Flow Reconstruction Research Articles

Flow reconstruction with uncertainty quantification from noisy measurements based on Bayesian physics-informed neural networks

Flow reconstruction with uncertainty quantification from noisy measurements based on Bayesian physics-informed neural networks

Ensemble Kalman Filter Data Assimilation into the Surface Flux Transport Model to Infer Surface Flows: An Observing System Simulation Experiment

Knowledge of the global magnetic field distribution and its evolution on the Sun’s surface is crucial for modeling the coronal magnetic field, understanding the solar wind dynamics, computing the heliospheric open flux distribution, and predicting the solar cycle strength. As the far side of the Sun cannot be observed directly and high-latitude observations always suffer from projection effects, we often rely on surface flux transport (SFT) simulations to model the long-term global magnetic field distribution. Meridional circulation, the large-scale north–south component of the surface flow profile, is one of the key components of the SFT simulation that requires further constraints near high latitudes. Prediction of the photospheric magnetic field distribution requires knowledge of the flow profile in the future, which demands reconstruction of that same flow at the current time so that it can be estimated at a later time. By performing Observing System Simulation Experiments, we demonstrate how the ensemble Kalman filter technique, when used with an SFT model, can be utilized to make “posterior” estimates of flow profiles into the future that can be used to drive the model forward to forecast the photospheric magnetic field distribution.

A conditional deep learning model for super-resolution reconstruction of small-scale turbulent structures in particle-Laden flows

Super-resolution reconstruction of turbulent flows using deep learning has gained significant attention, yet challenges remain in accurately capturing physical small-scale structures. This study introduces the Conditional Enhanced Super-Resolution Generative Adversarial Network (CESRGAN) for reconstructing high-resolution turbulent velocity fields from low-resolution inputs. CESRGAN consists of a conditional discriminator and a conditional generator, the latter being called CoGEN. CoGEN incorporates subgrid-scale (SGS) turbulence kinetic energy as conditional information, improving the recovery of small-scale turbulent structures with the desired level of energy. By being aware of SGS turbulence kinetic energy, CoGEN is relatively insensitive to the degree of detail in the input. As shown in the paper, its advantages become more pronounced when the model is applied to heavily filtered input. We evaluate the model using direct numerical simulation (DNS) data of forced homogeneous isotropic turbulence. The analysis of Q-criterion isosurfaces, energy spectra, and probability density functions shows that the proposed CoGEN reconstructs fine-scale vortical structures more precisely and captures turbulent intermittency better compared to the traditional generator. Particle-pair dispersion simulations validate the physical fidelity of CoGEN-reconstructed fields, closely matching DNS results across various Stokes numbers and filtering levels. This paper demonstrates how incorporating available physical information enhances super-resolution models for turbulent flows.

Comparative analysis of machine learning models for particle flow reconstruction

Abstract. Using the simulation data of different calorimeters, we investigate the use of machine learning and python algorithms for the simulation and reconstruction of particle flow energy in high-energy physics. We train models based on simulated pixel value image instead of common numerical data. We define two models that use different Regressor algorithms. Multi-layer Perceptron (MLP) Regressor offer stable and accurate prediction under less affection situation. Convolutional Neutral Networks (CNN) Regressor provided better and stronger modeling and reconstruction ability; however, it could cause overfitting results in certain situations. Furthermore, we optimize our models with the use of PyTorch. These models can serve as fast method for particle flow reconstruction in future studies and experiments.

Predictive value of myocardial contrast echocardiography in evaluating myocardial perfusion and prognosis after percutaneous coronary intervention in patients with acute myocardial infarction

