Neural Operators as Efficient Function Interpolators
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914544890150912 |
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| author | Niarchos, Vasilis Sirbu, Angelos Trifinopoulos, Sokratis |
| author_facet | Niarchos, Vasilis Sirbu, Angelos Trifinopoulos, Sokratis |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07792 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Neural Operators as Efficient Function Interpolators Niarchos, Vasilis Sirbu, Angelos Trifinopoulos, Sokratis Machine Learning Artificial Intelligence Numerical Analysis Nuclear Theory 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. |
| title | Neural Operators as Efficient Function Interpolators |
| topic | Machine Learning Artificial Intelligence Numerical Analysis Nuclear Theory |
| url | https://arxiv.org/abs/2605.07792 |