Probabilistic locked mode predictor in the presence of a resistive wall and finite island saturation*

We present a framework for estimating the locking probability for a rotating tokamak plasma with an  error field. This approach uses machine learning methods trained on the results of a reduced mode-locking model, which includes a resistive MHD model of the plasma, a resistive wall (RW), an external vacuum region, and an error field, leading to a 5th order ODE system. It is an extension of the third order model without a RW introduced in Ref. 1. A saturation model for the tearing perturbation by finite island width is also included. We choose two control parameters, the applied torque and an error field. The order parameters are the five time-asymptotic values of the dependent variables. We show that a normalization of these order parameters allows the classification of states as locked (L) or unlocked (U) in terms of only two order parameters and improves a clustering algorithm for the classification. This classification splits the control parameter space into 3 distinct regions: only L states, only U states, and a hysteresis H region, with both L and U states. This classification is then used to estimate the locking probability, conditional on the control parameters, using a neural network. This conditional probability is between 0 and 1 in the H region. We also explore using different pairs of control parameters and explore finding an estimate of the locking probability for a sparse data set, using a transfer learning method based on a dense model data set.