Dynamical System Identification by Bayesian Inference
Robert K. Niven, Ali Mohammad‐Djafari, Laurent Cordier, Markus Abel, Markus Quade · Proceedings of the Australasian Fluid Mechanics Conference/Proceedings - Australasian Fluid Mechanics Conference · 2020
Fluid flow systems provide physical expressions of dynamical systems, typically written x = f(x), where x is the state vector and f is the system function or model. The identification of the dynamical system f from time-series data {x1, ..., xn}, an inverse problem, is a long-held challenge. Historically, this has been examined by linear or nonlinear regression, convolution methods, neural networks or evolutionary computation, but these mostly lie outside the rigorous framework of Bayesian inference. Here we examine the maximum a-posteriori (MAP) Bayesian method for system identification, which is shown to be equivalent to Tikhonov regularization, and in fact provides sound theoretical justifications for the choices of residual and regularization terms. The joint maximum a-posteriori (JMAP) and variational Bayesian approximation (VBA) are demonstrated by comparison to the popular SINDy regularization method, by application to the Rössler dynamical system.