Non-intrusive parametric model reduction for fast thermal simulation of phase-change materials and anisotropic battery cells: validated accuracy, online basis updates, and the failure of fixed hyper-reduction on moving fronts

High-fidelity thermal simulation of latent-heat storage and battery cells is dominated by moving phase boundaries, sharp mushy regions and strongly anisotropic conduction, which make full-order models too slow for parameter sweeps, real-time control and digital twins. We build and rigorously verify a family of reduced-order models (ROMs) on three progressively harder problems, reporting both what works and what does not. A non-intrusive parametric proper orthogonal decomposition (POD) reproduces unseen operating conditions without reassembling any operator: against a two-phase Neumann solution it predicts a one-dimensional Stefan front to within 0.30–5.10%, with field errors of 0.05–0.23% and an online single-point speed-up of about 770-fold; for two-dimensional corner melting with a curved front the field error is 0.35% with a 2.6×10^4-fold single-query speed-up (about 634-fold for a full trajectory); for a 100 mm anisotropic lithium-ion pouch cell over a two-parameter space, the error is 0.59–0.79%, the maximum absolute point error is about 0.038 °C, and the single-query speed-up reaches about 1,950-fold on 16,000 nodes. An intrusive POD–Galerkin projection destabilises on the moving front, and a fixed global discrete empirical interpolation (DEIM) stays at 43–45% error; a front-localised adaptive sampling scheme raises the fraction of nodes on the current front from 16.7% to 80.6% and lowers the error to a well-characterised 31% floor. A streaming incremental SVD matches a one-shot batch SVD to machine precision (maximum principal angle 2.8×10^-6 degree; unseen-case error identical to 15 digits). The selection rule is: use non-intrusive parametric POD for smooth thermal fields in production, and reserve intrusive, front-aligned hyper-reduction for contact, convection and turbulence problems that require an online residual. This is a non-peer-reviewed preprint; representative reproduction scripts are available from the corresponding author, while production software is not included.