Machine learning for the identification of scaling laws and dynamical systems directly from data in fusion

Original methods to extract equations directly from experimental signals are presented. These techniques have been applied first to the determination of scaling laws for the threshold between the L and H mode of confinement in Tokamaks. The required equations can be extracted from the weights of neural networks and the separating hyperplane of Support Vector Machines. More powerful tools are required for the identification of differential equations directly from the time series of the signals. To this end, recurrent neural networks have proved to be very effective to properly identify ordinary differential equations and have been applied to the coupling between sawteeth and ELMs.