# Physics-constrained deep learning framework for accurate AC loss prediction of high-temperature superconductors: impact of data scarcity and extrapolation beyond the range of experimental measurements

Article · Shahin Alipour Bonab, Wenjuan Song, Zhenan Jiang, Mohammad Yazdani-Asrami

- Archive id: doi:10.1088/1361-6668/ae2162
- Published: 2025-11-19
- Venue: Superconductor Science and Technology
- DOI: https://doi.org/10.1088/1361-6668/ae2162
- Citations: 4
- Source URL: https://doi.org/10.1088/1361-6668/ae2162
- PDF: https://iopscience.iop.org/article/10.1088/1361-6668/ae2162/pdf
- Provenance: openalex

## Abstract

Abstract Accurately predicting AC losses in high-temperature superconductors is critical for the efficient design of superconducting systems due to their contribution to the required cooling power at cryogenic temperatures. Experimental measurements are often expensive, time-consuming, and risky (in the case of measurements under liquid hydrogen cooling), so they are limited to a few measurement tests (datapoints), and analytical models lose fidelity as system geometries and boundaries become more complicated or operating conditions deviate from their underlying assumptions. On the other hand, although traditional finite element (FE) modelling techniques, such as H -formulation FE analysis, are accurate, they tend to have higher errors and get too slow in cases of complicated coil or system-level modelling. Despite the advantages of using purely data-driven artificial intelligence (AI) based models for AC loss prediction, this paper presents a physics-constrained deep learning (PCDL) framework for the first time that not only predicts AC losses accurately but also can extrapolate them from sparse experimental data. This novel PCDL model offers trustworthy predictions of AC losses even beyond the limited measured data range. By embedding the analytical formulation of the Norris model directly into the training process, the model can constrain the AI regressor to the physics-defined direction, which can significantly improve the prediction accuracy. Trained on a limited subset of experimental data, the proposed PCDL framework provides: (i) high-accuracy interpolation within the sparse experimental envelope—matching the accuracy and performance of purely data-driven AI models—and (ii) reliable extrapolation to current amplitudes and frequencies outside the measured range, where simple AI and machine learning techniques, including conventional neural networks and mathematical fittings fail. Benchmarked against a data-driven neural network trained on the same restricted set, PCDL consistently delivers the highest accuracy with a minimum goodness of fit of 91.05% at the worst-case scenario and 98.45% at the highest performance. Therefore, PCDL was found to be a potential intelligent solution for accurate AC loss estimations beyond experimental measurements.

_Abstract reproduced under CC-BY (publisher license, via OpenAlex)._

Topics: [Computational & AI-Driven Superconductor Discovery](https://space-kitty.com/topics/superconductor-discovery)

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