Data-Driven Discovery of Nonlinear Dynamical Systems from Noisy and Sparse Observations

Sparse Identification of Nonlinear Dynamics (SINDy) is a data-driven algorithm for interpretability mod-eling. SINDy has a strong ability to learn dynamical systems from time series data. Sparse Identification of Nonlinear Dynamics (SINDy) can extract equations from data, but its performance will degrade when data has noise or sparse. In order to deal with this case, the idea of Monte Carlo Markov Chain (MCMC) is introduced, which is used to optimally select models. The SINDy with MCMC (MCMC-SINDy) can comprehensively discover model structures by employing random samples in data space. Simulation results show that MCMC-SINDy is more robust than SINDy with 1 % -15 % levels of noise or sparse 0.5. These results are promising for the discovery of governing equations for complex systems in neuroscience, power grids, epidemiology, finance or ecology, where governing equations have remained elusive. mportantly, compared to existing machine learning methods, the accuracy of modeling using MCMC SINDy is higher.