Learning multivariate functions with low-dimensional structures using polynomial bases

In this paper we propose a method for the approximation of high-dimensional functions over finite intervals with respect to complete orthonormal systems of polynomials. An important tool for this is the multivariate classical analysis of variance (ANOVA) decomposition. For functions with a low-dimensional structure, i.e., a low superposition dimension, we are able to achieve a reconstruction from scattered data and simultaneously understand relationships between different variables. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper proposes a method for approximating high-dimensional functions over finite intervals using complete orthonormal systems of polynomials and multivariate classical analysis of variance (ANOVA) decomposition. For functions with low-dimensional structures, reconstruction from scattered data can be achieved while understanding relationships between different variables.