ß-Variational autoencoders and transformers for reduced-order modelling of fluid flows.

Variational autoencoder architectures have the potential to develop reduced-order models for chaotic fluid flows. We propose a method for learning compact and near-orthogonal reduced-order models using a combination of a ß-variational autoencoder and a transformer, tested on numerical data from a two-dimensional viscous flow in both periodic and chaotic regimes. The ß-variational autoencoder is trained to learn a compact latent representation of the flow velocity, and the transformer is trained to predict the temporal dynamics in latent-space. Using the ß-variational autoencoder to learn disentangled representations in latent-space, we obtain a more interpretable flow model with features that resemble those observed in the proper orthogonal decomposition, but with a more efficient representation. Using Poincaré maps, the results show that our method can capture the underlying dynamics of the flow outperforming other prediction models. The proposed method has potential applications in other fields such as weather forecasting, structural dynamics or biomedical engineering.

Data-driven cardiovascular flow modelling: examples and opportunities.

High-fidelity blood flow modelling 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 resolution, and measurement noise. Additionally, extracting useful information from these datasets is challenging. Data-driven modelling techniques have the potential to overcome these challenges and transform cardiovascular flow modelling. Here, we review several data-driven modelling 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 modelling of cardiovascular flows, including the dynamic mode decomposition and the sparse identification of nonlinear dynamics. All techniques are presented in the context of cardiovascular flows with simple examples. These data-driven modelling techniques have the potential to transform computational and experimental cardiovascular research, and we discuss challenges and opportunities in applying these techniques in the field, looking ultimately towards data-driven patient-specific blood flow modelling.

Integrating multi-fidelity blood flow data with reduced-order data assimilation.

High-fidelity patient-specific modeling of cardiovascular flows and hemodynamics is challenging. Direct blood flow measurement inside the body with in-vivo measurement modalities such as 4D flow magnetic resonance imaging (4D flow MRI) suffer from low resolution and acquisition noise. In-vitro experimental modeling and patient-specific computational fluid dynamics (CFD) models are subject to uncertainty in patient-specific boundary conditions and model parameters. Furthermore, collecting blood flow data in the near-wall region (e.g., wall shear stress) with experimental measurement modalities poses additional challenges. In this study, a computationally efficient data assimilation method called reduced-order modeling Kalman filter (ROM-KF) was proposed, which combined a sequential Kalman filter with reduced-order modeling using a linear model provided by dynamic mode decomposition (DMD). The goal of ROM-KF was to overcome low resolution and noise in experimental and uncertainty in CFD modeling of cardiovascular flows. The accuracy of the method was assessed with 1D Womersley flow, 2D idealized aneurysm, and 3D patient-specific cerebral aneurysm models. Synthetic experimental data were used to enable direct quantification of errors using benchmark datasets. The accuracy of ROM-KF in reconstructing near-wall hemodynamics was assessed by applying the method to problems where near-wall blood flow data were missing in the experimental dataset. The ROM-KF method provided blood flow data that were more accurate than the computational and synthetic experimental datasets and improved near-wall hemodynamics quantification.