Deep Adaptive Basis Galerkin Method for High-Dimensional Evolution Equations With Oscillatory Solutions
DOI10.1137/21M1468383zbMath1506.65154arXiv2112.14418OpenAlexW4226337678MaRDI QIDQ5038412
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Publication date: 30 September 2022
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2112.14418
Galerkin methodparabolic equationmethod of lineshyperbolic equationdeep learning in spaceLegendre polynomials in time
Artificial neural networks and deep learning (68T07) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Rate of convergence, degree of approximation (41A25) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)
Uses Software
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