SKM 2023 – wissenschaftliches Programm
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BP: Fachverband Biologische Physik
BP 11: Poster Session I
BP 11.25: Poster
Dienstag, 28. März 2023, 12:30–15:30, P1
Parameter Optimization for 1D-0D Coupled Blood Flow Models: Physics-Informed Neural Networks versus Kernel Methods — •Tobias Köppl1, Benedikt Hoock1,3, and Gabriele Santin2 — 1Technische Universität München, School of Computation, Information and Technology — 2Digital Society Research Center, Fondazione Bruno Kessler, Italy — 3Support by Computing Facilities of Leibniz-Rechenzentrum München
The understanding of blood perfusion of organs is essential to improve motion therapy. Here, numerical simulations of the blood flow on the human arteries network have already come up to augment in-vivo measured data. A common approach is the coupled 1D-0D hydrodynamic model combining the simplified incompressible Navier-Stokes equations with the Windkessel model. Fine-tuning the free model parameters such as the resistance and capacity is computationally expensive so it is beneficial to find a simpler surrogate. To this purpose we apply two different machine-learning techniques: physics-informed neural networks and kernel-based methods. The first simultaneously minimizes the quadratic loss to existent reference data and the residuals of a physical system of differential equations by a neural network. The second builds a model from kernel functions and is purely data-driven. We refine these approaches to predict the blood pressure from the 1D-OD model in a single vessel at varying resistance, capacity and heart beat, sampled over time and space. Comparing them in terms of the training and test error and their run time, we conclude that they are equally applicable to be now integrated into quantum optimization.