Influence of warmup on LSTM cell state propagation

Ascertain how the LSTM-P architecture’s cell state c_k propagation is affected by the warmup procedure that overwrites the first element of the hidden state with the true normalized magnetic field, and compare this behavior to the GRU-P warmup where only a single hidden state is present.

Background

The authors use a warmup mechanism that injects the true H-field into the first element of the hidden state during the observed portion of the sequence. For GRUs, this mechanism is straightforward because there is a single hidden state, but for LSTMs the separate cell state may behave differently.

The paper explicitly states uncertainty about how this warmup influences the LSTM’s cell state, highlighting a methodological gap relevant to reliable training and initialization of LSTM-based models for magnetic hysteresis.

References

Note that for the \gls{lstm} it is not clear how the propagation of $\bm{c}_k$ is influenced by the warmup via~eq:lstm_out, compared to the \gls{gru} where a much smaller amount of operation is applied to the singular state of the model (cf.~eq:GRU_cell_eq).

— RHINO-MAG: Recursive H-Field Inference based on Observed Magnetic Flux under Dynamic Excitation  (2603.29745 - Vater et al., 31 Mar 2026) in Section 3.2 LSTM with direct prediction (LSTM-P)