PINNS 2024 course project

The goal of the project is to build a PINN that learns both magnetic hysteresis and eddy currents in one model.

The macroscopic contribution of field from the eddy currents can be simplified into a linear ODE. Similarly, the magnetic hysteresis is often defined as an ODE, for example in the Jiles-Atherton model and Flatley model where the relationship $\frac{\text{d}M}{\text{d}H}$ is modelled.

Consequently, we can define our problem as a wiki:Dynamical system as the following:

$$\begin{array}{rl}\text{dv}Bt& =f(B,\xi ,I,J)\\ \text{dv}\xi t& =g(\xi ,B)\\ \text{dv}Jt& =h(J,B)\end{array}$$

Under the assumption that $H\propto I$, we define state variables $\xi$ and $J$ that represent the hysteretic state, and eddy current density, respectively.

We solve this system using Neural ODEs [@chenNeuralOrdinaryDifferential2019] and PyTorch Lightning