A Bayesian Approach for Data-Driven Dynamic Equation Discovery

• Activity Number: 414 - ENVR Student Paper Award Winners
• Type: Topic Contributed
• Date/Time: Wednesday, August 10, 2022 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Joshua North* and Christopher K. Wikle and Erin Schliep
• Companies: University of Missouri Columbia and University of Missouri and University of Missouri
• Keywords: Nonlinear Dynamic Equation; System Discovery; Statistical Differential Equations

Abstract

Many real-world geophysical, ecological, and biological 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 well, they impose a rigid modeling structure that assumes the dynamics of the system are known. In many complex systems we may know some dynamical relationships a priori, but not the form of the governing equations. Discovering the form of the governing equations can lead to a better understanding of these complex systems and the interactions within. Here, we present a Bayesian data-driven approach to nonlinear dynamic equation discovery that can accommodate measurement noise and missing data. We show the effectiveness of our method on simulated data and apply the method to real-world processes.