用神经算子高效插值函数，参数少、速度快、精度高。
Neural Operators as Efficient Function Interpolators
- 将有限维函数视为基空间上的复合算子，重构神经算子应用范式。
- 在高维解析函数上，精度媲美甚至超过传统网络，参数量减少70%以上。
- 适用于科学数据建模，如核质量预测，兼具高效与高精度。
神经算子（NOs）旨在学习无限维函数空间之间的映射。本文提出一种新范式：通过引入辅助基空间，任意有限维函数可被视为作用于基空间函数的算子。在复杂度递增的解析函数基准测试中，NOs在精度上达到或超越标准多层感知机和柯尔莫哥洛夫-阿诺德网络，同时显著减少参数量和训练时间。作为真实应用，我们使用二维张量化傅里叶神经算子（TFNO）对核素图进行建模，学习先进核质量模型的残差修正场。一个TFNO集成模型在留出数据上达到198.2 keV的均方根误差，跻身当前最佳神经网络方法之列，且保持高参数效率与短训练时间。总体而言，这些结果将神经算子确立为从解析基准到结构化科学数据的可扩展函数插值框架。
原文摘要 · Abstract (English)
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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