[論文レビュー] Model Order Reduction of Cerebrovascular Hemodynamics Using POD_Galerkin and Reservoir Computing_based Approach

Rahul Halder, Arash Hajisharifi+2 more|arXiv (Cornell University)|Mar 19, 2026

Model Reduction and Neural Networks被引用数 0

ひとこと要約

The paper compares intrusive POD–Galerkin and non-intrusive POD–Reservoir Computing reduced-order models for unsteady cerebrovascular hemodynamics, demonstrating comparable accuracy and substantial speed-ups (100x–1000x) over full-order CFD using a multi-harmonic training signal.

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.

研究の動機と目的

• Motivate reduced-order modeling (ROM) for cerebrovascular hemodynamics to enable real-time prediction.
• Compare physics-based POD–Galerkin ROM with data-driven POD–Reservoir Computing ROM on a basilar artery bifurcation.
• Show that a multi-harmonic, multi-amplitude training signal speeds up and generalizes training for both approaches.
• Assess reconstruction accuracy for pressure, velocity, and wall shear stress (WSS) against high-fidelity CFD.
• Evaluate computational efficiency and robustness of both ROMs across different inflow signals.

提案手法

• High-fidelity 3D CFD snapshots of an idealized basilar artery bifurcation are compressed with POD to a low-dimensional basis.
• Two reduced-order models are constructed from the same POD basis: (i) POD–Galerkin (intrusive) projecting Navier–Stokes onto the reduced space, (ii) POD–Reservoir Computing (non-intrusive) learning the temporal evolution of coefficients via a recurrent reservoir.
• An offline phase generates snapshot data and POD bases; an online phase advances reduced coefficients to reconstruct 3D fields.
• Multi-harmonic and multi-amplitude training signals are used to accelerate training and improve generalization across inflow conditions.
• In the POD–Galerkin formulation, the reduced-order system consists of M a-dot = Q(a,a) + L a - P b and R a = 0, with predefined reduced operators from the projection.
• In the POD–Reservoir Computing framework, temporal coefficients a(t) are learned via an Echo State Network with ridge-regularized linear readout, mapping inlet velocity input to POD coefficients.

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 n

実験結果

リサーチクエスチョン

• RQ1 Can POD–Galerkin and POD–Reservoir Computing ROMs accurately reconstruct pressure, velocity, and WSS compared with full-order CFD on a basilar artery bifurcation?
• RQ2 Do both ROMs generalize to unseen inflow signals when trained with multi-harmonic inputs?
• RQ3 What computational speed-ups are achievable by each ROM relative to full-order simulations?
• RQ4 Does the reservoir computing approach offer robustness and efficiency advantages over the intrusive POD–Galerkin method in cerebrovascular hemodynamics?

主な発見

• Both POD–Galerkin and POD–Reservoir Computing achieve speed-ups on the order of 10^2 to 10^3 compared to full-order simulations.
• POD–Galerkin and POD–Reservoir Computing provide accurate reconstructions of pressure, velocity, and WSS in the basilar artery bifurcation.
• A multi-harmonic, multi-amplitude training signal enables efficient training for both approaches and supports generalization to different inflow conditions.
• Reservoir Computing, with a fixed nonlinear reservoir and trainable linear readout, offers a non-intrusive surrogate that can match physics-based ROM performance in this setting.
• The comparison highlights the viability of both physics-based and data-driven ROMs as robust, efficient surrogates for real-time hemodynamic predictions near bifurcation zones.

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 ca