Physics-Informed Neural Network for Blood Flow Simulation: Forward and Inverse Problem

Math+ML+X Seminar Series

Organizer：Angelica Aviles-Rivero (YMSC)

Speaker：

Han Zhang (City University of Hong Kong)

Time：

Thur., 16:00, May 14, 2026

Online：

Voov (Tencent): 294-173-543

Title:

Physics-Informed Neural Network for Blood Flow Simulation: Forward and Inverse Problem

Abstract:

Blood flow imaging plays a central role in understanding hemodynamic behavior and guiding medical diagnosis and treatment. However, obtaining high-quality flow fields is challenging due to limitations in imaging acquisition and the complexity of blood flow in deformable vessels. To address these issues, we propose a unified physics-informed framework for both forward simulation and inverse reconstruction of blood flow. For the forward problem, we employ a physics-informed neural network (PINN) to solve the incompressible Navier–Stokes equations in an Arbitrary Lagrangian–Eulerian (ALE) formulation, coupled with a linear elastic model for the vessel wall. This mesh-free, data-driven formulation allows for efficient simulation in complex and deformable vascular geometries without the need for traditional discretization or meshing, and benefits from GPU-based acceleration. For the inverse problem, we formulate blood flow image reconstruction as an optimization problem that enforces consistency with the Navier–Stokes equations while correcting geometric mismatches. The approach decomposes into two coupled subproblems: (i) a fluid subproblem that leverages PINNs to reconstruct the velocity field from noisy or artifact-laden measurements, and (ii) a geometry subproblem that infers the flow domain via quasi-conformal deformation of a reference geometry. These subproblems are solved alternately in a Gauss–Seidel manner, iteratively refining both the velocity and the domain.