Data-Driven Estimation of Net Toroidal Plasma Current Waveforms in OH-Programmed TJ-II Discharges

In the TJ-II stellarator, a finite net toroidal plasma current can modify the rotational transform profile and shift the radial position of low-order rational surfaces. Because these surfaces can influence edge gradients, turbulence and confinement in low-shear configurations, estimating the current waveform is relevant for the preparation and interpretation of scenarios programmed with the ohmic heating (OH) coil. This work compares two data-driven estimators using 87 selected OH-programmed discharges from the fixed magnetic configuration 100_44_64, divided into 50 training, 20 validation and 17 test cases. The first estimator uses MultiGene Genetic Programming (MGGP) to obtain explicit equations. The second is a nonlinear autoregressive recurrent neural network with exogenous inputs (NARX-RNN), implemented with long short-term memory (LSTM) branches. The symbolic equations and their settings were selected using the training and validation discharges, while the test set was used only for final evaluation. On the original 17-discharge test partition, the general OH-normalized equation achieved an overall root-mean-square error (RMSE) of 0.4898 kA, whereas the compact equation achieved 0.5700 kA with substantially lower expression complexity. After routine signal quality control, two test records were excluded, and the final comparison used 15 discharges. On this set, the mean discharge-wise RMSE was 0.350 kA for the NARX-RNN, 0.515 kA for the general symbolic equation and 0.576 kA for the compact equation. The NARX-RNN also gave a median RMSE of 0.230 kA. Whether this current error level is sufficient for positioning a particular rational surface depends on the local rotational transform response and magnetic shear, so no universal current error threshold for edge control is assigned here. The symbolic models were less accurate on average but provided explicit relations involving OH amplitude, previous current information, electron cyclotron resonance heating, fuelling and wall-conditioning variables.