Model order reduction of magnetic and MSE EFIT reconstructions with neural networks

We present a model order reduction (MOR) of magnetics-only (EFIT01) and magnetics plus motional Stark effect (MSE) EFITs (EFIT02) with neural network (NN) surrogates that have been trained on the 2019 DIII-D data. Our neural networks reconstruct DIII-D equilibria, given an input space comprising the external magnetic data and internal MSE measurements. The output space comprises the poloidal magnetic flux ψ and toroidal current density Jφ on the EFIT rectangular spatial grid; safety factor profile (for EFIT02); global parameters including the normalized beta, internal inductance, axial and edge safety factor; as well as the plasma boundary and quantities related to the magnetic topology such as the X-point locations. Including Jφ in the training imposes the magnetostatic force-balance condition on the NN. A fully-connected multi-layer perceptron (MLP) NN suffices to learn ψ(R,Z). However, various approaches are pursued to reconstruct Jφ concurrently with and from the NN ψ: 1) a convolutional NN that learns Jφ(R, Z) on the grid, 2) an MLP that learns the pressure and poloidal current flux function profiles to calculate Jφ (ψ), and 3) an MLP that learns the coefficients of the basis functions that form the profiles. Note the output space contracts in size to O(10⁴), O(10²), O(10)-many features, respectively for these three approaches. The neural network reconstructions for EFIT01 demonstrate good accuracy with an R²>0.99 and R²>0.98 for ψ and JφThis work is supported by the Department of Energy under Award Numbers DE-SC0021203 and DE-FC02-04ER54698 , respectively; and R²~0.98 for the plasma boundary and global quantities, with the exception of internal inductance, which has been challenging for the NNs to learn so far.