Machine learning identifies nullclines in oscillatory dynamical systems

Abstract

We introduce CLINE (Computational Learning and Identification of Nullclines), a neural network-based method that uncovers the hidden structure of nullclines from oscillatory time series data. Unlike traditional approaches aiming at direct prediction of system dynamics, CLINE identifies static geometric features of the phase space that encode the (non)linear relationships between state variables. It overcomes challenges such as multiple time scales and strong nonlinearities while producing interpretable results convertible into symbolic differential equations. We validate CLINE on various oscillatory systems, showcasing its effectiveness.