Flow Reconstruction Research Articles

Micro-scale reconstruction and CFD-DEM simulation of proppant-laden flow in hydraulic fractures

A comprehensive investigation of the dynamical characteristics of proppant-laden flow systems in hydraulic fractures is important for the development of unconventional oil and gas resources. In this paper, we combine the micro-scale reconstruction technique and CFD-DEM method to numerically investigate the mobility and distribution rules of proppant-laden fluid in rough hydraulic fractures. To characterize realistic fracture surface morphology, six synthetic fracture models were assembled based on optical scanning data of real shale from three sets of hydraulic fracturing experiments. In order to accurately simulate the fluid-particle two-phase flow in rough fractures, the lift forces and particle rolling effect are considered in the CFD-DEM model. First, the effectiveness of the used CFD-DEM solver was validated by comparing it to the experimental data. We then examined mechanisms for the typical flow behaviors of proppant particles and fracturing fluid in smooth and rough fractures. Subsequently, the surface area ratio of the synthetic fracture model is adopted to characterize the cross-scale relationship between the micro-scale proppant distribution and fracture’s geometric features induced by the macroscale fracturing parameters (i.e., confining stress, fluid viscosity, flow rate, and sand ratio). Lastly, the parameter effects of the fracturing fluid, proppant particle, and fracture aperture on the dynamic characteristics of particulate flow in the hydraulic fracture are further discussed. In summary, the presented numerical model and findings can help better understand particle transport and distribution in real rock fractures and bridge the connectivity of the micro-scale particle flow and macroscopic fracturing parameter, which is vital for hydraulic fracturing process optimization.

Flow reconstruction by multiresolution optimization of a discrete loss with automatic differentiation.

We present a potent computational method for the solution of inverse problems in fluid mechanics. We consider inverse problems formulated in terms of a deterministic loss function that can accommodate data and regularization terms. We introduce a multigrid decomposition technique that accelerates the convergence of gradient-based methods for optimization problems with parameters on a grid. We incorporate this multigrid technique to the Optimizing a DIscrete Loss (ODIL) framework. The multiresolution ODIL (mODIL) accelerates by an order of magnitude the original formalism and improves the avoidance of local minima. Moreover, mODIL accommodates the use of automatic differentiation for calculating the gradients of the loss function, thus facilitating the implementation of the framework. We demonstrate the capabilities of mODIL on a variety of inverse and flow reconstruction problems: solution reconstruction for the Burgers equation, inferring conductivity from temperature measurements, and inferring the body shape from wake velocity measurements in three dimensions. We also provide a comparative study with the related, popular Physics-Informed Neural Networks (PINNs) method. We demonstrate that mODIL has three to five orders of magnitude lower computational cost than PINNs in benchmark problems including simple PDEs and lid-driven cavity problems. Our results suggest that mODIL is a very potent, fast and consistent method for solving inverse problems in fluid mechanics.

Flow reconstruction from sparse sensors based on reduced-order autoencoder state estimation

The reconstruction of accurate and robust unsteady flow fields from sparse and noisy data in real-life engineering tasks is challenging, particularly when sensors are randomly placed. To address this challenge, a novel Autoencoder State Estimation (AE-SE) framework is introduced in this paper. The framework integrates sensor measurements into a machine learning-based reduced-order model (ROM) by leveraging the low-dimensional representation of flow fields. The proposed approach is tested on two direct numerical simulation benchmark examples, namely, circular and square cylinders and wake flow fields at Re = 100. The results demonstrate satisfactory performance in terms of accuracy and reconstruction efficiency. It achieves the same accuracy as traditional methods while improving reconstruction efficiency by 70%. Moreover, it preserves essential physical properties and flow characteristics even in the noisy data, indicating its practical applicability and robustness. Experimental data validation confirms a relative error below 5% even at a noise level of 12%. The flexibility of the model is further evaluated by testing it with a trained ROM under varying Reynolds numbers and benchmark cases, demonstrating its ability to accurately estimate and recognize previously unseen flow fields with appropriate training datasets. Overall, the proposed AE-SE flow reconstruction method efficiently and flexibly leverages ROM for the low-dimensional representation of complex flow fields from sparse measurements. This approach contributes significantly to the development of downstream applications such as design optimization and optimal control.

Green's function integral method for pressure reconstruction from measured pressure gradient and the interpretation of omnidirectional integration

Accurately and efficiently measuring the pressure field is of paramount importance in many fluid mechanics applications. The pressure gradient field of a fluid flow can be determined from the balance of the momentum equation based on the particle image velocimetry measurement of the flow kinematics, which renders the experimental evaluation of the material acceleration and the viscous stress terms possible. In this paper, we present a novel method of reconstructing the instantaneous pressure field from the error-embedded pressure gradient measurement data. This method utilized the Green's function of the Laplacian operator as the convolution kernel that relates pressure to the pressure gradient. A compatibility condition on the boundary offers equations to solve for the boundary pressure. This Green's function integral (GFI) method has a deep mathematical connection with the state-of-the-art omnidirectional integration (ODI) for pressure reconstruction. As mathematically equivalent to ODI in the limit of an infinite number of line integral paths, GFI spares the necessity of line integration along zigzag integral paths, rendering generalized implementation schemes for both two and three-dimensional problems with arbitrary inner and outer boundary geometries while bringing in improved computational simplicity. In the current work, GFI is applied to pressure reconstruction of simple canonical and isotropic turbulence flows embedded with error in two-dimensional and three-dimensional domains, respectively. Uncertainty quantification is performed by eigenanalysis of the GFI operator in domains with both simply and multiply connected shapes. The accuracy and the computational efficiency of GFI are evaluated and compared with ODI.

Full-Volume 3D Fluid Flow Reconstruction With Light Field PIV.

