Accounting for Hysteresis and Eddy Currents in Finite Element Simulations of Ferromagnetic Laminated Cores using a Recurrent Neural Network

What the math gives to ML

The paper contains a useful state-update structure beyond its use of an RNN surrogate: each latent reversible state is obtained by projecting its previous value onto a ball centered at the current input, with a branch-specific radius controlling memory persistence. This creates a piecewise-smooth, bounded-memory recurrent cell that preserves state during small input reversals and updates only when the input moves beyond a threshold. The transferable asset is the explicit geometric hysteresis operator, which can serve as an inductive bias for sequence models handling regime changes, temporal hysteresis, or noisy trajectories. A practical first test is to replace part of a GRU or state-space layer with several differentiable threshold-projection memory branches and evaluate long-range forecasting and stability.