Data Assimilation based on Physics-Informed Neural Networks for Hemodynamics

Traditional methods for solving partial differential equations (PDEs), such as Computational Fluid Dynamics (CFD) simulations, present several challenges. These include high sensitivity to uncertainties in boundary conditions, the complexity of generating meshes conforming to the geometry of the domain, and significant difficulties in addressing high-dimensional problems. In this context, Physics-Informed Neural Networks (PINNs) represent an advanced deep learning technique that directly incorporates the physical laws governing a given phenomenon, offering an alternative and flexible approach to solving such equations. This work investigates the use of Physics-Informed Neural Networks for solving both direct and inverse problems, with a particular focus on inverse problems involving data assimilation, where observational data are integrated into the modeling process. To validate the proposed method, several test cases were considered using the Navier–Stokes equations in both steady and unsteady forms, across two-dimensional and three-dimensional configurations. In a preliminary phase, simple geometries were used to test the model’s effectiveness, performing fine-tuning by varying several network parameters, as well as the number, quality, and placement of the data employed. This was followed by the analysis of more complex geometries resembling anatomical structures, with the aim of studying hemodynamic behavior in physiologically realistic conditions, while seeking methods that were both efficient and accurate. Particular attention was given to the study of velocity and pressure fields, and to the computation of Wall Shear Stress (WSS), a clinically relevant parameter as it is considered a key risk factor for atherosclerosis. The primary goal of this thesis is to demonstrate that PINNs represent an innovative approach, characterized by numerous advantages in terms of computational efficiency, reducing costs compared to traditional methods, and in handling sparse or noisy data. The results obtained, compared with analytical solutions and those derived from simulations using the Finite Element Method (FEM), highlight the potential of this methodology. In particular, PINNs demonstrated superior effectiveness in solving inverse problems by integrating observational data into the solution process, achieving greater accuracy than methods based solely on physical modeling. Nonetheless, this work represents only an initial step: future developments will involve the application of PINNs to real anatomical models, such as blood vessels, to further evaluate their effectiveness in clinically relevant scenarios.