Nonlinear System Identification: Learning while respecting physical models using a sequential Monte Carlo method

TL;DR

This paper introduces a sequential Monte Carlo approach for nonlinear system identification that incorporates physical models and learns unknown parameters without bias, demonstrated on water tank and disease spread models.

Contribution

It presents a novel application of sequential Monte Carlo methods to nonlinear system identification, integrating physical knowledge and Bayesian parameter estimation.

Findings

Effective in modeling water tank overflow system

Successfully applied to disease spread compartmental model

Provides unbiased parameter learning in nonlinear systems

Abstract

Identification of nonlinear systems is a challenging problem. Physical knowledge of the system can be used in the identification process to significantly improve the predictive performance by restricting the space of possible mappings from the input to the output. Typically, the physical models contain unknown parameters that must be learned from data. Classical methods often restrict the possible models or have to resort to approximations of the model that introduce biases. Sequential Monte Carlo methods enable learning without introducing any bias for a more general class of models. In addition, they can also be used to approximate a posterior distribution of the model parameters in a Bayesian setting. This article provides a general introduction to sequential Monte Carlo and shows how it naturally fits in system identification by giving examples of specific algorithms. The methods are illustrated on two systems: a system with two cascaded water tanks with possible overflow in both tanks and a compartmental model for the spreading of a disease.