Modeling of 3D Blood Flows with Physics-Informed Neural Networks: Comparison of Network Architectures

Machine learning-based modeling of physical systems has attracted significant interest in recent years. Based solely on the underlying physical equations and initial and boundary conditions, these new approaches allow to approximate, for example, the complex flow of blood in the case of fluid dynamics. Physics-informed neural networks offer certain advantages compared to conventional computational fluid dynamics methods as they avoid the need for discretized meshes and allow to readily solve inverse problems and integrate additional data into the algorithms. Today, the majority of published reports on learning-based flow modeling relies on fully-connected neural networks. However, many different network architectures are introduced into deep learning each year, each with specific benefits for certain applications. In this paper, we present the first comprehensive comparison of various state-of-the-art networks and evaluate their performance in terms of computational cost and accuracy relative to numerical references. We found that while fully-connected networks offer an attractive balance between training time and accuracy, more elaborate architectures (e.g., Deep Galerkin Method) generated superior results. Moreover, we observed high accuracy in simple cylindrical geometries, but slightly poorer estimates in complex aneurysms. This paper provides quantitative guidance for practitioners interested in complex flow modeling using physics-based deep learning.