Machine-learning perspectives on Volterra system identification

The Volterra series has been used in nonlinear system identification (NLSI) for decades; its frequency-domain counterpart allows a generalization of 'resonance curves' for nonlinear systems-so-called higher-order frequency-response functions (HFRFs). Estimating the terms in the series has often proved to be a challenge; however, the (comparatively) recent uptake of machine-learning technology into engineering dynamics has led to advances in the identification of the series-both for the Volterra kernels themselves and for the HFRFs. The current paper provides an overview of a number of approaches based on neural networks, Gaussian processes (GPs) and reproducing kernel Hilbert spaces (RKHSs), and presents new results for multi-input multi-output (MIMO) systems based on neural networks.This article is part of the theme issue 'Frontiers of applied inverse problems in science and engineering'.