grids, limiting comparisons on most public datasets. In this paper we introduce SPFNO, a novel SOL method, to learn the target operators on uniform grid datasets for PDEs with non-periodic BCs. Numerical results for various PDEs such as viscous Burgers’ equation, Darcy flow and coupled Allen–Cahn equations demonstrate the computational efficiency, resolution invariant property, and BC-satisfaction behaviour of proposed model. An accuracy improvement of approximately 1.7X–4.7X over non-BC-satisfying baseline is also noted. Furthermore, studies on SOL emphasizes the imporance of respecting BCs as a criterion for deep surrogate models of PDEs.
Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)
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Submission Number: 3461
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