Neural Operator: Learning Maps Between Function Spaces With Applications to PDEs

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Neural operators for accelerating scientific simulations and design (2023, unknown): “On the Darcy equation, we train each fixed architecture UNet, FNO, and GNO at a given resolution and test at that same resolution [6] (no superresolution).”
Transolver: A Fast Transformer Solver for PDEs on General Geometries (2024, methodology): “Neural operators Another paradigm is to learn neural operators to approximate the input-output mappings in PDE-governed tasks, such as predicting the future fluid based on past observations or estimating the inner stress of solid materials (Lu et al., 2021; Kovachki et al., 2023).”
Factorized Fourier Neural Operators (2021, background): “More generally, Kovachki et al. (2021a) prove that the FNO can approximate any continuous operator.”
Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere (2023, background): “, 2020) and their variants (Guibas et al., 2021; Wen et al., 2022; Rahman et al., 2022; Kovachki et al., 2023; Kossaifi et al., 2023) possess the advantage of learning mappings between function spaces, which act globally on the entire domain.”
KAN: Kolmogorov-Arnold Networks (2024, unknown): “We refer to Deep Ritz Method [79], PINNs [22, 23] for PDE solving, and Fourier Neural operator [80], PINOs [81, 82, 83], DeepONet [84] for operator learning methods learning the solution map.”