Neural ODE

In theory, if we define the hysteretic response as a dynamical system

$$\text{dv}Bt=f(t,B)$$

where there is a constant $I$ and $\dot{I}$ for each time step $t$, which then is assumed to also model $\text{dv}BI$.

Since we don’t know the true ODE describing a hysteretic system, we parameterize $f$ with a neural network, and use a neural ODE to solve the differential equation.

Tips and tricks

The time axis in each sample in each batch should start with $0$ and be normalized so that $t\in [0,1]$, as with any neural network input. This requires the max time span in any sample to be known a priori.

Other neural network inputs should also be normalized.

$I$ and $\dot{I}$ must be passed to the ODE solver as an args, to be passed to the function to be solved, and then be linearly interpolated at $t$, since $t$ can be any continuous value between $0$ and $1$.

To investigate

• Combine Adam and L-BFGS for faster Neural ODE convergence [priority:: medium]
• Re-investigate Neural ODEs for hysteresis prediction for journal paper [priority:: medium] [completion:: 2025-09-01]
• Re-investigate Fourier Neural Operators for hysteresis prediction for journal paper [priority:: medium] [completion:: 2025-09-01]