报告题目：A Meshless Solver for Blood Flow Simulations in Elastic Vessels Using Physics-Informed Neural Network

报告人：Xue-Cheng Tai教授，挪威研究中心

报告时间：2024年4月12日（周五）9:00-10:00

报告地点：20-200

报告摘要：Investigating blood flow in the cardiovascular system is crucial for assessing cardiovascular health. Computational approaches offer some non-invasive alternatives to measure blood flow dynamics. Numerical simulations based on traditional methods such as finite-element and other numerical discretizations have been extensively studied and have yielded excellent results. However, adapting these methods to real-life simulations remains a complex task. In this paper, we propose a method that offers flexibility and can efficiently handle real-life simulations. We suggest utilizing the physics-informed neural network (PINN) to solve the Navier-Stokes equation in a deformable domain, specifically addressing the simulation of blood flow in elastic vessels. Our approach models blood flow using an incompressible, viscous Navier-Stokes equation in an Arbitrary Lagrangian-Eulerian form. The mechanical model for the vessel wall structure is formulated by an equation of Newton’s second law of momentum and linear elasticity to the force exerted by the fluid flow. Our method is a mesh-free approach that eliminates the need for discretization and meshing of the computational domain. This makes it highly efficient in solving simulations involving complex geometries. Additionally, with the availability of well-developed open-source machine learning framework packages and parallel modules, our method can easily be accelerated through GPU computing and parallel computing. To evaluate our approach, we conducted experiments on regular cylinder vessels as well as vessels with plaque on their walls. We compared our results to a solution calculated by Finite Element Methods using a dense grid and small time steps, which we considered as the ground truth solution. We report the relative error and the time consumed to solve the problem, highlighting the advantages of our method. This talk is based on a joint work with Raymond Chan and Han Zhang.

报告人简介：Xue-Cheng Tai教授现任挪威研究中心（Norwegian Research Centre）首席科学家，曾任香港浸会大学数学系主任和讲席教授、挪威卑尔根大学数学系教授。长期从事计算数学、图像计算及反问题、变分优化算法及应用、对水平集的变分优化算法、区域分割和多重网格的变分计算等方面的研究。对大规模优化计算等计算数学基础问题作出突出贡献，共发表各类学术论文260余篇，并编辑多本学术专著；主持组织各类专业国际学术会议，同时担任多个顶级专业期刊，如SIAM J. Num. Analysis, SIAM Imaging Science，Journal of Scientific Computing，SIAM Numerical Analysis等编委成员。1993年获德国洪堡学者；2009年，由于在科学计算方面的突出贡献，获得第8届“冯康奖”；2011年，获得新加坡南洋理工大学“南洋突出研究贡献奖”。

邀请人：向道红