Reconstruction Of Velocity Field Research Articles

Neural network reconstruction of density and velocity fields from the 2MASS Redshift Survey

Aims. Our aim is to reconstruct the 3D matter density and peculiar velocity fields in the local Universe up to a distance of 200 h−1 Mpc from the Two-Micron All-Sky Redshift Survey (2MRS) using a neural network (NN). Methods. We employed an NN with a U-net autoencoder architecture and a weighted mean squared error loss function trained separately to output either the density or velocity field for a given input grid of galaxy number counts. The NN was trained on mocks derived from the Quijote N-body simulations, incorporating redshift-space distortions (RSDs), galaxy bias, and selection effects closely mimicking the characteristics of 2MRS. The trained NN was benchmarked against a standard Wiener filter (WF) on a validation set of mocks before applying it to 2MRS. Results. The NN reconstructions effectively approximate the mean posterior estimate of the true density and velocity fields conditioned on the observations. They consistently outperform the WF in terms of reconstruction accuracy and effectively capture the nonlinear relation between velocity and density. The NN-reconstructed bulk flow of the total survey volume exhibits a significant correlation with the true mock bulk flow, demonstrating that the NN is sensitive to information on “super-survey” scales encoded in the RSDs. When applied to 2MRS, the NN successfully recovers the main known clusters, some of which are partially in the Zone of Avoidance. The reconstructed bulk flows in spheres of different radii less than 100 h−1 Mpc are in good agreement with a previous 2MRS analysis that required an additional external bulk flow component inferred from directly observed peculiar velocities. The NN-reconstructed peculiar velocity of the Local Group closely matches the observed Cosmic Microwave Background dipole in amplitude and Galactic latitude, and only deviates by 18° in longitude. The NN-reconstructed fields are publicly available.

Fusion of Lagrangian drifter data and numerical model outputs for improved assessment of turbulent dispersion

Abstract. Transport and dispersion processes in the ocean are crucial, as they determine the lifetime and fate of biological and chemical quantities drifting with ocean currents. Due to the complexity of the coastal ocean environment, numerical circulation models have difficulties to accurately simulate highly turbulent flows and dispersion processes, especially in highly energetic tidal basins such as the eastern English Channel. A method of improving the results of coastal circulation modeling and tracer dispersion in the Dover Strait is proposed. Surface current velocities derived from Lagrangian drifter measurements in November 2020 and May 2021 were optimally interpolated in time and space to constrain a high-resolution coastal circulation MARS model, with careful attention given to selecting ensemble members composing the model covariance matrix. The space–time velocity covariances derived from model simulations were utilized by the optimal interpolation algorithm to determine the most likely evolution of the velocity field under constraints provided by Lagrangian observations and their error statistics. The accuracy of the velocity field reconstruction was evaluated at each time step. The results of the fusion of model outputs with surface drifter velocity measurements show a significant improvement (by ∼ 50 %) of the model capability to simulate the drift of passive tracers in the Dover Strait. Optimized velocity fields were used to quantify the absolute dispersion in the study area. The implications of these results are important, as they can be used to improve existing decision-making support tool or design new tools for monitoring the transport and dispersion in a coastal ocean environment.

Velocity field reconstruction of mixing flow in T-junctions based on particle image database using deep generative models

Velocity field reconstruction of mixing flow in T-junctions based on particle image database using deep generative models

A Particle Based Approach For Improved Resolution PIV And TOMO-PIV Based On The Coherent Point Drift And The Affine Least-Squares Transformation

Particle Image Velocimetry (PIV) is a widely used method for flow diagnostics, but there is still potential for improvement, particularly in terms of velocity gradient estimation and computational cost when considering three-dimensional problems. This paper presents a framework that combines a Particle Tracking Velocity (PTV) approach with local gradient-based Eulerian reconstruction to improve PIV performance. The approach uses the Coherent Point Drift (CPD) method for particle pairing and introduces the Affine Least-Squares Transformation (ALST) for local deformation gradient estimation. The CPD method consists of pairing particles whose positions at two successive instants have been obtained from the images. The ALST estimates local deformation gradients, allowing the Eularian reconstruction of the velocity field. The effectiveness of the proposed method compared to traditional PIV algorithms is demonstrated by synthetic test cases in both 2D and 3D configurations. In 2D cases, the CPD+ALST approach outperforms standard PIV methods, especially in capturing local velocity gradients. In 3D cases, comparisons with TOMO-PIV show the improved performance of CPD+ALST in the context of locally large velocity gradients. However, the linear nature of ALST makes it less efficient than quadratic binning techniques. The study demonstrates the potential of CPD+ALST to improve velocity field reconstruction in complex flows.

