# Neural Operators as Efficient Function Interpolators

arXiv: https://arxiv.org/abs/2605.07792 · HTML: https://mlsanity.com/paper/2605.07792/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 37 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 10 of 10)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Multi-Grid Tensorized Fourier Neural Operator for High-Resolution PDEs](https://mlsanity.com/paper/2310.00120/) (2023)
- [A Library for Learning Neural Operators](https://mlsanity.com/paper/2412.10354/) (2024)
- [An operator learning perspective on parameter-to-observable maps](https://mlsanity.com/paper/2402.06031/) (2024)
- [From Neurons to Neutrons: A Case Study in Interpretability](https://mlsanity.com/paper/2405.17425/) (2024)
- [Interpolating Neural Network-Tensor Decomposition (INN-TD): a scalable and interpretable approach for large-scale physics-based problems](https://mlsanity.com/paper/2503.02041/) (2025)
- [NuCLR: Nuclear Co-Learned Representations](https://mlsanity.com/paper/2306.06099/) (2023)
- [Further exploration of binding energy residuals using machine learning and the development of a composite ensemble model](https://mlsanity.com/paper/2503.11066/) (2025)
- [The DNA of nuclear models: How AI predicts nuclear masses](https://mlsanity.com/paper/2508.08370/) (2025)

## Abstract (arXiv)

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.