Physics-Structured POD–Neural Networks for Reduced-Order Modeling of the Three-Dimensional Temperature Field in HVDC Cables Across Operating Conditions

The temperature field of a high-voltage direct-current (HVDC) cable governs its current rating and insulation lifetime and must therefore be predicted accurately across diverse operating conditions. Finite-element (FE) simulation is accurate but too costly for repeated evaluation, whereas data-driven reduced-order models (ROMs) often extrapolate poorly beyond the training-current range. This paper proposes a physics-structured POD–neural ROM to address this limitation. Specially, proper orthogonal decomposition (POD) compresses the three-dimensional temperature-rise field into a few modal coefficients, which are predicted from the operating conditions by a neural network. The key innovation is to embed the Joule-heating law directly into the architecture: the leading coefficient is represented as a current-squared factor multiplied by a learned current-independent shape. This construction guarantees the correct current scaling of the dominant mode, including its zero-current limit and extrapolation beyond the training range. On FE data for an eight-layer cross-linked polyethylene cable, the model achieves 2.4% mean relative error under current extrapolation and remains below 5% at twice the maximum training current, outperforming Gaussian-process, dynamic-mode-decomposition, autoregressive, and black-box baselines. The full field is evaluated in approximately one millisecond per condition, with a cost independent of the training-set size. Controlled ablations show that the improvement arises from structurally enforcing the scaling law rather than merely supplying I2 as an input feature. Embedding known physical scaling into a surrogate architecture therefore provides a principled route to reliable extrapolation.