Sparse Identification of Evolution Equations via Bayesian Model Selection
A data-driven method for discovering the governing differential equations of a nonlinear dynamical system that extends SINDy's thresholded least-squares regression with two error measures, the deviation from the data's time derivative and a Wasserstein-metric forecasting score, combined in a Bayesian optimization framework that tunes thresholding and error-weighting hyperparameters with per-equation regularization. It is robust to poor time-derivative estimates and low sampling rates, and is demonstrated on cylinder wake flow and on extracting differential equations from a trained recurrent network for explainable AI.
Sparse identification of evolution equations via bayesian model selection Tim W. Kroll1, 2, ∗and
Sparse identification recovers a governing system of differential equations for a dynamical system directly from observed trajectories by selecting a few active terms from a large candidate library, …