Spectral neural operators

DOI10.1134/S1064562423701107arXiv2205.10573MaRDI QIDQ6124382

Ivan V. Oseledets, V. S. Fanaskov

Publication date: 27 March 2024

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.10573

zbMATH Keywords

partial differential equationsneural operators

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Best approximation, Chebyshev systems (41A50) Numerical methods for wavelets (65T60) Numerical methods for discrete and fast Fourier transforms (65T50) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Numerical methods for partial differential equations, boundary value problems (65N99) General integral transforms (44A05)

Cites Work

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• Discretization-invariant Bayesian inversion and Besov space priors
• Wavelet neural operator for solving parametric partial differential equations in computational mechanics problems
• The Korteweg-de Vries Two-Soliton Solution as Interacting Two Single Solitons
• A numerical and theoretical study of certain nonlinear wave phenomena
• Spectral Methods in MATLAB
• Learning data-driven discretizations for partial differential equations
• Comparing Numerical Methods for Ordinary Differential Equations

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