Model Order Reduction of Cerebrovascular Hemodynamics Using POD_Galerkin and Reservoir Computing_based Approach

Abstract

We investigate model order reduction (MOR) strategies for simulating unsteady hemodynamics within cerebrovascular systems, contrasting a physics-based intrusive approach with a data-driven non-intrusive framework. High-fidelity 3D Computational Fluid Dynamics (CFD) snapshots of an idealised basilar artery bifurcation are first compressed into a low-dimensional latent space using Proper Orthogonal Decomposition (POD). We evaluate the performance of a POD-Galerkin (POD-G) model, which projects the Navier-Stokes equations onto the reduced basis, against a POD-Reservoir Computing (POD-RC) model that learns the temporal evolution of coefficients through a recurrent architecture. A multi-harmonic and multi-amplitude training signal is introduced to improve training efficiency. Both methodologies achieve computational speed-ups on the order of 10^2 to 10^3 compared to full-order simulations, demonstrating their potential as efficient and accurate surrogates for predicting flow quantities such as wall shear stress.

Figures (15)

• Figure 1: Full 3D cerebrovascular network and zoomed view of the basilar artery bifurcation. The highlighted bifurcation region corresponds to the anatomical segment used to construct the idealized 3D computational model employed in this study. Both the basilar artery mesh and the cerebrovascular network geometry were generated using the meshing framework of Decroocq et al. decroocq2023meshing and subsequently merged for visualization purposes.
• Figure 2: Synthetic inlet velocity boundary conditions used in this work. The training waveform is a multi-harmonic signal, while the test waveform is a single-frequency sinusoid. These signals drive the unsteady inflow in the FOM and are used to evaluate the temporal learning and generalization capability of the surrogate models.
• Figure 3: Schematic of the surrogate workflow. The Offline Phase (gray) consists of FOM data generation and POD basis extraction. In the Online Phase (blue), the temporal coefficients are predicted either by an intrusive POD--Galerkin ROM or by a non-intrusive POD--RC surrogate; reconstructed fields are then evaluated against the FOM reference.
• Figure 4: Layers of Reservoir Computing Architecture, first Layer is the input layer, second one is fixed and randomly initialized, and only the final output layer is trainable.
• Figure 5: First six POD modes of the velocity magnitude field for the cerebrovascular bifurcation geometry. The modes are ordered according to decreasing energetic contribution with the first mode representing the dominant flow structure.