Model structures and fitting criteria for system identification with neural networks

TL;DR

This paper presents a novel approach for system identification using neural networks that incorporates domain knowledge, employs regularized multi-step simulation error minimization, and discusses limitations of naive methods.

Contribution

It introduces a new fitting criterion combining multi-step simulation error with regularization to improve neural network-based system identification.

Findings

Efficient estimation of neural network parameters and initial conditions.

Regularization enforces consistency with system dynamics.

Discussion of pitfalls in naive prediction and simulation error minimization.

Abstract

This paper focuses on the identification of dynamical systems with tailor-made model structures, where neural networks are used to approximate uncertain components and domain knowledge is retained, if available. These model structures are fitted to measured data using different criteria including a computationally efficient approach minimizing a regularized multi-step ahead simulation error. In this approach, the neural network parameters are estimated along with the initial conditions used to simulate the output signal in small-size subsequences. A regularization term is included in the fitting cost in order to enforce these initial conditions to be consistent with the estimated system dynamics. Pitfalls and limitations of naive one-step prediction and simulation error minimization are also discussed.