Differentiable Graph-Based Finite Volume Solver for Patient-Specific Cardiovascular Flow Simulation

Cardiovascular disease remains a leading global health challenge, and image-based computational fluid dynamics (CFD) has become an indispensable tool for understanding patient-specific hemodynamics. However, traditional CFD solvers are computationally intensive, often CPU-based, and lack native differentiability. Even when adjoint methods are used for sensitivity analysis, they require complex and error-prone manual coding. On the other hand, deep learning–based surrogate models, while fast, suffer from limited generalizability and require extensive training data.

In this work, we develop a first-of-its-kind finite volume method (FVM) solver implemented entirely using graph neural network operators on the JAX platform, enabling end-to-end GPU acceleration and automatic differentiation. Our solver directly solves the incompressible Navier–Stokes equations and supports specialized boundary conditions critical for cardiovascular modeling, including transient pulsatile inlet waveforms and Windkessel outlet models. We demonstrate the solver’s efficiency, scalability, and gradient-tracking capabilities on aortic flow simulations, and benchmark its performance and accuracy against widely used CFD tools such as OpenFOAM and SimVascular. This approach provides a differentiable, mesh-aware, and physiologically informed solver for advancing cardiovascular modeling and optimization workflows.