Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equation

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Jose Antonio Lara Benitez, Takashi Furuya, Florian Faucher, Anastasis Kratsios, Xavier Tricoche, Maarten V. de Hoop

Published: 01 Jan 2024, Last Modified: 13 Nov 2025J. Comput. Phys. 2024EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: Highlights•Transformer-motivated neural operator.•Enhancing neural operators' generalization.•Hypernetworks as a surrogate model for forward operators.•Generalization error bounds for neural operators.•Out-of-distribution for Gaussian measures on Banach spaces.