Physics-statistics decoupled operators for ensemble-averaged intensity prediction in turbulent laser propagation

Infrared laser propagation through atmospheric turbulence produces random, non-reproducible speckle patterns, while engineering assessment requires the conditional ensemble-averaged irradiance. Conventional beam propagation methods obtain this average through hundreds of Monte Carlo realizations at a cost scaling with distance, and data-driven approaches fall into a pixel-smoothing trap when forced to fit single shots. Here we propose the physics-informed averaging cascade for turbulence (PACT), which decouples stochastic phase perturbations from deterministic amplitude evolution to learn the conditional ensemble-averaged intensity envelope. The architecture cascades a phase-context module, an analytic propagator, a Fourier neural operator residual corrector, and an intensity envelope head, trained with a multi-physics loss that matches the radial spectral statistics of the finite-N averaging residual. PACT outperforms U-Net, Swin U-Net, and physics-only BPM baselines by 38.9%, 35.5%, and 43.2% in Composite Score, and ablations show the spectral loss to be the critical enabler against the smoothing trap. Validation on a 500-m cross-sea path at C _n ² below the single training condition, within the weak-scintillation regime, yields radial-profile NMSE below 0.035 with power spectra consistent with phase-screen Kolmogorov scaling. PACT provides a physically consistent, computationally efficient surrogate for rapid turbulence assessment.