Neural Operators as Efficient Function Interpolators

TL;DR

Neural operators are presented as efficient, scalable function interpolators that outperform traditional neural networks in accuracy and training efficiency, demonstrated through benchmarks and a nuclear physics application.

Contribution

The paper introduces a novel reframing of neural operators using an auxiliary base-space, enhancing their efficiency and applicability for finite-dimensional function interpolation.

Findings

Neural operators match or outperform MLPs and Kolmogorov--Arnold Networks in accuracy.

Neural operators require fewer parameters and less training time.

A Tensorized Fourier Neural Operator achieves state-of-the-art results in nuclear mass modeling.

Abstract

Neural operators (NOs) are designed to learn maps between infinite-dimensional function spaces. We propose a novel reframing of their use. By introducing an auxiliary base-space, any finite-dimensional function can be viewed as an operator acting by composition on functions of the base-space. Through a range of benchmarks on analytic functions of increasing complexity and dimensionality, we demonstrate that NOs can match or outperform standard multilayer perceptrons and Kolmogorov--Arnold Networks in accuracy while requiring significantly fewer parameters and training time. As a real-world application, we apply a two-dimensional Tensorized Fourier Neural Operator (TFNO) to the nuclear chart, learning a correction to state-of-the-art nuclear mass models as a partially observed residual field. A TFNO ensemble reaches a held-out root-mean-square error of 198.2 keV, placing it among the best recent neural-network approaches while retaining high parameter efficiency and short training times. More broadly, these results introduce NOs as a scalable framework for finite-dimensional function interpolation, from analytic benchmarks to structured scientific data.