Micol Bracco
Data Assimilation based on Physics-Informed Neural Networks for Hemodynamics.
Rel. Umberto Morbiducci, Alessandro Veneziani. Politecnico di Torino, Corso di laurea magistrale in Ingegneria Biomedica, 2025
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Abstract
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
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