arXiv:2610.31504v1 Announce Type: cross Abstract: We build structure-preserving reduced-order models for both challenge problems of the AePW-4 High-Speed Working Group. They are a clamped thin panel at Mach 1.92 (RC-19) and a cantilever plate at Mach 5.85 (HyMAX). The published data for each case hold no time-resolved response and no repeated runs. The physics must therefore be carried by the form of the model. One construction gives two models per problem. A Ritz-Galerkin reference model describes the plate. A learned model keeps the reference model's exact potential, fits the remaining generalized forces, and trains only a dissipation that cannot add energy. Its energy balance holds for any weights by construction. On the trained model the worst relative residual is 2.2e-15. On RC-19, shock relations predict a pressure ratio of 1.521 across the panel. Pressure-sensitive paint measured the same value. Thirty runs of the learned model place the mean dominant frequency within 1.0% of the measured 236 Hz. At one periodic and one chaotic condition, the learned model reproduces the response regime of a published reduced-order model in all sixteen runs. It does so without that model's 113 Hz spectral peak, which the measurements do not show. Measured displacements can also correct the chaotic response through one more force that respects the energy balance. We tested this on synthetic data at the experiment's 5 kHz sampling rate. The state error is 1.25% of the panel thickness without noise and 3.5% with 10 micrometers of noise. On HyMAX the learned model follows the reference model's trailing-edge displacement for 65 ms with a relative error of 3.7%. These results show that a model whose structure carries the physics can match measured flutter behavior when the available data cannot train it.