A Structured Neural ODE Approach for Real-Time Evaluation of AC Losses in 3-D Superconducting Tapes

Efficient modeling of high-temperature superconductors (HTSs) is crucial for real-time quench monitoring; however, full-order electromagnetic simulations remain prohibitively costly due to the strong nonlinearities. Conventional projection-based reduced-order modeling pipelines for nonlinear problems, such as (POD)-Discrete Empirical Interpolation Method (DEIM), alleviate this cost but often require intrusive access to the Full Order Model (FOM) operators and a substantial number of interpolation points for hyperreduction. This work investigates reduced-order strategies for Integral Equation Method (IEM) of HTS systems. We present the first application of POD-DEIM to IEM-based HTS models, and introduce a Structured Neural Ordinary Differential Equation (Neural ODE) approach that learns nonlinear dynamics directly in the reduced space. The benchmark results show that Neural ODE outperforms POD-DEIM both in efficiency and accuracy, highlighting its potential for simulations of real-time superconducting.