Learning Governing Equations of Unobserved States in Dynamical Systems
This work addresses a gap in data-driven modeling for partially-observed dynamical systems, which is incremental as it builds on existing neural ODE and symbolic regression techniques.
The authors tackled the problem of learning governing equations for partially-observed dynamical systems, demonstrating that their hybrid neural ODE and symbolic regression method successfully learned the true underlying equations for unobserved states in Lotka-Volterra and Lorenz systems, with robustness to measurement noise.
Data-driven modelling and scientific machine learning have been responsible for significant advances in determining suitable models to describe data. Within dynamical systems, neural ordinary differential equations (ODEs), where the system equations are set to be governed by a neural network, have become a popular tool for this challenge in recent years. However, less emphasis has been placed on systems that are only partially-observed. In this work, we employ a hybrid neural ODE structure, where the system equations are governed by a combination of a neural network and domain-specific knowledge, together with symbolic regression (SR), to learn governing equations of partially-observed dynamical systems. We test this approach on two case studies: A 3-dimensional model of the Lotka-Volterra system and a 5-dimensional model of the Lorenz system. We demonstrate that the method is capable of successfully learning the true underlying governing equations of unobserved states within these systems, with robustness to measurement noise.