Physics-informed neural networks (PINNs) have emerged as a promising approach for solving complex fluid dynamics problems, yet their application to fluid-structure interaction (FSI) problems with moving boundaries remains largely unexplored. This work addresses the critical challenge of modeling FSI systems with moving interfaces, where traditional unified PINN architectures struggle to capture the distinct physics governing fluid and structural domains simultaneously. We present an innovative Eulerian-Lagrangian PINN architecture that integrates immersed boundary method (IBM) principles to solve FSI problems with moving boundary conditions. Our approach fundamentally departs from conventional unified architectures by introducing domain-specific neural networks: an Eulerian network for fluid dynamics and a Lagrangian network for structural interfaces, coupled through physics-based constraints. Additionally, we incorporate learnable B-spline activation functions with SiLU to capture both localized high-gradient features near interfaces and global flow patterns. Empirical studies on a 2D cavity flow problem involving a moving solid structure show that while baseline unified PINNs achieve reasonable velocity predictions, they suffer from substantial pressure errors (12.9%) in structural regions. Our Eulerian-Lagrangian architecture with learnable activations (EL-L) achieves better performance across all metrics, improving accuracy by 24.1-91.4% and particularly reducing pressure errors from 12.9% to 2.39%. These results demonstrate that domain decomposition aligned with physical principles, combined with locality-aware activation functions, is essential for accurate FSI modeling within the PINN framework.

Accurate assessment of intraventricular blood flow is essential for evaluating hemodynamic conditions in patients supported by Left Ventricular Assist Devices (LVADs). However, clinical imaging is either incompatible with LVADs or yields sparse, low-quality velocity data. While Computational Fluid Dynamics (CFD) simulations provide high-fidelity data, they are computationally intensive and impractical for routine clinical use. To address this, we propose LVADNet3D, a 3D convolutional autoencoder that reconstructs full-resolution intraventricular velocity fields from sparse velocity vector inputs. In contrast to a standard UNet3D model, LVADNet3D incorporates hybrid downsampling and a deeper encoder-decoder architecture with increased channel capacity to better capture spatial flow patterns. To train and evaluate the models, we generate a high-resolution synthetic dataset of intraventricular blood flow in LVAD-supported hearts using CFD simulations. We also investigate the effect of conditioning the models on anatomical and physiological priors. Across various input configurations, LVADNet3D outperforms the baseline UNet3D model, yielding lower reconstruction error and higher PSNR results.

In recent decades, the use of 4D Flow MRI images has enabled the quantification of velocity fields within a volume of interest and along the cardiac cycle. However, the lack of resolution and the presence of noise in these biomarkers are significant issues. As indicated by recent studies, it appears that biomarkers such as wall shear stress are particularly impacted by the poor resolution of vessel segmentation. The Phase Contrast Magnetic Resonance Angiography (PC-MRA) is the state-of-the-art method to facilitate segmentation. The objective of this work is to introduce a new handcraft feature that provides a novel visualisation of 4D Flow MRI images, which is useful in the segmentation task. This feature, termed Weighted Mean Frequencies (WMF), is capable of revealing the region in three dimensions where a voxel has been passed by pulsatile flow. Indeed, this feature is representative of the hull of all pulsatile velocity voxels. The value of the feature under discussion is illustrated by two experiments. The experiments involved segmenting 4D Flow MRI images using optimal thresholding and deep learning methods. The results obtained demonstrate a substantial enhancement in terms of IoU and Dice, with a respective increase of 0.12 and 0.13 in comparison with the PC-MRA feature, as evidenced by the deep learning task. This feature has the potential to yield valuable insights that could inform future segmentation processes in other vascular regions, such as the heart or the brain.

This article introduces a novel methodology that integrates singular value decomposition (SVD) with a shallow linear neural network for forecasting high resolution fluid mechanics data. The method, termed LC-SVD-DLinear, combines a low-cost variant of singular value decomposition (LC-SVD) with the DLinear architecture, which decomposes the input features-specifically, the temporal coefficients-into trend and seasonality components, enabling a shallow neural network to capture the non-linear dynamics of the temporal data. This methodology uses under-resolved data, which can either be input directly into the hybrid model or downsampled from high resolution using two distinct techniques provided by the methodology. Working with under-resolved cases helps reduce the overall computational cost. Additionally, we present a variant of the method, LC-HOSVD-DLinear, which combines a low-cost version of the high-order singular value decomposition (LC-HOSVD) algorithm with the DLinear network, designed for high-order data. These approaches have been validated using two datasets: first, a numerical simulation of three-dimensional flow past a circular cylinder at $Re = 220$; and second, an experimental dataset of turbulent flow passing a circular cylinder at $Re = 2600$. The combination of these datasets demonstrates the robustness of the method. The forecasting and reconstruction results are evaluated through various error metrics, including uncertainty quantification. The work developed in this article will be included in the next release of ModelFLOWs-app

We present a stochastic method for reconstructing missing spatial and velocity data along the trajectories of small objects passively advected by turbulent flows with a wide range of temporal or spatial scales, such as small balloons in the atmosphere or drifters in the ocean. Our approach makes use of conditional generative diffusion models, a recently proposed data-driven machine learning technique. We solve the problem for two paradigmatic open problems, the case of 3D tracers in homogeneous and isotropic turbulence, and 2D trajectories from the NOAA-funded Global Drifter Program. We show that for both cases, our method is able to reconstruct velocity signals retaining non-trivial scale-by-scale properties that are highly non-Gaussian and intermittent. A key feature of our method is its flexibility in dealing with the location and shape of data gaps, as well as its ability to naturally exploit correlations between different components, leading to superior accuracy, with respect to Gaussian process regressions, for both pointwise reconstruction and statistical expressivity. Our method shows promising applications also to a wide range of other Lagrangian problems, including multi-particle dispersion in turbulence, dynamics of charged particles in astrophysics and plasma physics, and pedestrian dynamics.

