Power-law-anchored residual learning for H-mode energy confinement time in tokamaks: interpolation and parameter-defined extrapolation

Abstract

Reliable prediction of the energy confinement time is essential for magnetic-confinement fusion. Conventional power-law scalings provide constrained extrapolation trends but cannot represent complex nonlinearities, whereas neural networks interpolate accurately but may behave unpredictably outside the training distribution. We propose a unified power-law-anchored residual-learning framework in which a frozen empirical power-law scaling supplies the global trend and a nonlinear model learns only the systematic residual in logarithmic space. PLR-KAN is developed as the primary implementation, while a parameter-matched PLR-MLP serves as a controlled architecture replacement. Using the ITPA DB5.2.3 H-mode confinement database, we evaluate interpolation and parameter-defined held-out cohorts over ten complete training pipelines. PLR-KAN retains near-best interpolation accuracy, achieving R2=0.9671+/-0.0027, while substantially improving the stability of direct KAN under parameter-defined distribution shifts. It outperforms direct KAN across all five non-epsilon single-parameter-defined cohorts and the core-five joint cohort, reaching R2=0.9263+/-0.0157 in the latter. Results from PLR-MLP further demonstrate that the benefit of power-law anchoring is not specific to KAN, although the effectiveness of residual transfer remains architecture and direction dependent. As an exploratory extension, a Mahalanobis-distance-based prediction-time gate improves stability in selected shifted regions but is not universally beneficial and cannot compensate for missing device or physics-regime coverage. Overall, power-law-anchored residual learning provides a practical balance between nonlinear interpolation capability and empirically constrained extrapolation behavior.