Learning Dynamics of Oscillators with Applications to Circadian Rhythms
The ability to accurately forecast the dynamics of a complex oscillating system is fundamental to the study of many physical and biological systems. This is especially important for understanding and predicting the bodies natural 24 hour oscillations in physiology and behavior known as circadian rhythms. The response of oscillators to external perturbations can be traced out either theoretically or experimentally into phase response curves. In this work, we study the application of model discovery techniques to complex nonlinear oscillator systems using phase response data. Using simulated data we examine how well these techniques perform when the perturbations are generalized from the training data. Finally, we discuss the application of these techniques to the study of circadian rhythms and discuss some preliminary results for using wearable data (apple watch, fitbit) to build personalized models of circadian rhythms.