Objective: To evaluate myocardial microcirculation perfusion with myocardial contrast echocardiography (MCE) in patients with acute myocardial infarction after percutaneous coronary intervention (PCI), and to explore the prognostic value of different types of myocardial microcirculation perfusion. Methods: This is a prospective cohort study. Patients with acute myocardial infarction who underwent successful PCI in Nanfang Hospital of Southern Medical University and Kanghua Hospital of Dongguan City from October 2019 to June 2021 were selected. All the enrolled patients completed MCE examination within 72 hours after PCI. According to the examination results, the patients were divided into normal microcirculation perfusion group, delayed microcirculation perfusion group, and blocked microcirculation perfusion group. Adverse cardiovascular events including all-cause death, cardiovascular death, and angina re-hospitalization were followed up, and left ventricular ejection fraction (LVEF) review results were collected at six months to one year after surgery. Kaplan-Meier survival curve was used to investigate the difference in the incidence of adverse cardiovascular events in different myocardial perfusion groups, and Cox regression analysis was used to evaluate the effect of myocardial perfusion on adverse cardiovascular events. Results: A total of 113 patients with acute myocardial infarction were included, aged (56.3±11.5) years, with 88(78%) males. There were 31 cases in the normal microcirculation perfusion group, 43 cases in the delayed microcirculation perfusion group and 39 cases in the blocked microcirculation perfusion group. LVEF was reviewed in 49 patients, and LVEF in the delayed microcirculation perfusion group was significantly improved compared with baseline at follow-up ((63.3±1.2) % vs. (58.6±1.8) %, P=0.043), and there was no statistically significant difference between the other two groups (all P>0.05). The median follow-up time was 473 days, during follow-up period 30 adverse cardiovascular events occurred. Kaplan-Meier survival curve analysis showed that there was a statistically significant difference in the incidence of adverse cardiovascular events among the three groups (Plog-rank=0.029). Cox regression analysis showed that abnormal microcirculation perfusion (defined as delayed and blocked microcirculation perfusion) was an independent predictor of adverse cardiovascular events in patients with acute myocardial infarction after PCI (HR=1.90, 95%CI1.16-3.12, P=0.011). Conclusions: Microcirculatory perfusion decrease or lost is common in patients with acute myocardial infarction after PCI. Timely restoration of blood flow reconstruction can save heart function when microcirculatory perfusion decreases. Microcirculatory perfusion is a predictor of adverse cardiovascular events in patients with acute myocardial infarction, and patients with poor myocardial perfusion are more likely to experience adverse cardiovascular events.

Inferring Parameters and Reconstruction of Two-dimensional Turbulent Flows with Physics-informed Neural Networks

Inferring Parameters and Reconstruction of Two-dimensional Turbulent Flows with Physics-informed Neural Networks

An Efficient Approach for Detection of Compromised SDN Switches and Restoration of Network Flow

In Software Defined Networking (SDN) the data plane is separated from the controller plane to achieve better functionality than the traditional networking. Although this approach poses a lot of security vulnerabilities due to its centralized approach. One significant issue is compromised SDN switches because the switches are dumb in SDN architecture and in absence of any intelligence it can be a easy target to the attackers. If one or more switches are attacked and compromised by the attackers, then the whole network might be down or defunct. Therefore, in this work we have devised a strategy to successfully detect the compromised SDN switches, isolate them and then reconstruct the whole network flow again by bypassing the compromised switches. In our proposed approach of detection, we have used two controllers, one as primary and another as secondary which is used to run and validate our algorithm in the detection process. Flow reconstruction is the next job of the secondary controller which after execution is conveyed to the primary controller. A two-controller strategy has been used to balance the additional load of detection and reconstruction activity from the master controller and thus achieved a balanced outcome in terms of running time and CPU utilization. All the propositions are validated by experimental analysis of the results and compared with existing state of the art to satisfy our claim.

Three-dimensional spatiotemporal wind field reconstruction based on LiDAR and multi-scale PINN

In this numerical study, we use a multi-scale version of physics-informed neural network (PINN) for wind field reconstruction from LiDAR measurements. The reference velocity field is obtained from high-fidelity large-eddy simulation of neutral atmospheric boundary layer, and the LiDAR measurement strategy is restricted to that of a real LiDAR. The multi-scale PINN reconstructs the velocity field by minimizing a combination of the L2-error with respect to the LiDAR measurements and residuals of the governing equations. Our most significant finding is that adding a multi-scale layer to PINN enables us to: (i) capture wider range of scales, (ii) reconstruct the flow field outside the LiDAR scanning area, and (iii) reach faster convergence. We also find that for volumetric flow reconstruction and to deal with uncertainty in the wind direction, the reconstruction accuracy can be greatly improved by employing multiple LiDAR devices. Overall, our results show that the normalized errors in the reconstructed wind field are lower than 5% for all the experiments conducted in this study and that the errors do not increase even in the presence of measurement noise levels of typical LiDAR. These findings show the feasibility of three-dimensional dynamic wind field reconstruction across large wind farms using LiDAR devices.

