Graph Neural Networks for fluid mechanics: data-assimilation and optimization

This PhD thesis investigates the application of Graph Neural Networks (GNNs) in the field of Computational Fluid Dynamics (CFD), with a focus on data-assimilation and optimization. The work is structured into three main parts: data-assimilation for Reynolds-Averaged Navier-Stokes (RANS) equations based on GNN models; data-assimilation augmented by GNN and adjoint-based enforced physical constraint; fluid systems optimization by ML techniques. In the first part, the thesis explores the potential of GNNs to bypass traditional closure models, which often require manual calibration and are prone to inaccuracies. By leveraging high-fidelity simulation data, GNNs are trained to directly learn the unresolved flow quantities, offering a more flexible framework for the RANS closure problem. This approach eliminates the need for manually tuned closure models, providing a generalized and data-driven alternative. Moreover, in this first part, a comprehensive study of the impact of data quantity on GNN performance is conducted, designing an Active Learning strategy to select the most informative data among those available. Building on these results, the second part of the thesis addresses a critical challenge often faced by ML models: the lack of guaranteed physical consistency in their predictions. To ensure that the GNNs not only minimize errors but also produce physically valid results, this part integrates physical constraints directly into the GNN training process. By embedding key fluid mechanics principles into the machine learning framework, the model produces predictions that are both reliable and consistent with the underlying physical laws, enhancing its applicability to real-world problems. In the third part, the thesis demonstrates the application of GNNs to optimize fluid dynamics systems, with a particular focus on wind turbine design. Here, GNNs are employed as surrogate models, enabling rapid predictions of various design configurations without the need for performing a full CFD simulation at each iteration. This approach significantly accelerates the design process and demonstrates the potential of ML-driven optimization in CFD workflows, allowing for more efficient exploration of design spaces and faster convergence toward optimal solutions. On the methodology side, the thesis introduces a custom GNN architecture specifically tailored for CFD applications. Unlike traditional neural networks, GNNs are inherently capable of handling unstructured mesh data, which is common in fluid mechanics problems involving irregular geometries and complex flow domains. To this end, the thesis presents a two-fold interface between Finite Element Method (FEM) solvers and the GNN architecture. This interface transforms FEM vector fields into numerical tensors that can be efficiently processed by the neural network, allowing data exchange between the simulation environment and the learning model.