Learning sparse dynamic linear systems using stable spline kernels and exponential hyperpriors
We introduce a new Bayesian nonparametric approach to identification of sparse dynamic linear systems. The impulse responses are modeled as Gaussian processes whose autocovariances encode the BIBO stability constraint, as defined by the recently introduced “Stable Spline kernel”. Sparse solutions are obtained by placing exponential hyperpriors on the scale factors of such kernels. Numerical experiments regarding estimation of ARMAX models show that this technique provides a definite advantage over a group LAR algorithm and state-of-the-art parametric identification techniques based on prediction error minimization.
Code (0)
등록된 구현이 없습니다.
Tasks
Gaussian ProcessesSimilar Papers 제목 키워드 기반
Physics-informed Spline Learning for Nonlinear Dynamics Discovery
Dynamical systems are typically governed by a set of linear/nonlinear differential equations. Distilling the analytical form of these equations from very limited data remains intractable in many disciplines such as physi…
SplineFlow: Flow Matching for Dynamical Systems with B-Spline Interpolants
Flow matching is a scalable generative framework for characterizing continuous normalizing flows with wide-range applications. However, current state-of-the-art methods are not well-suited for modeling dynamical systems,…
Bayesian Spline Learning for Equation Discovery of Nonlinear Dynamics with Quantified Uncertainty
Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable governing equations from measurement data c…
Equation DiscoveryDifferentiable Sparse Identification of Lagrangian Dynamics
Data-driven discovery of governing equations from data remains a fundamental challenge in nonlinear dynamics. Although sparse regression techniques have advanced system identification, they struggle with rational functio…
Stable spline identification of linear systems under missing data
A different route to identification of time-invariant linear systems has been recently proposed which does not require committing to a specific parametric model structure. Impulse responses are described in a nonparametr…
Gaussian Processes