PR-MLP: a physics-regularized deep learning framework for rapid prediction of impurity-mode instabilities in tokamaks

Microinstabilities associated with impurities in tokamak plasmas can affect particle transport and radiative power loss; rapid identification of weakly unstable regimes is essential for parameter scans near stability boundaries. In this work, we develop MLP surrogate models for the HD7 gyrokinetic impurity-mode solver, including a conventional MLP and PR-MLP. The models are trained on 15,994 valid HD7 samples from 264 independent scan curves to predict the normalized real frequency ωr and normalized growth rate γ directly output by HD7. To avoid overoptimistic evaluation, the data are partitioned by scan curve rather than by random points. Near marginal stability, the PR-MLP supervised loss is supplemented with a non-negativity penalty on the predicted growth rate and a quasi-neutrality-based soft regularization term. On the primary test split, PR-MLP achieved RMSEs of 0.0054 and 0.0067 in predicting the normalized growth rate γ and normalized real frequency ωr, respectively. In the weakly unstable regime (γ < 0.05) on this normalized scale, it reduced the mean absolute error of the predicted growth rate, γ̂, from 0.0070 for the conventional MLP to 0.0043 (39.3%). These results show that physics-based regularization improves local surrogate accuracy near stability boundaries. PR-MLP thus provides an efficient and physically informed tool for rapid parameter-space prescreening followed by targeted HD7 verification.