A Bayesian Approach for Spatio-Temporal Data-Driven Dynamic Equation Discovery

TL;DR

This paper introduces a Bayesian framework for discovering nonlinear spatio-temporal dynamic equations from noisy and incomplete data, enhancing understanding of complex systems in science and engineering.

Contribution

It presents a novel Bayesian method that handles measurement noise and missing data for data-driven discovery of dynamic equations, with applications to simulated and real-world systems.

Findings

Successfully inferred governing equations from noisy data

Demonstrated robustness to missing observations

Applied to real-world vorticity data in fluid dynamics

Abstract

Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent real-world dynamics well. Since the true dynamics of these complex systems are generally unknown, learning the governing equations can improve our understanding of the mechanisms driving the systems. Here, we develop a Bayesian approach to data-driven discovery of non-linear spatio-temporal dynamic equations. Our approach can accommodate measurement noise and missing data, both of which are common in real-world data, and accounts for parameter uncertainty. The proposed framework is illustrated using three simulated systems with varying amounts of observational uncertainty and missing data and applied to a real-world system to infer the temporal evolution of the vorticity of the streamfunction.