Scientific Machine Learning Advances for Fluid Flow and Transport Modeling

Modeling coupled fluid flow and transport phenomena, such as turbidity currents and thermal convection, is computationally intensive due to strong nonlinear coupling and multiscale behavior. This chapter provides a comprehensive review of recent advancements in Scientific Machine Learning (SciML) aimed at creating efficient surrogate models for these systems, which are governed by incompressible Navier-Stokes and scalar transport equations. The review covers state-of-the-art SciML techniques, including linear reduced-order methods like Singular Value Decomposition (e.g., Dynamic Mode Decomposition) and nonlinear neural network approaches such as Physics-Informed Neural Networks (PINNs) and beta-Variational Autoencoders (beta-VAEs). It also discusses the integration of these models with High Performance Computing strategies, including Adaptive Mesh Refinement/Coarsening (AMR/C) and scientific floating-point data compression. The chapter introduces two new contributions: the application of PINNs for surrogate modeling of turbidity currents and the extraction of disentangled nonlinear modes from thermal flows using beta-VAEs. Through examples like lock-exchange flows and Rayleigh-Bénard convection, it illustrates how SciML enables fast, accurate approximations of complex coupled systems within specific data regimes, substantially reducing computational costs compared to full-order simulations. While real-time prediction and uncertainty quantification remain active research areas, this work highlights the current capabilities of SciML in this domain.