An operator learning perspective on parameter-to-observable maps

Computationally efficient surrogates for parametrized physical models play a crucial role in science and engineering. Operator learning provides data-driven surrogates that map between function spaces. However, instead of full-field measurements, often the available data are only finite-dimensional parametrizations of model inputs or finite observables of model outputs. Building off of Fourier Neural Operators, this paper introduces the Fourier Neural Mappings (FNMs) framework that is able to accommodate such finite-dimensional inputs and outputs. The paper develops universal approximation theorems for the …

building cs.lg data data-driven engineering fourier function inputs map maps math.st observable operators perspective role science spaces stat.ml stat.th