Machine learning identifies nullclines in oscillatory dynamical systems
This addresses a challenge in dynamical systems analysis for researchers, but it appears incremental as it builds on existing neural network approaches for feature identification.
The paper tackles the problem of identifying nullclines from oscillatory time series data, introducing CLINE, a neural network-based method that uncovers hidden geometric structures in phase space and converts them into symbolic differential equations, with validation on various systems.
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.