Nonlinear system identification with regularized Tensor Network B-splines
This addresses the problem of efficient nonlinear system identification for engineers and researchers, offering a novel method for handling high-dimensional inputs and lags.
The paper tackles the curse of dimensionality in identifying nonlinear systems using multivariate B-splines by introducing a Tensor Network B-spline model that reduces computational and storage complexity, achieving state-of-the-art performance on a benchmark system with a 16-dimensional B-spline identified in 4 seconds.
This article introduces the Tensor Network B-spline model for the regularized identification of nonlinear systems using a nonlinear autoregressive exogenous (NARX) approach. Tensor network theory is used to alleviate the curse of dimensionality of multivariate B-splines by representing the high-dimensional weight tensor as a low-rank approximation. An iterative algorithm based on the alternating linear scheme is developed to directly estimate the low-rank tensor network approximation, removing the need to ever explicitly construct the exponentially large weight tensor. This reduces the computational and storage complexity significantly, allowing the identification of NARX systems with a large number of inputs and lags. The proposed algorithm is numerically stable, robust to noise, guaranteed to monotonically converge, and allows the straightforward incorporation of regularization. The TNBS-NARX model is validated through the identification of the cascaded watertank benchmark nonlinear system, on which it achieves state-of-the-art performance while identifying a 16-dimensional B-spline surface in 4 seconds on a standard desktop computer. An open-source MATLAB implementation is available on GitHub.