Spectral features for Neural-initalized-Newton Solvers in Cardiovascular CFD simulations

Abstract

Computational Fluid Dynamics (CFD) simulations of cardiovascular systems hold promise for personalized clinical care, but are hindered by their high computational cost. Neural- initialized-Newton (NiN) methods combine deep learning with iterative solvers to accelerate convergence, but existing approaches lack features that capture long-range physical couplings critical to cardiovascular flow. In this work, I propose a modified MeshGraphNets architecture augmented with spectral features derived from the finite element stiffness matrix K, enabling the model to encode global boundary condition information absent from standard message-passing. The modified Spectral MGN achieves a test RMSE of 1.082, with strong directional alignment between predicted and true solution deltas.