Zygomatic Anterolateral Temporal Approach for P1/P2 segment complex posterior cerebral aneurysm: a single-center retrospective study.

Treating complex posterior cerebral artery (PCA) aneurysms, such as fusiform, giant, and dissecting aneurysms, poses significant challenges. Parent artery occlusion carries a risk of ischemic stroke and fails to alleviate mass effects. This study aims to analyze the technical nuances and patient outcomes of treating complex PCA aneurysms, ranging from the P1 to P2P segments, using a Zygomatic Anterolateral Temporal Approach(ZATA) combined with flow reconstruction. This study was a retrospective study. Surgical treatment was performed on twelve patients with complex PCA aneurysms located in the P1 to P2P segments. Ten patients underwent flow reconstruction including Superficial Temporal Artery(STA)-Middle Cerebral Artery(MCA),Internal Maxillary Artery(IMA)-Radial Artery(RA)-MCA,STA-PCA(P2), and IMA-RA-PCA(P2). The aneurysm occlusion rate, surgical complications, and patient prognosis, including stroke occurrence/ modified Rankin Scale(mRS), were recorded and analyzed. Using the ZATA, all twelve complex PCA aneurysms were successfully clipped/resected/trapped. This included two high-position aneurysms (> 3mm above the posterior clinoid process) at the P1/P2 junction and three P2P aneurysms. The mass effects of six large or giant aneurysms were resolved or alleviated. Postoperative and follow-up CTA/DSA confirmed the patency of the bypass vessels. Four patients experienced strokes in the perioperative period, with three ischemic and one hemorrhagic. The median follow-up period was 28.5months. At the last follow-up, the good prognosis rate (mRS ≤ 2) was 83.3%, and one patient had died. Clipping/resection/trapping of aneurysms via the ZATA, combined with flow reconstruction, is a feasible option for treating complex PCA aneurysms from the P1 to P2P segments. This approach helps maintain or improve cerebral perfusion in the affected vascular territory.

Parallel and scalable AI in HPC systems for CFD applications and beyond

This manuscript presents the library AI4HPC with its architecture and components. The library enables large-scale trainings of AI models on High-Performance Computing systems. It addresses challenges in handling non-uniform datasets through data manipulation routines, model complexity through specialized ML architectures, scalability through extensive code optimizations that augment performance, HyperParameter Optimization (HPO), and performance monitoring. The scalability of the library is demonstrated by strong scaling experiments on up to 3,664 Graphical Processing Units (GPUs) resulting in a scaling efficiency of 96%, using the performance on 1 node as baseline. Furthermore, code optimizations and communication/computation bottlenecks are discussed for training a neural network on an actuated Turbulent Boundary Layer (TBL) simulation dataset (8.3 TB) on the HPC system JURECA at the Jülich Supercomputing Centre. The distributed training approach significantly influences the accuracy, which can be drastically compromised by varying mini-batch sizes. Therefore, AI4HPC implements learning rate scaling and adaptive summation algorithms, which are tested and evaluated in this work. For the TBL use case, results scaled up to 64 workers are shown. A further increase in the number of workers causes an additional overhead due to too small dataset samples per worker. Finally, the library is applied for the reconstruction of TBL flows with a convolutional autoencoder-based architecture and a diffusion model. In case of the autoencoder, a modal decomposition shows that the network provides accurate reconstructions of the underlying field and achieves a mean drag prediction error of ≈5%. With the diffusion model, a reconstruction error of ≈4% is achieved when super-resolution is applied to 5-fold coarsened velocity fields. The AI4HPC library is agnostic to the underlying network and can be adapted across various scientific and technical disciplines.

Research on the jet active control mechanism of gas-liquid separation in helical-axial multiphase pumps

