Advisor: Dr. Meilin Yu

Title: Invariance-Embedded Machine Learning Sub-Grid-Scale Stress Models for Meso-Scale Hurricane Boundary Layer Simulations: Model Development, a priori Assessment, and a posteriori Tests with WRF

Abstract: Accurately simulating the turbulent dynamics of hurricane boundary layers is critical for improving hurricane intensity forecasts and understanding extreme weather systems. Traditional sub-grid-scale (SGS) models, such as the Smagorinsky scheme, often fail to capture the bidirectional energy transfer characteristic of these flows, particularly the energy backscatter essential in mesoscale simulations. This work develops and evaluates an invariance-embedded machine learning (ML) framework for SGS stress modeling, designed to improve large-eddy simulations (LES) of hurricane boundary layer flows. The proposed approach integrates physical and geometric invariant features into a hybrid ML architecture that couples classification and regression models, predicting signed Smagorinsky coefficients to capture both forward energy cascade and backscatter.

We systematically assess the performance of various ML classifiers (logistic regression, SVM, random forest, gradient boosting, and neural networks) and regression models, demonstrating that ensemble neural networks with invariance embedding outperform dynamic Smagorinsky models in a priori tests. Building on these results, we outline a two-stage plan to implement the ML SGS model into the Weather Research and Forecasting (WRF) model, starting with offline evaluations using stored mesoscale outputs, followed by in-line coupling within WRF’s turbulence modules. Additionally, we propose an extension of the ML framework to jointly predict the Smagorinsky coefficient and deviatoric stress tensor components, comparing Bayesian regularization and ADAM optimization strategies. This dissertation bridges the gap between data-driven SGS modeling and operational weather prediction, with the ultimate goal of enhancing the realism and reliability of mesoscale hurricane simulations.