An airflow velocity field reconstruction method with sparse or incomplete data using physics-informed neural network

Velocity field is critical for creating a healthy and comfortable indoor environment but it is difficult to be measured experimentally. Due to the limitations of measurement instruments and site conditions, the captured data are usually sparse, incomplete, and low-dimensional, which limits further research on indoor velocity field. This study proposes a practical reconstruction and super-resolution method based on physics-informed learning that seamlessly integrates imperfect measured data and physical laws. The ability to reconstruct the airflow velocity field with imperfect data as the training dataset was validated using a three-dimensional and three-component airflow field generated with an axial fan. This method successfully recovered the airflow field from sparse or insufficient data (even when the amount of data was only 5 % of the original vector fields) and incomplete data. This indicates that the proposed method can reconstruct and super-resolve the airflow velocity vector fields from sparse, incomplete, and low-dimensional data.

Measured Regional Division Optimization for Acoustic Tomography Velocity Field Reconstruction in a Circular Area.

The acoustic tomography (AT) velocity field reconstruction technique has become a research hotspot in recent years due to its noninvasive nature, high accuracy, and real-time measurement advantages. However, most of the existing studies are limited to the reconstruction of the velocity field in a rectangular area, and there are very few studies on a circular area, mainly because the layout of acoustic transducers, selection of acoustic paths, and division of measured regions are more difficult in a circular area than in a rectangular area. Therefore, based on AT and using the reconstruction algorithm of the Markov function and singular value decomposition (MK-SVD), this paper proposes a measured regional division optimization algorithm for velocity field reconstruction in a circular area. First, an acoustic path distribution based on the multipath effect is designed to solve the problem of the limited emission angle of the acoustic transducer. On this basis, this paper proposes an adaptive optimization algorithm for measurement area division based on multiple sub-objectives. The steps are as follows: first, two optimization objectives, the condition number of coefficient matrix and the uniformity of acoustic path distribution, were designed. Then, the weights of each sub-objective are calculated using the coefficient of variation (CV). Finally, the measured regional division is optimized based on particle swarm optimization (PSO). The reconstruction effect of the algorithm and the anti-interference ability are verified through the reconstruction experiments of the model velocity field and the simulated velocity field.

Fast reconstruction of boiler numerical physical field based on proper orthogonal decomposition and conditional deep convolutional generative adversarial networks

ABSTRACT Obtaining real-time physical field data inside the boiler furnace is crucial for combustion diagnostics and optimization. In this work, we propose a fast reconstruction technique for the physical fields in a tangentially-fired coal boiler. The method combines the Proper Orthogonal Decomposition (POD) and Conditional Deep Convolutional Generative Adversarial Networks (cDCGAN) based on the boiler physical field obtained by computational fluid dynamics (CFD). Firstly, CFD simulations are performed using data from the boiler Distributed Control System (DCS). After verifying the CFD results, we expanded the simulation to 105 operational condition cases sample sets. Then, the physical fields of the sample set undergo POD to determine the appropriate number of POD bases, thereby ensuring the accuracy of the reconstruction. Finally, the cDCGAN method is employed to establish the correlation between the POD bases and the operational conditions of the boiler. Results show that the POD-cDCGAN method achieves rapid and accurate reconstruction of temperature and velocity fields, with mean relative error (MRE) below 1.5% and root relative squared error (RRSE) below 5.7%. The reconstruction time is reduced to 10.57s, significantly faster than direct CFD methods. The POD-cDCGAN method offers an efficient approach for online operational diagnosis and digital twin construction of boiler equipment.

Approximations for the divergence of the reconstructed local large-scale structure velocity field and its possible implications for Cosmology

We characterize the peculiar velocity field of the local large-scale structure reconstructed from the 2M++ survey, by treating it as a fluid, extracting the divergence via different approximations over a range of averaged scales. This reconstructed field is important for cosmology, since it was used to correct the peculiar redshifts of the last SNIA compilation Pantheon+. The results have intriguing implications for the LLSS fluid dynamics and particularly for the “Tilted Cosmology” model, although those results have to be taken carefully as the velocity field could contain significant bias due to the reconstruction procedure. Those possible bias and its influence in our results are discussed. Representative values of the apparent deceleration parameter (q̃) are computed, in order to compare our results with the theoretical predictions of the tilted-universe scenario. We conclude that better velocity field reconstructions are necessary in order to constrain the parameters implied in LLSS research and alternative cosmologies.

