Dipole modeling methods overview

PhyLSTM

• W/o polynomial subtracted
• W/ (autofitted) polynomial subtracted
• W/ calibration function polynomial (linear) subtracted
• W/ calibration function subtracted Transformer
• W/o polynomial subtracted
• W/ (autofitted) polynomial subtracted
• W/ calibration function polynomial (linear) subtracted
• W/ calibration function subtracted

PINNs

Challenges

• Large amounts of data …
• … but low variety (first I/B quadrant only)
• noisy data ($10^{-6}$)
• high accuracy required ($10^{-5}$)
• discontinuous hysteresis ODE
• No “known” initial state, besides ($I_0$, $B_0$)
• Can we autoregressive predictions? For how long?

We need to deal with

• Hysteresis ODE (time independent), many to choose from
• Eddy current ODE (time dependent), linear first order
• Potentially irregularly sampled data (in case of Adaptive downsampling)
  • Gaps could be very small (ms) or large (s)