This paper focuses on developing a bearings-only measurement-based three-dimensional window traversal guidance method for quadrotor Uninhabitated Aerial Vehicles (UAVs). The desired flight path and heading angles of the quadrotor are proposed as functions of the bearing angle information of the four vertices of the window. These angular guidance inputs employ a bearing angle bisector term and an elliptic shaping angle term, which directs the quadrotor towards the centroid of the window. Detailed stability analysis of the resulting kinematics demonstrates that all quadrotor trajectories lead to the centroid of the window along a direction which is normal to the window plane. A qualitative comparison with existing traversal methodologies showcases the superiority of the proposed guidance approach with regard to the nature of information, computations for generating the guidance commands, and flexibility of replanning the traversal path. Realistic simulations considering six degree-of-freedom quadrotor model and Monte Carlo studies validate the effectiveness, accuracy, and robustness of the proposed guidance solution. Representative flight validation trials are carried out using an indoor motion capture system.

Abstract--Vortices are studied in various scientific disciplines, offering insights into fluid flow behavior. Visualizing the boundary of vortices is crucial for understanding flow phenomena and detecting flow irregularities. This paper addresses the challenge of accurately extracting vortex boundaries using deep learning techniques. While existing methods primarily train on velocity components, we propose a novel approach incorporating particle trajectories (streamlines or pathlines) into the learning process. By leveraging the regional/local characteristics of the flow field captured by streamlines or pathlines, our methodology aims to enhance the accuracy of vortex boundary extraction. In aerodynamics, researchers focus on studying vortices that form in the wake of an aircraft, aiming to mitigate the creation of vortices with long lifetimes; persistent vortices can potentially impede commercial aviation's operational capacity [1]-[3]. Oceanographers, on the other hand, study mesoscale eddies modeled as vortices, to understand the transportation of nutrients and heat in ocean currents [4]- [6].

Due to costs and practical constraints, field campaigns in the atmospheric boundary layer typically only measure a fraction of the atmospheric volume of interest. Machine learning techniques have previously successfully reconstructed unobserved regions of flow in canonical fluid mechanics problems and two-dimensional geophysical flows, but these techniques have not yet been demonstrated in the three-dimensional atmospheric boundary layer. Here, we conduct a numerical analogue of a field campaign with spatially limited measurements using large-eddy simulation. We pose flow reconstruction as an inpainting problem, and reconstruct realistic samples of turbulent, three-dimensional flow with the use of a latent diffusion model. The diffusion model generates physically plausible turbulent structures on larger spatial scales, even when input observations cover less than 1% of the volume. Through a combination of qualitative visualization and quantitative assessment, we demonstrate that the diffusion model generates meaningfully diverse samples when conditioned on just one observation. These samples successfully serve as initial conditions for a large-eddy simulation code. We find that diffusion models show promise and potential for other applications for other turbulent flow reconstruction problems.

Inference problems for two-dimensional snapshots of rotating turbulent flows are studied. We perform a systematic quantitative benchmark of point-wise and statistical reconstruction capabilities of the linear Extended Proper Orthogonal Decomposition (EPOD) method, a non-linear Convolutional Neural Network (CNN) and a Generative Adversarial Network (GAN). We attack the important task of inferring one velocity component out of the measurement of a second one, and two cases are studied: (I) both components lay in the plane orthogonal to the rotation axis and (II) one of the two is parallel to the rotation axis. We show that EPOD method works well only for the former case where both components are strongly correlated, while CNN and GAN always outperform EPOD both concerning point-wise and statistical reconstructions. For case (II), when the input and output data are weakly correlated, all methods fail to reconstruct faithfully the point-wise information. In this case, only GAN is able to reconstruct the field in a statistical sense. The analysis is performed using both standard validation tools based on $L_2$ spatial distance between the prediction and the ground truth and more sophisticated multi-scale analysis using wavelet decomposition. Statistical validation is based on standard Jensen-Shannon divergence between the probability density functions, spectral properties and multi-scale flatness.

The Strait of Gibraltar is a region characterized by intricate oceanic sub-mesoscale features, influenced by topography, tidal forces, instabilities, and nonlinear hydraulic processes, all governed by the nonlinear equations of fluid motion. In this study, we aim to uncover the underlying physics of these phenomena within 3D MIT general circulation model simulations, including waves, eddies, and gyres. To achieve this, we employ Dynamic Mode Decomposition (DMD) to break down simulation snapshots into Koopman modes, with distinct exponential growth/decay rates and oscillation frequencies. Our objectives encompass evaluating DMD's efficacy in capturing known features, unveiling new elements, ranking modes, and exploring order reduction. We also introduce modifications to enhance DMD's robustness, numerical accuracy, and robustness of eigenvalues. DMD analysis yields a comprehensive understanding of flow patterns, internal wave formation, and the dynamics of the Strait of Gibraltar, its meandering behaviors, and the formation of a secondary gyre, notably the Western Alboran Gyre, as well as the propagation of Kelvin and coastal-trapped waves along the African coast. In doing so, it significantly advances our comprehension of intricate oceanographic phenomena and underscores the immense utility of DMD as an analytical tool for such complex datasets, suggesting that DMD could serve as a valuable addition to the toolkit of oceanographers.