SUPERCOND-GNN: SCALABLE GRAPH NEURAL NETWORK SURROGATE FOR SUPERCONDUCTING CIRCUIT SIMULATIONS

High-temperature superconducting (HTS) magnets are critical for fusion and accelerator technologies, but their protection is hindered by complex current-sharing behaviors that are difficult to model in real-time. Conventional SPICE-based circuit solvers are computationally expensive and struggle to scale as magnet complexity increases. This paper investigates whether a Graph Neural Network (GNN) can serve as a scalable, topology-agnostic surrogate model to predict nodal voltage distributions, providing a foundation for real-time digital twins in magnet monitoring.

SuperCond-GNN (SC-GNN) treats HTS circuits as graphs where circuit nodes represent graph nodes and electrical components (resistors, superconductors, current sources) represent edges. This representation allows the model to handle variable circuit sizes and topologies without needing to retrain for every new configuration. The architecture uses a MeshGraphNet-based design with an encoder, a message-passing processor, and a decoder. To improve physical accuracy, the authors incorporate a physics-informed regularization term based on Kirchhoff's Current Law (KCL), which penalizes violations of current conservation at each node.

The model was trained on data generated from ngspice simulations of REBCO tape stacks. It achieved a mean MAPE of 4.3% within the tested design space. By utilizing graph-based message passing, the model successfully generalizes to unseen circuit topologies through zero-shot inference and few-shot fine-tuning. The results demonstrate that SC-GNN can effectively capture the nonlinear resistive behavior of HTS conductors and the complex current redistribution pathways that occur in multi-tape stacks, offering a significantly faster alternative to traditional circuit solvers.