In the field of deep-water oil and gas extraction, the intermittent gas blocking phenomenon in helical-axial multiphase pumps leads to decreased pump performance and reliability, severely limiting their large-scale application and promotion in engineering projects. To address this challenge, this study is based on the principle of jet flow field control to flow separation, utilizing external energy for active intervention to suppress the separation phenomena and improve the hydraulic efficiency within the impeller flow channel. The research reveals that the jets achieved a reconstruction of the internal flow in the helical-axial gas-liquid mixed transport pumps. Using orthogonal experimental methods, a preliminary predictive analysis of the factors influencing the effectiveness of the jet system was conducted. The study explored the impact of jet parameters on enhancing the performance of helical-axial gas-liquid mixed transport pumps from the perspective of diminishing gas aggregation at the trailing edge of the rotor cascade and curtailing backflow conditions, and established a mathematical model for the head and efficiency of helical-axial multiphase pumps under jet active control. Research indicates that the jet velocity significantly impacts the efficiency enhancement of multiphase pumps, with an optimal jet speed coefficient, Cjet = 10, identified. Beyond this speed, the benefits brought by increased jet velocity do not compensate for the costs of introducing high-speed jets, and instead, may lead to a reduction in the efficiency of the pump. Jet flow field control methods alleviate the suction side gas aggregation downstream of the jet holes and in the flow domain traversed by the jets, effectively reducing the aggregation of gas phases in the rear channel of the rotor and suppressing backflow near the trailing edge of the rotor cascade. Jet control measures strengthen the working capacity of the blade in the flow direction beyond 0.35 times the length of the streamline, expanding the working range of the blade and enhancing the work efficiency of the multiphase mixed transport pump. Higher jet velocities result in more significant enhancements of blade working power, especially under conditions of high initial gas content, where the relative increase in blade load is more pronounced.

Wall Shear Stress (WSS) Analysis in Atherosclerosis in Partial Ligated Apolipoprotein E Knockout Mouse Model through Computational Fluid Dynamics (CFD).

Atherosclerosis involves an inflammatory response due to plaque formation within the arteries, which can lead to ischemic stroke and heart disease. It is one of the leading causes of death worldwide, with various contributing factors such as hyperlipidemia, hypertension, obesity, diabetes, and smoking. Wall shear stress (WSS) is also known as a contributing factor of the formation of atherosclerotic plaques. Since the causes of atherosclerosis cannot be attributed to a single factor, clearly understanding the mechanisms and causes of its occurrence is crucial for preventing the disease and developing effective treatment strategies. To better understand atherosclerosis and define the correlation between various contributing factors, computational fluid dynamics (CFD) analysis is primarily used. CFD simulates WSS, the frictional force caused by blood flow on the vessel wall with various hemodynamic changes. Using apolipoprotein E knockout (ApoE-KO) mice subjected to partial ligation and a high-fat diet at 1-week, 2-week, and 4-week intervals as an atherosclerosis model, CFD analysis was conducted along with the reconstruction of carotid artery blood flow via magnetic resonance imaging (MRI) and compared to the inflammatory factors and pathological staining. In this experiment, a comparative analysis of the effects of high WSS and low WSS was conducted by comparing the standard deviation of time-averaged wall shear stress (TAWSS) at each point within the vessel wall. As a novel approach, the standard deviation of TAWSS within the vessel was analyzed with the staining results and pathological features. Since the onset of atherosclerosis cannot be explained by a single factor, the aim was to find the correlation between the thickness of atherosclerotic plaques and inflammatory factors through standard deviation analysis. As a result, the gap between low WSS and high WSS widened as the interval between weeks in the atherosclerosis mouse model increased. This finding not only linked the occurrence of atherosclerosis to WSS differences but also provided a connection to the causes of vulnerable plaques.

Some effects of limited wall-sensor availability on flow estimation with 3D-GANs

In this work we assess the impact of the limited availability of wall-embedded sensors on the full 3D estimation of the flow field in a turbulent channel with Reτ=200\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Re_{\ au }=200$$\\end{document}. The estimation technique is based on a 3D generative adversarial network (3D-GAN). We recently demonstrated that 3D-GANs are capable of estimating fields with good accuracy by employing fully-resolved wall quantities (pressure and streamwise/spanwise wall shear stress on a grid with DNS resolution). However, the practical implementation in an experimental setting is challenging due to the large number of sensors required. In this work, we aim to estimate the flow fields with substantially fewer sensors. The impact of the reduction of the number of sensors on the quality of the flow reconstruction is assessed in terms of accuracy degradation and spectral length-scales involved. It is found that the accuracy degradation is mainly due to the spatial undersampling of scales, rather than the reduction of the number of sensors per se. We explore the performance of the estimator in case only one wall quantity is available. When a large number of sensors is available, pressure measurements provide more accurate flow field estimations. Conversely, the elongated patterns of the streamwise wall shear stress make this quantity the most suitable when only few sensors are available. As a further step towards a real application, the effect of sensor noise is also quantified. It is shown that configurations with fewer sensors are less sensitive to measurement noise.

