Wind profiles in the atmospheric boundary layer (ABL) drive short-range forecasting and wind-energy siting, yet sparse radiosonde coverage forces practitioners to interpolate them from a handful of physical predictors. We benchmark modern tabular learners against analytical parameterizations on 158,097 IGRA soundings. CatBoost, TabM, and FT-Transformer reduce RMSE to 1.3-1.6 m/s, against approximately 3 m/s for power-law and Monin-Obukhov fits; once the predictor set is fixed the three architectures differ by less than 0.05 m/s, so accuracy is driven by predictors rather than architecture. A cohort analysis of within-bin profile dispersion places an empirical floor of approximately 1.77 m/s on any point-wise predictor that uses standard radiosonde features, consistent with prior eddy-viscosity inversions. A one-dimensional Fourier Neural Operator applied as a post-hoc corrector to frozen tabular predictions reduces near-surface RMSE on U.S. stations from 1.5 to 1.2 m/s, while leaving upper-layer error unchanged. Further gains should come from new predictors rather than larger models.
Kirill Katsuba, Oleg Rudenko, Egor Bugaev, Alexander Tarakanov
原文摘要
Neural surrogates for engineering models are often trained on large collections of simulated solutions. We investigate whether physics-informed neural networks (PINNs) can achieve accurate predictions from scarce labelled observations by incorporating governing equations and prescribed initial and boundary conditions. We introduce hierarchical loss weighting (H-PINN) and its gradient-direction-aware extension (HO-PINN), which adjust the emphasis on physical constraints according to higher-priority losses. Hierarchical PINNs are compared with Vanilla PINN, tuned gradient boosting, support-vector regression, and Gaussian-process regression on a heat equation and three heterogeneous two-phase-flow benchmarks. Experiments use 20--1000 labelled states and ten paired seeds. Each label is one coordinate--state observation, not a complete simulation. At least one PINN variant achieves the highest mean primary-target \(R^2\) in each interpolation and equation-assisted forecasting comparison at 20 and 50 labels. The advantage for water saturation persists across all tested budgets. Hierarchical weighting reduces variability across runs in selected settings. These results demonstrate that known physics can support accurate neural surrogate predictions from very few solution observations, at substantially higher fitting cost than the tested classical regressors.