A statistical method for model extraction and model selection applied to the temperature scaling of the L-H transition

Access to the H mode of confinement in tokamaks is characterized by an abrupt transition, which has been the subject of continuous investigation for decades. Various theoretical models have been developed and multi-machine databases of experimental data have been collected. In this paper, a new methodology is reviewed for the investigation of the scaling laws for the temperature threshold to access the H mode. The approach is based on symbolic regression via genetic programming and allows first the extraction of the most statistically reliable models from the available experimental data. Nonlinear fitting is then applied to the mathematical expressions found by symbolic regression; this second step permits to easily compare the quality of the data-driven scalings with the most widely accepted theoretical models. The application of a complete set of statistical indicators shows that the data-driven scaling laws are qualitatively better than the theoretical models. The main limitations of the theoretical models are that they are all expressed as power laws, which are too rigid to fit the available experimental data and to extrapolate to ITER. The proposed method is absolutely general and can be applied to the extraction or scaling law from any experimental database of sufficient statistical relevance.