Bayesian system ID: optimal management of parameter, model, and measurement uncertainty
- PDF / 4,090,459 Bytes
- 27 Pages / 547.087 x 737.008 pts Page_size
- 96 Downloads / 181 Views
ORIGINAL PAPER
Bayesian system ID: optimal management of parameter, model, and measurement uncertainty Nicholas Galioto
· Alex Arkady Gorodetsky
Received: 13 April 2020 / Accepted: 28 August 2020 © Springer Nature B.V. 2020
Abstract System identification of dynamical systems is often posed as a least squares minimization problem. The aim of these optimization problems is typically to learn either propagators or the underlying vector fields from trajectories of data. In this paper, we study a first principles derivation of appropriate objective formulations for system identification based on probabilistic principles. We compare the resulting inference objective to those used by emerging data-driven methods based on dynamic mode decomposition (DMD) and system identification of nonlinear dynamics (SINDy). We show that these and related least squares formulations are specific cases of a more general objective function. We also show that the more general objective function yields more robust and reliable recovery in the presence of sparse data and noisy measurements. We attribute this success to an explicit accounting of imperfect model forms, parameter uncertainty, and measurement uncertainty. We study the computational complexity of an approximate marginal Markov Chain Monte Carlo method to solve the resulting inference problem and numerically compare our results on a number of canonical systems: linear pendulum, nonlinear pendulum, the Van der Pol oscillator, the Lorenz system, and a reaction–diffusion system. The results of N. Galioto (B)· A. A. Gorodetsky Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109, USA e-mail: [email protected] A. A. Gorodetsky e-mail: [email protected]
these comparisons show that in cases where DMD and SINDy excel, the Bayesian approach performs equally well, and in cases where DMD and SINDy fail to produce reasonable results, the Bayesian approach remains robust and can still deliver reliable results. Keywords System ID · Approximate marginal MCMC · UKF-MCMC · Bayesian inference · DMD · SINDy
1 Introduction Recovering nonlinear models of dynamical systems from data is quickly becoming a primary enabling technology for analysis and decision making in fields spanning science and engineering where first principles models are often incomplete or simply unavailable. Examples range from forecasting the weather and climate [1–3], predicting fluid flows [4–6], and enabling adaptive control [7–10]. All of these fields have a long history of developing estimation and system identification techniques such as advanced Kalman filtering in forecasting [11,12], decomposition methods for computational fluid dynamics [13–15], and a wide ranging set of schemes in adaptive control [16– 18]. In this paper, we compare the implicit and explicit optimization formulations posed by several representative approaches, and we demonstrate that algorithms that appropriately manage parameter, model, and measurement uncertainty in a cohesive manner are often
123
N. Galioto, A. A. G
Data Loading...
