PSTNet: Physically-Structured Turbulence Network

PSTNet achieves superior turbulence estimation with 552 parameters, outperforming larger models by integrating atmospheric physics directly into its architecture, leading to better real-time guidance and safety-critical deployment.

Reliable real-time estimation of atmospheric turbulence intensity remains an open challenge for aircraft operating across diverse altitude bands, particularly over oceanic, polar, and data-sparse regions that lack operational nowcasting infrastructure. Classical spectral models such as Dryden and von Kármán encode climatological averages rather than the instantaneous atmospheric state, while generic machine-learning regressors offer adaptivity but provide no guarantee that predictions respect fundamental scaling laws. This paper introduces the Physically-Structured Turbulence Network (PSTNet), a lightweight mixture-of-experts architecture that embeds atmospheric physics directly into its computational structure. PSTNet couples four components: (i) a zero-parameter analytical backbone derived from Monin-Obukhov similarity theory, (ii) a regime-gated mixture of four specialist sub-networks—convective, neutral, stable, and stratospheric—supervised by Richardson-number-derived soft targets, (iii) Feature-wise Linear Modulation layers conditioning hidden representations on local air-density ratio, and (iv) a Kolmogorov spectral constraint enforcing ε^1/3 inertial-subrange scaling as a hard architectural constraint. The entire model contains only 552 learnable parameters, requiring fewer than 2.5 kB of storage and executing in under 12 µs on a Cortex-M7 microcontroller. We validate PSTNet on 340 paired six-degree-of-freedom guidance simulations spanning three vehicle classes (Mach 2.8, 4.5, and 8.0) and six operational categories with real-time satellite weather ingestion. PSTNet achieves a mean miss-distance improvement of +2.8% with a 78% win rate and a statistically significant effect size (Cohen's d = 0.408, p < 10^-9), outperforming all baselines—including a 6819-parameter deep MLP and a ~9000-parameter gradient-boosted ensemble—by a wide margin. A Friedman test across all five models rejects the null hypothesis of equal performance (χ² = 48.3, p < 10^-9), with Nemenyi post-hoc analysis ranking PSTNet first. Notably, the learned gating network recovers classical atmospheric stability regimes without explicit regime labels, providing physically interpretable and transparent routing. Our results demonstrate that encoding domain physics as architectural priors yields a more efficient and interpretable path to turbulence estimation accuracy than scaling model capacity, establishing PSTNet as a viable drop-in replacement for legacy look-up tables in resource-constrained, safety-critical on-board guidance systems.