Function-On-Function Regression Through Separable Neural Operators

2026-08-19

AI Summary

本文提出了一种可分离神经算子方法，用于函数对函数回归模型中一般回归算子的估计，解决了传统线性或非线性扩展模型的局限。

Abstract

This paper investigates the estimation of the regression operator in function-on-function regression models. While traditional research has predominantly focused on linear models or their immediate nonlinear extensions, we propose a neural operator approach to accommodate general regression operators under mild smoothness assumptions. Operator learning has emerged as an active area of machine learning, particularly for solving physical models governed by partial differential equations. Using this paradigm, our methodology introduces the separable neural operator, a neural-operator architecture that represents the regression operator through input-dependent coefficient functions and output-dependent basis functions. Beyond adapting this architecture to the regression operator estimation problem, we establish the consistency of the estimator under relatively mild smoothness and sampling conditions, allowing functional data to be observed on dense, possibly irregular, discrete grids. We also apply the proposed approach to the BGC Argo data and demonstrate its potential for oceanographic research.

Problem

• function-on-function regression
• regression operator
• neural operator

Innovation

• separable neural operator
• function-on-function regression
• operator learning
• functional data