Geometric Deep Neural Differentiable Modeling for Efficient 3-D Patient-Specific Aortic Flow Simulations*

Computational modeling of hemodynamics plays an increasing role in the diagnosis and treatment planning of cardiovascular diseases. However, traditional CFD-based patient-specific models suffer from high computational costs and large modeling uncertainties. With the rapid development in AI and GPU computing, there has been a growing interest in developing deep learning (DL)-based surrogate models due to their higher efficiency and scalability. Nonetheless, most existing DL models are subject to approximation error, poor generalizability, and high dependency on training labels. To address these issues, we propose to integrate the governing physics into the learning structures by leveraging both advantages of numerical solvers and DL techniques within a differentiable programming framework. Specifically, a hybrid neural differentiable model based on graph neural networks and differentiable CFD solvers is developed for fast predictions of transient aortic flows given various input flow boundary conditions. Multi-resolution data and physics will be integrated for optimized efficiency and accuracy. The proposed model is compared with state-of-the-art DL-based surrogate models and pure CFD models, showing significant superiority in terms of efficiency, accuracy, and generalizability.