Machine learning methods for probabilistic locked-mode predictors in tokamak plasmas

We have extended the model of Ref.[1], including a resistive wall and an error field. This leads from 3rd order to 5th order, with the RP-RW stability index Delta(t,rw) taking the place of the RP-IW index Delta(t) of [1]. This model also includes quasilinear saturation by finite island width. The error field and the applied torque are the control parameters. The normalized order parameters are determined from the variables of the 5th order ODE system. As in [1], we have applied machine learning (ML) methods, starting with clustering algorithms used to classify into locked (L) and unlocked (U) states. The normalizations greatly aid in this step. In terms of the 2D control parameter space, there is a region (L') of only L states, a region (U') of U states, and a hysteresis region (H'), where both L and U states occur. The second step is to use the classification into L and U to determine the locking probability p(L). We find that a neural network (NN) scheme gives a good estimate of p(L). We have computed the internal and external fields from the measured fields, and used these to search for a signature of incipient locking in H'. We have also explored adding a new layer to the NN, and used it with much more sparse data to update p(L).