The large-scale velocity field from the Cosmicflows-4 data

ABSTRACT The reconstruction of the large-scale velocity field from the grouped Cosmicflows-4 (CF4) database is presented. The lognormal bias of the inferred distances and velocities data is corrected by the Bias Gaussianization correction scheme, and the linear density and velocity fields are reconstructed by means of the Wiener filter and constrained realizations (CRs) algorithm. These tools are tested against a suite of random and constrained Cosmicflows-3-like mock data. The CF4 data consist of three main subsamples – the 6dFGS and the SDSS data – and the ‘others’. The individual contributions of the subsamples have been studied. The quantitative analysis of the velocity field is done mostly by the mean overdensity (ΔL(R)) and the bulk velocity (Vbulk(R)) profiles of the velocity field out to $300\, {{h^{-1}\, {\rm Mpc}}}$. The Vbulk(R) and ΔL(R) profiles of the CF4 data without its 6dFGS component are consistent with the cosmic variance to within 1σ. The 6dFGS sample dominates the Vbulk (ΔL) profile beyond $\sim 120\, {{h^{-1}\, {\rm Mpc}}}$, and drives it to roughly a 3.4σ (−1.9σ) excess (deficiency) relative to the cosmic variance at $R\sim 250\ (190)\ \, {{h^{-1}\, {\rm Mpc}}}$. The excess in the amplitude of Vbulk is dominated by its Supergalactic X component, roughly in the direction of the Shapley Concentration. The amplitude and alignment of the inferred velocity field from the CF4 data are at $\sim (2{-}3)\, \sigma$ discrepancy with respect to the Lambda cold dark matter model. Namely, it is somewhat atypical but yet there is no compelling tension with the model.

Simultaneous reconstruction of 3D non-uniform temperature and velocity fields in a furnace using a bidirectional acoustic path separation tracking method

Acoustic measurement techniques applied to furnace measurements are based on the coupling of multiple fields, such as sound, temperature, and flow. To better measure high-temperature fluids within furnaces using acoustic technology, this study establishes a physical model that separates the bidirectional propagation path of sound. Additionally, a novel nonlinear acoustic ray-tracing method is proposed that allows the simultaneous measurement of temperature and flow. The combustion process of high-temperature swirling flow in a furnace is simulated, the effective path of sound propagation is tracked, and the existence of a sound shadow zone in the low-temperature jet region of the burner is discovered. After reasonably arranging sensor positions, three-dimensional nonuniform temperature and complex flow fields are simultaneously reconstructed by combining ray tracing and nonlinear acoustic tomography. The feasibility of the method is analyzed via the error analysis of the computational fluid dynamics simulation data and the reconstructed data. The proposed method provides a solution for improving the existing acoustic measurement techniques in furnaces.

Adaptive restoration and reconstruction of incomplete flow fields based on unsupervised learning

Due to experimental limitations and data transmission constraints, we often encounter situations where we can only obtain incomplete flow field data. However, even with incomplete data, we can still extract valuable information about the main structural characteristics of the flow field. In this study, we propose a novel unsupervised learning reconstruction method to restore the incomplete flow field data. Our method comprises several key steps: First, based on the temporal evolution characteristics of the flow field, we employ the Autoregressive Integrated Moving Average model method to pre-reconstruct the incomplete data. Next, we introduce the Fuzzy Spatial Consistency Index (FSCI), which measures the spatial coherence among neighboring data variations. By utilizing FSCI as a guiding metric, we iteratively optimize and replace missing values using the Proper Orthogonal Decomposition method. Importantly, our reconstruction process does not rely on expensive high-fidelity data fusion or external intervention, making it highly efficient and cost-effective. We focus our research on the classic problem of flow around the hydrofoil and apply the unsupervised learning reconstruction method to restore incomplete flow fields with varying missing rates. We also investigate the impact of flow field stability, snapshot sampling frequency, and missing structure on reconstruction accuracy. Our results indicate that these factors significantly influence the reconstruction of velocity fields with a high missing rate compared with a lower missing rate. Additionally, we observe that the reconstruction performance of the streamwise velocity field is relatively inferior compared to the normal velocity field, and the reconstruction accuracy is higher for relatively stable flow fields. These findings provide valuable insights and further validate the effectiveness and applicability of the unsupervised learning reconstruction method for restoring incomplete flow fields.

