Many inference problems relate to the dynamical system, x’=f(x). One primary problem in applications is that of system identification, i.e., how should the user accurately and efficiently identify the model f(x), including its functional family or parameter values, from discrete time-series data? One of the most successful algorithms to this end is the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm, which provides an interpretable representation of f(x) by performing sparse linear regression to represent f(x) as a sparse linear combination of elements of a large library of candidate nonlinear functions. We propose recasting this deterministic linear regression problem as a Bayesian inference problem, with the representation of f(x) in terms of the candidate functions determined by the posterior distribution determined by data and an appropriate sparsity-inducing prior. This allows for explicit quantification of aleatoric uncertainty of the inferred model, providing an important advantage over deterministic methods. Various methods and implementations for performing the inference and sparsity enforcement are considered and compared in terms of accuracy and computational efficiency.

Zoom: https://ncsu.zoom.us/j/98139608681?pwd=Z3RnRGRYL3JCRnlNT0NFdmZLRzRtdz09