Decoupling multivariate functions using a non-parametric Filtered CPD approach

TL;DR

This paper introduces a non-parametric filtered CPD method for decoupling multivariate functions, enabling the extraction of underlying structures even with non-unique decompositions, which benefits various modeling applications.

Contribution

The paper presents a novel filtered CPD approach that effectively decouples multivariate functions without relying on parametric basis expansions, even in non-unique cases.

Findings

Successfully decouples complex multivariate functions.

Handles non-uniqueness in tensor decompositions.

Reduces parameters and reveals underlying structure.

Abstract

Black-box model structures are dominated by large multivariate functions. Usually a generic basis function expansion is used, e.g. a polynomial basis, and the parameters of the function are tuned given the data. This is a pragmatic and often necessary step considering the black-box nature of the problem. However, having identified a suitable function, there is no need to stick to the original basis. So-called decoupling techniques aim at translating multivariate functions into an alternative basis, thereby both reducing the number of parameters and retrieving underlying structure. In this work a filtered canonical polyadic decomposition (CPD) is introduced. It is a non-parametric method which is able to retrieve decoupled functions even when facing non-unique decompositions. Tackling this obstacle paves the way for a large number of modelling applications.