SuperCond-GNN: Scalable Graph Neural Network Surrogate for Superconducting Circuit Simulations

This paper presents SuperCond-GNN, a graph neural network-based surrogate model for predicting the voltage distribution in high-temperature superconducting (HTS) magnets. HTS magnets are modeled as lumped-element equivalent circuits and mapped onto graph representations, enabling message passing GNNs to learn the electrical response as a function of circuit topology, material properties, and operating current. As a proof of concept, tape stacks of up to 10 tapes are considered across a range of circuit topologies and operating conditions. The surrogate is trained on data generated from circuit simulations and achieves a mean MAPE of 4.3 % within the prescribed design space. The predicted nodal voltages enable fast and scalable inference of current redistribution and local operating conditions across a wide range of circuit configurations. The effect of incorporating physics-informed regularization via Kirchhoff's current law is also evaluated, and generalizability to unseen topologies is assessed through zero-shot inference and few-shot fine-tuning. While demonstrated on tape stack circuits, the graph-based framework is topology-agnostic and naturally extensible to more complex HTS cable and magnet configurations, offering a scalable alternative to conventional circuit solvers for downstream applications such as design space exploration, current sharing analysis, and real-time magnet monitoring.