Abstract

Data-driven methods for approximating the underlying dynamics of a complex system have emerged in many different fields of science and engineering. Many approaches posit an autonomous model for the dynamics, such that in the limit of no noise the future state of the system is predictable entirely by its past. Several established methods, such as Dynamic Mode Decomposition (DMD) and Sparse Identification of Nonlinear Dynamics (SINDy), have achieved great success in simultaneously predicting the structure of unknown dynamical systems and their parameter values in autonomous systems. However, many systems of interest, particularly in biology and neuroscience, are connected to an outside environment and thus are not autonomous, and in many cases the stimulation is completely unknown. We propose an extension of these established methods for simultaneously learning an external control signal along with model structure and parameter values. This requires first extending the methods to a Bayesian framework, and successfully separates the underlying dynamical systems and control signals even in chaotic and noisy? systems.