Emergent statistical behavior in fluid dynamics
Giulio Ortali defended his PhD thesis at the Department of Applied Physics and Science 果冻传媒 on January 14.
The PhD thesis of Giulio Ortali delves into the data-driven discovery of emergent behavior in the context of fluid dynamics and is structured into three major topics. The first two projects focused on turbulence modeling, specifically within the context of the shell model of turbulence and the Lattice Boltzmann Method (LBM). The third project explored the dynamics of droplets in stabilized dense emulsions. All three projects involved systems with nontrivial statistical properties where traditional physical modeling is not best suited, hence motivating the need for data-driven approaches alongside conventional methods.
Shell models
In the first project, developed a data-driven turbulence sub-grid closure in the context of shell models of turbulence using Long Short-Term Memory neural networks (LSTM).
This preliminary step sought to verify the feasibility of data-driven techniques for turbulence modeling. His goal was to show that a neural network-based subgrid closure model could accurately reproduce the statistics of filtered Direct Numerical Simulations (DNS) up to very high statistical orders.
Shell models were chosen for their computational efficiency and ability to generate sufficient statistical data, making them ideal for this validation. Ortali鈥檚 findings indicate that the neural network model could statistically replicate the dynamics of a fully resolved simulation up to very high statistical order, outperforming traditional physics-based methods and supporting the potential of data-driven turbulence modeling.
Lattice Boltzmann Method
In the second project, Ortali developed a data-driven turbulence subgrid closure within the context of the Lattice Boltzmann Method (LBM). In this setting, he employed a physics constrained Multilayer Perceptron (MLP) to learn a local collision operator acting as a subgrid closure model, trained from fully resolved Direct Numerical Simulation (DNS) data.
This mesoscopic formulation enabled locality in space and time and enhanced computational efficiency and generalization capabilities in the process.
Ortali鈥檚 results showed that this neural LBM approach outperformed traditional methods, such as the Smagorinsky model, by being less dissipative, thus better capturing the intermittency of higher-order velocity correlations, and supporting the inverse transfer of energy from small to large scales, a feature absent in conventional models. This work marks a first step in advancing data-driven turbulence modeling in the context of the LBM.
Dynamics of droplets
In the final project, the researcher modeled the dynamics of droplets in stabilized dense emulsions using Graph Neural Networks (GNNs).
Emulsions are mixtures of two immiscible fluids, where one fluid is dispersed in the form of droplets within the other.
Combining a GNN with a handcrafted physical model, Ortali achieved both accurate and stable predictions. This hybrid approach significantly improved long-term stability and accuracy over standalone models, marking a crucial step towards a deeper understanding of droplet dynamics and more efficient and precise simulations of emulsions.
Title of PhD thesis: . Supervisors: Federico Toschi and Gianluigi Rozza (External).