A Bayesian Approach for Data-Driven Dynamic Equation Discovery

Many real-world scientific and engineering processes are governed by complex nonlinear interactions, and differential equations are commonly used to explain the dynamics of these complex systems. While the differential equations generally capture the dynamics of the system, they impose a rigid modeling structure that assumes the dynamics of the system are known. Even when some of the dynamical relationships are known, rarely do we know the form of the governing equations. Learning these governing equations can improve our understanding of the mechanisms driving the complex systems. Here, we present a Bayesian data-driven approach to nonlinear dynamic equation discovery. The Bayesian framework can accommodate measurement noise and missing data, which are common in these systems, and accounts for model parameter uncertainty. We illustrate our method using simulated data as well as three real-world applications for which dynamic equations are used to study real-world processes. Supplementary materials accompanying this paper appear online.