Learning Governing Equations of Unobserved States in Dynamical Systems
CoRR(2024)
Abstract
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.
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