Modeling a Physical Chaotic System by Measuring its Dynamics in Time using Gradient Descent Algorithms

A non-linear electrical circuit consisting of a resistor, inductor and diode exhibits complicated dynamics such as period doubling bifurcations and chaos. Due to the non-linearity of the circuit components, especially the diode, such a circuit is hard to model physically. Nonetheless, using gradient descent algorithms on voltage measurements over the different components of the circuit, we solve the inverse problem and give a dynamical model of the circuit. The model is in the form of an ordinary differential equation dependant only on standard variables in electric circuits such as voltage and cummulative charge on the circuit components. Our method can be further implemented to other systems that show intrinsically unpredictable dynamics.