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math.NA2025
Nemytskii neural operator: a nonlinear model reduction method for parametrized partial differential equations
Jingye Li, Alex Bespalov, Jinglai Li
We introduce a Nemytskii neural operator framework for nonlinear model reduction of parametrized steady-state partial differential equations. The method generalizes reduced basis a…
math.NA2025
An adaptive multimesh rational approximation scheme for the spectral fractional Laplacian
Alex Bespalov, Raphaël Bulle
We propose a novel multimesh rational approximation scheme for the numerical solution of the (homogeneous) Dirichlet problem for the spectral fractional Laplacian. The scheme combi…