Neural Operators as Efficient Function Interpolators

• URL: http://arxiv.org/abs/2605.07792v1
• Date: Fri, 08 May 2026 14:30:12 GMT
• Title: Neural Operators as Efficient Function Interpolators
• Abstract summary: Neural operators (NOs) are designed to learn maps between infinite-dimensional function spaces.<n>We show that NOs can match or outperform standard multilayer perceptrons and Kolmogorov-Arnold Networks in accuracy.<n>A TFNO ensemble reaches a held-out root-mean-square error of 198.2 keV, placing it among the best recent neural-network approaches.
• Score: 0.764671395172401
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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