MRCNN: Multi-input residual convolution neural network for three-dimensional reconstruction of bubble flows from light field images

Accurate measurement of bubbles in air-water two-phase flows holds immense significance in the realm of thermal hydraulics assessments within nuclear reactors. Nevertheless, conventional bubble measurement techniques grapple with challenges encompassing system intricacy, limited real-time capabilities, and inaccuracies stemming from their inherent two-dimensional (2-D) nature. In response, we pioneered an innovative three-dimensional (3-D) analysis approach that leverages light field (LF) imaging diagnosis and deep learning algorithms. Unlike traditional 2-D reconstruction methods, our approach enables direct computation of bubble depth from LF images using digital refocusing technology. Following calibration, a seamless transformation is established between the camera coordinate system and the real-world coordinate system using a sharpness evaluation algorithm. This calibration process ensures precise alignment of refocused images with real-world positions. Subsequently, fully automated and highly accurate computations of bubble depth are realized from input images via the incorporation of a multi-input residual convolution neural network (MRCNN). The limitations of traditional two-dimensional imaging techniques are effectively addressed by this methodology, resulting in a reduction in measurement errors. The study confirms the feasibility of employing LF imaging diagnosis and deep learning algorithms for bubble measurements in an air-water two-phase flow, offering a significant improvement over traditional methods.

Embolize, supercharge, resect: Embolization to enhance hepatic vascularization prior to en-bloc pancreas and arterial resection

IntroductionEmbolization could increase the resectability of pancreatic tumors by supercharging visceral arterial perfusion prior to pancreatic surgery with arterial en-bloc resection. Its indications, however, are controversial. MethodsWe retrospectively analyzed the results of a single-center database of patients undergoing pancreatic surgery with arterial resection (AR) after preoperative arterial embolization (PAE) to increase hepatic vascular flow and spare arterial reconstruction. ResultsPAE was planned in 15 patients with arterial involvement due to pancreatic tumors. Three patients were excluded due to the finding of irresectable disease during surgery. Twelve cases were resected because of pancreatic cancer (10), distal cholangiocarcinoma (1), and pancreatic neuroendocrine tumor (1). Arterial involvement in these cases required embolization of the substitute right hepatic artery (RHA) (5), left hepatic artery (1), and common hepatic artery (CHA) (6) to enhance liver vascularization. Two patients presented migration of the vascular plug after PAE. Six pancreatoduodenectomies and 6 distal pancreatectomies were performed, the latter associated with en-bloc celiac trunk and CHA resection. R0 was achieved in 7 out of 12 patients, and pathological vascular involvement was confirmed in 8. Postoperative complications included one patient who developed gastric ischemia and underwent gastrectomy, and one patient who underwent reoperation for acute cholecystitis with liver abscesses. ConclusionPreoperative arterial embolization before pancreatic surgery with hepatic arterial resection enables surgeons to precondition hepatic vascularization and prevent hepatic ischemia. In addition, this avoids having to perform arterial anastomosis in the presence of pancreatic suture.

An unsupervised video anomaly detection method via Optical Flow decomposition and Spatio-Temporal feature learning

The purpose of this paper is to present an unsupervised video anomaly detection method using Optical Flow decomposition and Spatio-Temporal feature learning (OFST). This method employs a combination of optical flow reconstruction and video frame prediction to achieve satisfactory results. The proposed OFST framework is composed of two modules: the Multi-Granularity Memory-augmented Autoencoder with Optical Flow Decomposition (MG-MemAE-OFD) and a Two-Stream Network based on Spatio-Temporal feature learning (TSN-ST). The MG-MemAE-OFD module is composed of three functional blocks: optical flow decomposition, autoencoder, and multi-granularity memory networks. The optical flow decomposition block is used to extract the main motion information of objects in optical flow, and the granularity memory network is utilized to memorize normal patterns and improve the quality of the reconstructions. To predict video frames, we introduce a two-stream network based on spatiotemporal feature learning (TSN-ST), which adopts parallel standard Transformer blocks and a temporal block to learn spatiotemporal features from video frames and optical flows. The OFST combines these two modules so that the prediction error of abnormal samples is further increased due to the larger reconstruction error. In contrast, the normal samples obtain a lower reconstruction error and prediction error. Therefore, the anomaly detection capability of the method is greatly enhanced. Our proposed model was evaluated on public datasets. Specifically, in terms of the area under the curve (AUC), our model achieved an accuracy of 85.74% on the Ped1 dataset, 99.62% on the Ped2 dataset, 93.89% on the Avenue dataset, and 76.0% on the ShanghaiTech Dataset. Our experimental results show an average improvement of 1.2% compared to the current state-of-the-art.