Euclid: Cosmology forecasts from the void-galaxy cross-correlation function with reconstruction

We have investigated the cosmological constraints that can be expected from measurement of the cross-correlation of galaxies with cosmic voids identified in the Euclid spectroscopic survey, which will include spectroscopic information for tens of millions of galaxies over 15 000 deg2 of the sky in the redshift range 0.9 ≤ z < 1.8. We have done this using simulated measurements obtained from the Flagship mock catalogue, the official Euclid mock that closely matches the expected properties of the spectroscopic dataset. To mitigate anisotropic selection-bias effects, we have used a velocity field reconstruction method to remove large-scale redshift-space distortions from the galaxy field before void-finding. This allowed us to accurately model contributions to the observed anisotropy of the cross-correlation function arising from galaxy velocities around voids as well as from the Alcock–Paczynski effect, and we studied the dependence of constraints on the efficiency of reconstruction. We find that Euclid voids will be able to constrain the ratio of the transverse comoving distance DM and Hubble distance DH to a relative precision of about 0.3%, and the growth rate fσ8 to a precision of between 5% and 8% in each of the four redshift bins covering the full redshift range. In the standard cosmological model, this translates to a statistical uncertainty ΔΩm = ±0.0028 on the matter density parameter from voids, which is better than what can be achieved from either Euclid galaxy clustering and weak lensing individually. We also find that voids alone can measure the dark energy equation of state to a 6% precision.

Fast reconstruction of the orbital velocity field of sea surface by sinusoidal decomposition neural network

A neural network called sinusoidal decomposition neural network (SDNN) is proposed to reconstruct the digital elevation model (DEM) and orbital velocity field (OVF) of sea surface. According to the linear wave theory, DEM can be regarded as the superposition of a series of sine waves, from which OVF can be obtained. The SDNN adopts a fully connected network (FCN) to fit the DEM, which is similar to the inverse discrete Fourier transform (IDFT) model and regression model. The two-dimensional and three-dimensional SDNN are introduced in detail and their validities are demonstrated. A major advantage of the SDNN is that it requires only one scene of the wave height to reconstruct the OVF. By the applications to wind-driven sea surface and ship wake, respectively, the correctness and efficiency of the reconstruction are verified.

Uncertainty guided ensemble self-training for semi-supervised global field reconstruction

Recovering the global accurate complex physics field from limited sensors is critical to the measurement and control of the engineering system. General reconstruction methods for recovering the field, especially the deep learning with more parameters and better representational ability, usually require large amounts of labeled data which is unaffordable in practice. To solve the problem, this paper proposes uncertainty guided ensemble self-training (UGE-ST), using plentiful unlabeled data to improve reconstruction performance and reduce the required labeled data. A novel self-training framework with the ensemble teacher and pre-training student designed to improve the accuracy of the pseudo-label and remedy the impact of noise is first proposed. On the other hand, uncertainty guided learning is proposed to encourage the model to focus on the highly confident regions of pseudo-labels and mitigate the effects of wrong pseudo-labeling in self-training, improving the performance of the reconstruction model. Experiments including the airfoil velocity and pressure field reconstruction and the electronic components’ temperature field reconstruction indicate that our UGE-ST can save up to 90% of the data with the same accuracy as supervised learning.

The investigation of the correction factor for ultrasonic flow meters

The aim of this work is to combine analytical and computational techniques in investigation of correction factor for ultrasonic flow meters to improve their accuracy.Exploring velocity profiles that do not have axial symmetry we applied reconstruction of two-dimensional velocity field based on the inverse Abel’s transform.For velocity profiles that do not have rotational symmetry around the axis of the pipeline, the value of the correction factor will depend on the angle of measuring plane orientation relative to the diametrical plane of the flow meter. The calculation of the actual average flow velocity in the cross section of the meter was obtained from a specific mathematical dependencies describing velocity distribution by integration technique.This study allows us to conclude that even under conditions of distorted non-symmetric flows it is possible to determine the performance of ultrasonic flowmeters with sufficient accuracy using both methods of theoretical research and computational hydrodynamics.

