High-fidelity cardiovascular flow modeling depends critically on accurate velocity boundary data, which directly influences pressure and wall-shear-related diagnostics. However, clinical measurements such as 4D Flow MRI are often noisy, incomplete, or too coarse to be used directly in computational models.

In this work, we developed a stochastic data-assimilation framework that integrates computational fluid dynamics (CFD) with an advanced Ensemble Kalman–based inference method to recover both:

• unknown inlet velocity profiles (constant, time-dependent, and space–time-dependent), and

• the full flow state, including velocity and pressure fields, within complex vascular geometries.

The method continuously refines boundary estimates by assimilating sparse or noisy measurements into the CFD solver, enabling real-time correction of physical model parameters. We tested the framework on both idealized and patient-specific vascular models, demonstrating its ability to produce more reliable hemodynamic reconstructions, particularly for quantities of interest such as wall shear stress and flow topology.

This study represents a step toward data-driven cardiovascular digital twins by combining physics-based modeling, statistical inference, and uncertainty-aware parameter estimation, approaches that form the foundation of modern Scientific Machine Learning (SciML).