PSTNet: Physically-Structured Turbulence Network

Abstract

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 encode climatological averages rather than the instantaneous atmospheric state, and generic ML regressors offer adaptivity but provide no guarantee that predictions respect fundamental scaling laws. This paper introduces the Physically-Structured Turbulence Network (PSTNet), a lightweight architecture that embeds physics directly into its structure. PSTNet couples four components: (i) a zero-parameter backbone derived from Monin-Obukhov theory, (ii) a regime-gated mixture of specialist sub-networks 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 output layer enforcing inertial-subrange scaling as an architectural constraint. The entire model contains only 552 learnable parameters, requiring fewer than 2.5 kB of storage and executing in under 12s 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. 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.

Figures (6)

• Figure 1: PSTNet architecture overview.
• Figure 2: Training loss convergence for PSTNet (552 parameters). The smooth, monotonic decay to a final MSE of $0.0063$ reflects the strong inductive bias provided by the analytical backbone.
• Figure 3: Regime gate activation maps for the four PSTNet experts. Brighter regions indicate higher gate weight $\alpha_j$. The gating network recovers classical stability regimes: convective ($\mathrm{Ri}<0$, low altitude), neutral ($\mathrm{Ri}\!\approx\!0$), stable ($\mathrm{Ri}>0.25$, mid-altitude), and stratospheric (high altitude, all $\mathrm{Ri}$).
• Figure 4: Improvement (%) over the no-turbulence reference, broken down by scenario category (rows) and model (columns). PSTNet leads in five of six categories; the sole exception is edge cases (E), where the Vanilla MLP benefits from over-fitting to rare conditions.
• Figure 5: Cohen's $d$ by vehicle type for all five models. PSTNet (blue) achieves the largest effect size in every regime. The red vertical line marks $d=0$ (no effect); shaded bands denote conventional small / medium / large thresholds.