Decoupling P-NARX models using filtered CPD

Abstract Nonlinear Auto-Regressive eXogenous input (NARX) models are a popular class of nonlinear dynamical models. Often polynomial basis expansion is used to describe the internal multivariate mapping (P-NARX). Resorting fixed functions convenient since it results in closed form solution estimation problem. The drawback, however, that predefined does not necessarily lead sparse representation relationship, typically resulting very large numbers parameters. So-called decoupling techniques were specifically designed reduce functions. It was found that, often, more efficient parameterisation can be retrieved by rotating towards new basis. Characteristic decoupled structure expressed basis, relationship structured such only single-input single-output required. Classical unfit deal with case NARX In this work, limitation overcome adopting filtered CPD method Decuyper et al. (2021b). approach illustrated on data from Sliverbox benchmark: measurement an electronic circuit implementation forced Duffing oscillator.