  High-fidelity modeling of blood flow is crucial for enhancing our
understanding of cardiovascular disease. Despite significant advances in
computational and experimental characterization of blood flow, the knowledge
that we can acquire from such investigations remains limited by the presence of
uncertainty in parameters, low spatiotemporal resolution, and measurement
noise. Additionally, extracting useful information from these datasets is
challenging. Data-driven modeling techniques have the potential to overcome
these challenges and transform cardiovascular flow modeling. In this paper, we
review several data-driven modeling techniques, highlight the common ideas and
principles that emerge across numerous such techniques, and provide
illustrative examples of how they could be used in the context of
cardiovascular fluid mechanics. In particular, we discuss principal component
analysis (PCA), robust PCA, compressed sensing, the Kalman filter for data
assimilation, low-rank data recovery, and several additional methods for
reduced-order modeling for cardiovascular flows, including the dynamic mode
decomposition (DMD), and the sparse identification of nonlinear dynamics
(SINDy). All of these techniques are presented in the context of cardiovascular
flows with simple examples. These data-driven modeling techniques have the
potential to transform computational and experimental cardiovascular flow
research, and we discuss challenges and opportunities in applying these
techniques in the field, looking ultimately towards data-driven
patient-specific blood flow modeling.
