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

Clinical decision-making for coronary intervention relies mainly on angiography and fractional flow reserve (FFR). However, angiography is two-dimensional and lacks depth information for 3D lesion characterization, while FFR provides only a single functional index, offering limited hemodynamic insight. Among existing methods, numerical analysis is computationally expensive, whereas learning-based approaches require extensive supervision and often lack physical consistency. To address these limitations, we propose physics-informed hemodynamic modeling, an integrated deep learning framework for 3D coronary blood flow analysis from dual-view angiography. First, an attention-enhanced CNN reconstructs coronary geometry from angiography. The resulting point clouds are then mapped to a reference domain and Fourier-encoded for joint representation. A decoupled network separately predicts velocity and pressure fields, with embedded physical priors enabling efficient transfer across physiological conditions. Across 32 clinical patients evaluated under four flow conditions, the trans-stenotic pressure-drop mean absolute percentage error was 2.02%, while the velocity and pressure relative-L2 errors were 0.054 and 0.023, respectively. Validation against hospital-measured FFR further achieved 93.8% diagnostic accuracy (30/32; exact 95% CI, 79.2%-99.2%). The framework also supports illustrative revascularization comparisons and sparse-data assimilation, with the full angiography-to-hemodynamics pipeline completed within 20 minutes per patient.

Cardiovascular modeling has rapidly advanced over the past few decades due to the rising needs for health tracking and early detection of cardiovascular diseases. While 1-D arterial models offer an attractive compromise between computational efficiency and solution fidelity, their application on large populations or for generating large in silico cohorts remains challenging. Certain hemodynamic parameters like the terminal resistance/compliance, are difficult to clinically estimate and often yield non-physiological hemodynamics when sampled naively, resulting in large portions of simulated datasets to be discarded. In this work, we present a systematic framework for training machine learning (ML) models, capable of instantaneous hemodynamic prediction and parameter estimation. We initially start with generating a parametric virtual cohort of patients which is based on the multivariate correlations observed in the large Asklepios clinical dataset, ensuring that physiological parameter distributions are respected. We then train a deep neural surrogate model, able to predict patient-specific arterial pressure and cardiac output (CO), enabling rapid a~priori screening of input parameters. This allows for immediate rejection of non-physiological combinations and drastically reduces the cost of targeted synthetic dataset generation (e.g. hypertensive groups). The model also provides a principled means of sampling the terminal resistance to minimize the uncertainties of unmeasurable parameters. Moreover, by assessing the model's predictive performance we determine the theoretical information which suffices for solving the inverse problem of estimating the CO. Finally, we apply the surrogate on a clinical dataset for the estimation of central aortic hemodynamics i.e. the CO and aortic systolic blood pressure (cSBP).

We study a hybrid proposal--correction architecture for reduced-order PDE forecasting in which a pure-state quantum reservoir computer (QRC) predicts latent coefficient dynamics and a PINN-based physics-informed corrector (PIC) refines local rollout windows. The method is evaluated on Burgers and Kuramoto--Sivashinsky (KS), with KS as the primary chaotic benchmark. On KS, QRC+PIC consistently improves over QRC alone in RMSE, NRMSE, and PDE residual, while Burgers highlights a regime in which simple baselines remain strong. These results suggest that QRC proposals with local physics-informed correction are a viable benchmark-dependent reduced-order forecasting strategy.