A Surrogate model for High Temperature Superconducting Magnets to Predict Current Distribution with Neural Network

TL;DR

A surrogate model based on a fully connected residual neural network (FCRN) is developed to predict the current density distribution in REBCO solenoids, and finds the optimal solution within the parameter space under constraints.

Abstract

Finite element methods (FEM) for high-temperature superconducting (HTS) magnets become time-consuming at larger scales, restricting the rapid optimization of meter-scale REBCO solenoids. In this work, a surrogate model based on a fully connected residual neural network (FCRN) is developed to predict the current density distribution in REBCO solenoids. Trained on datasets generated from FEM simulations by the T-A formulation, the FCRN model is evaluated under both fast ramping and steady-state scenarios, showing a lower validation loss than the fully connected network (FCN). When extrapolating geometric parameters beyond the training set, the model achieves a relative error of below 10 % for magnetization losses in Case 1 and an average error of 1.2 % for the central magnetic field in Case 2. Furthermore, deploying the steady-state surrogate model for rapid magnet design found the optimal solution within the parameter space under constraints, with a relative central magnetic field error of 0.2 % compared to FEM results. With rapid predictions, this surrogate model offers an efficient tool for the intelligent design of large-scale HTS magnets.

Figures (12)

• Figure 1: (a) Geometry of the HTS solenoid, where $R_{\mathrm{ID}}$ denotes the inner diameter, $N$ the number of turns, and $N_{\mathrm{p}}$ the number of pancakes. (b) Schematic of the surrogate model, with inputs representing the HTS solenoid coil parameters (e.g., inner diameter, number of turns and pancakes, operation current) and outputs given as the spatial distribution of the current density.
• Figure 2: Operating current profiles for the two scenarios considered in this study: (a) fast ramping, and (b) steady operation. Circular markers indicate the time points sampled for neural network training.
• Figure 3: (a) The one-quarter FEM used to reduce computational cost. (b) The current density and magnetic field distributions calculated using the $T$–$A$ formulation.
• Figure 4: Different neural network structures: (a) conventional fully connected network and (b) residual network with a shortcut connection adding the input directly to the output of the second linear transformation.
• Figure 5: Training strategy of the neural network. The model is saved only when both training and validation losses decrease, and training stops after 500 epochs with the final model corresponding to the relatively lowest combined losses.