Reconstructing blood flow in data-poor regimes: a vasculature network kernel for Gaussian process regression.

Blood flow reconstruction in the vasculature is important for many clinical applications. However, in clinical settings, the available data are often quite limited. For instance, transcranial Doppler ultrasound is a non-invasive clinical tool that is commonly used in clinical settings to measure blood velocity waveforms at several locations. This amount of data is grossly insufficient for training machine learning surrogate models, such as deep neural networks or Gaussian process regression. In this work, we propose a Gaussian process regression approach based on empirical kernels constructed by data generated from physics-based simulations-enabling near-real-time reconstruction of blood flow in data-poor regimes. We introduce a novel methodology to reconstruct the kernel within the vascular network. The proposed kernel encodes both spatiotemporal and vessel-to-vessel correlations, thus enabling blood flow reconstruction in vessels that lack direct measurements. We demonstrate that any prediction made with the proposed kernel satisfies the conservation of mass principle. The kernel is constructed by running stochastic one-dimensional blood flow simulations, where the stochasticity captures the epistemic uncertainties, such as lack of knowledge about boundary conditions and uncertainties in vasculature geometries. We demonstrate the performance of the model on three test cases, namely, a simple Y-shaped bifurcation, abdominal aorta and the circle of Willis in the brain.

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

Physics-informed neural network for turbulent flow reconstruction in composite porous-fluid systems

This study explores the implementation of physics-informed neural networks (PINNs) to analyze turbulent flow in composite porous-fluid systems. These systems are composed of a fluid-saturated porous medium and an adjacent fluid, where the flow properties are exchanged across the porous-fluid interface. The segregated PINN model employs a novel approach combining supervised learning and enforces fidelity to flow physics through penalization by the Reynolds-averaged Navier-Stokes (RANS) equations. Two cases were simulated for this purpose: solid block, i.e. porous media with zero porosity, and porous block with a defined porosity. The effect of providing internal training data on the accuracy of the PINN predictions for prominent flow features, including flow leakage, channeling effect and wake recirculation was investigated. Additionally, L2 norm error, which evaluates the prediction accuracy for flow variables was studied. Furthermore, PINN training time in both cases with internal training data was considered in this study. Results showed that the PINN model predictions with second-order internal training data achieved high accuracy for the prominent flow features compared to the RANS data, within a 20% L2 norm error of second-order statistics in the solid block case. In addition, for the porous block case, providing training data at the porous-fluid interface showed errors of 18.04% and 19.94% for second-order statistics, representing an increase in prediction accuracy by 7% compared to without interface training data. The study elucidates the impact of the internal training data distribution on the PINN training in complex turbulent flow dynamics, underscoring the necessity of turbulent second-order statistics variables in PINN training and an additional velocity gradient treatment to enhance PINN prediction.

Two-Field Excitation for Contactless Inductive Flow Tomography.

Contactless inductive flow tomography (CIFT) is a flow measurement technique allowing for visualization of the global flow in electrically conducting fluids. The method is based on the principle of induction by motion: very weak induced magnetic fields arise from the fluid motion under the influence of a primary excitation magnetic field and can be measured precisely outside of the fluid volume. The structure of the causative flow field can be reconstructed from the induced magnetic field values by solving the according linear inverse problem using appropriate regularization methods. The concurrent use of more than one excitation magnetic field is necessary to fully reconstruct three-dimensional liquid metal flows. In our laboratory demonstrator experiment, we impose two excitation magnetic fields perpendicular to each other to a mechanically driven flow of the liquid metal alloy GaInSn. In the first approach, the excitation fields are multiplexed. Here, the temporal resolution of the measurement needs to be kept as high as possible. Consecutive application by multiplexing enables determining the flow structure in the liquid with a temporal resolution down to 3 s with the existing equipment. In another approach, we concurrently apply two sinusoidal excitation fields with different frequencies. The signals are disentangled on the basis of the lock-in principle, enabling a successful reconstruction of the liquid metal flow.