Data-Driven Approach to Nonlinear Dynamic Equation Discovery

• Activity Number: 131 - Methods for Spatial, Temporal, and Spatio-Temporal Data
• Type: Contributed
• Date/Time: Monday, August 9, 2021 : 1:30 PM to 3:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Joshua S North* and Erin M Schliep and Christopher Wikle
• Companies: University of Missouri and University of Missouri and University of Missouri
• Keywords: Stochastic Differential Equation; Stochastic Gradient MCMC; Equation Discovery; Non-linear Modeling

Abstract

Many real-world atmospheric, ecological, and economic processes are governed by complex, non-linear, interactions, and differential equations are commonly used to approximate the dynamics of these complex systems. While the approximating differential equations generally capture the dynamics of the system well, they impose a rigid modeling structure that assumes the dynamics of the system. Recently, there has been work in the applied math and computer science community to use a data-driven approach to learn the dynamics that govern complex systems. Here, we present a Bayesian data-driven approach to non-linear dynamic equation discovery that is robust to measurement noise and stochastic forcing. We show the effectiveness of our method on simulated systems and then apply the method to a real-world environmental process.