Data-driven Reynolds stress models based on the frozen treatment of Reynolds stress tensor and Reynolds force vector

For developing a reliable data-driven Reynold stress tensor (RST) model, successful reconstruction of the mean velocity field based on high-fidelity information (i.e., direct numerical simulations or large-eddy simulations) is crucial and challenging, considering the ill-conditioning problem of Reynolds-averaged Navier–Stokes (RANS) equations. It is shown that the frozen treatment of the Reynolds force vector (RFV) reduced the ill-conditioning problem even for the cases with a very high Reynolds number; therefore, it has a better potential to be used in the data-driven development of the RANS models. In this study, we compare the algebraic RST correction models that are trained based on the frozen treatment of both RFV and RST for the aforementioned potential. We derive a vector-based framework for the RFV similar to the tensor-based framework for the RST. Regarding the complexity of the models, we compare sparse regression on a set of candidate functions and a multi-layer perceptron network. The training process is applied to the high-fidelity data of three cases, including square-duct secondary flow, roughness-induced secondary flow, and periodic hills flow. The results showed that using the RFV discrepancy values, instead of the RST discrepancy values, generally does not improve the reconstruction of the mean velocity field despite the fact that the propagation of the RFV discrepancy data shows lower errors in the propagation process of all three cases. Regarding the complexity, using multi-layer perceptron improves the prediction of the cases with secondary flows, but it shows similar performance in the case of periodic hills.

Research on PIV algorithm for reconstruction of velocity field of fluid with high Reynolds number

ABSTRACT For the problems of distortion and rotation in the image matching of turbulent motion with high Reynolds number, according to the nature of affine transformation, using log-polar coordinate transformation, the matching of turbulent particle images is achieved by performing correlation calculations on the image line by line and developed a matching algorithm (Turbulent Particle Image Matching, abbreviation: TPIM) for particle image pairs with affine transformation and rigid body transformation: by moving the interpretation window, the algorithm is no longer restricted by displacements of particles; by setting the affine lines according to the angle of the image in the log-polar coordinate system and using the affine line as the matching unit, the decoupling of different transformation factors is realized; according to the characteristic of non-uniform sampling in log-polar coordinate transformation, based on the principle of not losing image information, by reasonably setting the image mask and the rate of sampling, establishing the image pyramid and the relative coordinate system, the algorithm complexity is reduced to about 15% of the original. The experimental results of various types of particle images show that the matching accuracy of the TPIM algorithm can reach more than 99%.

An unsupervised deep learning model for dense velocity field reconstruction in particle image velocimetry (PIV) measurements

Supervised deep learning methods reported recently have shown promising capability and efficiency in particle image velocimetry (PIV) processes compared to the traditional cross correlation and optical flow methods. However, the deep learning-based methods in previous reports require synthesized particle images and simulated flows for training prior to applications, conflicting with experimental scenarios. To address this crucial limitation, unsupervised deep learning methods have also been proposed for flow velocity reconstruction, but they are generally limited to rough flow reconstructions with low accuracy in velocity due to, for example, particle occlusion and out-of-boundary motions. This paper proposes a new unsupervised deep learning model named UnPWCNet-PIV (an unsupervised optical flow network using Pyramid, Warping, and Cost Volume). Such a pyramidical network with specific enhancements on flow reconstructions holds capabilities to manage particle occlusion and boundary motions. The new model showed comparable accuracy and robustness with the advanced supervised deep learning methods, which are based on synthesized images, together with superior performance on experimental images. This paper presents the details of the UnPWCNet-PIV architecture and the assessments of its accuracy and robustness on both synthesized and experimental images.

Particle tracking for face-based flux data on general polyhedral grids with applications to groundwater flow modelling

Abstract A particle tracking method based on face fluxes data calculated using finite volume methods is developed for unstructured three-dimensional polyhedral grids. The flow velocity field reconstruction on grid cells using a mixed finite element method is proposed. Cases of sinks and sources in cells as well as different cell partitionings are considered. Algorithms for streamlines and time of flight calculation are provided. Performance and convergence of the method are demonstrated on a set of reference problems.

Decomposition of power number in a stirred tank and real time reconstruction of 3D large-scale flow structures from sparse pressure measurements

We consider the flow inside an unbaffled stirred tank at Re = 600 and decompose the pressure field into components that are constant, linear and quadratic with respect to the temporal coefficients of velocity POD (proper orthogonal decomposition) modes. The pressure components are used to analyse the power number of individual blades and blade combinations. We also employ an identification algorithm to derive a linear dynamic estimator that allows the reconstruction (in real time) of the instantaneous 3D velocity field from sparse pressure measurements at the impeller blades. The first pair of POD modes are reconstructed with reasonable accuracy using the pressure signal from a single sensor. The results improve with 6 or 12 sensors. Application of the estimator to Re=500 and 700 shows that it is robust to changes in operating conditions. The work opens the possibility for real time control of mixing with targeted feeding location and rate.