This work presents a fast neural surrogate capable of reconstructing fully three-dimensional hemodynamic velocity fields in stenotic and bifurcating microvascular geometries with satisfactory accuracy, avoiding repeated, computationally demanding computational fluid dynamics (CFD) simulations. A Fourier-augmented, coordinate-neural surrogate is presented and assessed for rapid computation of three-dimensional blood-flow fields in a sample geometry. The model is trained on detailed CFD data across a parameter set of stenosis severities that feed a direct mapping from spatial coordinates to velocity components. To mitigate spectral bias and improve accuracy in regions of steep gradients, the input space is embedded with random Fourier features and compared against a conventional multilayer perceptron (MLP) backbone. Predictive ability is assessed upon strict hold-out testing, during which certain arteriolar stenosis cases are excluded from training and treated with the Fourier surrogate. Direct comparison with CFD results reveals that the Fourier MLP achieves nearly CFD fidelity with the coefficient of determination R2 ≥ 0.994 and offers more than 80% reduction in the normalized errors as provided by conventional MLP, with the precise improvement depending on the severity of stenosis. Centerline velocity and cross-sectional profiles further show that the Fourier MLP reconstructs stenosis speed-up and radial profiles more reliably compared to conventional MLP. These results indicate that Fourier feature embedding provides a simple and effective route to robust full-field hemodynamic surrogates for efficient screening of stenosis configurations without resorting to repeated, heavily demanding CFD simulations.
Papadopoulos et al. (Tue,) studied this question.