Particle Imaging Velocimetry (PIV) is a classical method that estimates fluid flow by analyzing the motion of injected particles. To reconstruct and track the swirling particles is a difficult computer vision problem, as the particles are dense in the fluid volume and have similar appearances. Further, tracking a large number of particles is particularly challenging due to heavy occlusion. Here we present a low-cost PIV solution that uses compact lenslet-based light field cameras as imaging device. We develop novel optimization algorithms for dense particle 3D reconstruction and tracking. As a single light field camera has limited capacity in resolving depth (z-dimension measurement), the resolution of 3D reconstruction on the x-y plane is much higher than along the z-axis. To compensate for the imbalanced resolution in 3D, we use two light field cameras positioned at an orthogonal angle to capture particle images. In this way, we can achieve high-resolution 3D particle reconstruction in the full fluid volume. For each time frame, we first estimate particle depths under a single viewpoint by exploiting the focal stack symmetry of light field. We then fuse the recovered 3D particles in two views by solving a linear assignment problem (LAP). Specifically, we propose an anisotropic point-to-ray distance as matching cost to handle the resolution mismatch. Finally, given a sequence of 3D particle reconstructions over time, we recover the full-volume 3D fluid flow with a physically-constrained optical flow, which enforces local motion rigidity and fluid incompressibility. We perform comprehensive experiments on synthetic and real data for ablation and evaluation. We show that our method recovers full-volume 3D fluid flows of various types. Two-view reconstruction results achieves higher accuracy than those with one view only.

Bent pipe flow reconstruction based on improved ultrasound Doppler velocimetry and radial basis function neural network

In piping systems, the flow through a bend is typically undeveloped, unsteady, and complicated. In this study, we proposed a novel method to accurately predict downstream flow in bent pipes based on radial basis function neural network (RBFNN) and ultrasound Doppler velocimetry (UDV). An improved UDV method was developed for the measurement of complex flow in bent pipes. The downstream flow characteristics of three different bend configurations were investigated using computational fluid dynamics (CFD). The proposed RBFNN models established the relationships between the velocity profile along the symmetric axis and the velocity distribution over the pipe cross-section. Numerical data were used for model training and validation, whereas the combined datasets with UDV data as inputs and the corresponding CFD data as outputs were used for model modification. The model prediction performance was then evaluated with new UDV inputs by comparing the predicted velocities with the associated CFD results. The results indicated that the velocity profiles obtained using modified UDV agreed well with the present numerical simulation. Finally, the trained model exhibited satisfactory flow reconstruction performance and high flowrate prediction accuracy, with a maximum error of approximately 3%. This work contributes to the application of the UDV method in complex flow measurements and further demonstrates that artificial neural networks (ANNs) are promising for modeling fluid mechanics.

Self-Supervised Joint Dynamic Scene Reconstruction and Optical Flow Estimation for Spiking Camera

Spiking camera, a novel retina-inspired vision sensor, has shown its great potential for capturing high-speed dynamic scenes with a sampling rate of 40,000 Hz. The spiking camera abandons the concept of exposure window, with each of its photosensitive units continuously capturing photons and firing spikes asynchronously. However, the special sampling mechanism prevents the frame-based algorithm from being used to spiking camera. It remains to be a challenge to reconstruct dynamic scenes and perform common computer vision tasks for spiking camera. In this paper, we propose a self-supervised joint learning framework for optical flow estimation and reconstruction of spiking camera. The framework reconstructs clean frame-based spiking representations in a self-supervised manner, and then uses them to train the optical flow networks. We also propose an optical flow based inverse rendering process to achieve self-supervision by minimizing the difference with respect to the original spiking temporal aggregation image. The experimental results demonstrate that our method bridges the gap between synthetic and real-world scenes and achieves desired results in real-world scenarios. To the best of our knowledge, this is the first attempt to jointly reconstruct dynamic scenes and estimate optical flow for spiking camera from a self-supervised learning perspective.

Super-resolution analysis via machine learning: a survey for fluid flows

This paper surveys machine-learning-based super-resolution reconstruction for vortical flows. Super resolution aims to find the high-resolution flow fields from low-resolution data and is generally an approach used in image reconstruction. In addition to surveying a variety of recent super-resolution applications, we provide case studies of super-resolution analysis for an example of two-dimensional decaying isotropic turbulence. We demonstrate that physics-inspired model designs enable successful reconstruction of vortical flows from spatially limited measurements. We also discuss the challenges and outlooks of machine-learning-based super-resolution analysis for fluid flow applications. The insights gained from this study can be leveraged for super-resolution analysis of numerical and experimental flow data.Graphical abstract

Improved historical reconstruction of daily flows and annual maxima in gauged and ungauged basins

This study presents a method to improve the reconstruction of historical flows on gauged and ungauged basins. To do so, a multi-model weighted averaging of hydrological model simulations for a large spatial domain in the province of Quebec, Canada, is used. The distributed hydrological model HYDROTEL was implemented over the region and covered 95 gauged basins. An optimal interpolation (OI) assimilation method was first implemented as a baseline to improve the HYDROTEL flow simulations over the 95 basins. Then, a series of multi-model averaging techniques were applied to an ensemble of 144 HYDROTEL simulations that were generated by modifying parameter sets, driving weather datasets and evapotranspiration modules. The averaging methods were applied in a leave-one-out cross-validation scheme, where all 94 gauged basins were pooled together to compute the weights, and those weights were applied to the 95th basin. All basins were evaluated in such a manner and compared to the OI method. Implementing a year-by-year (or shorter period) weighting scheme instead of computing weights over all available data significantly improved the results. This allowed the weights to better reflect each year’s hydrological characteristics rather than compromising to improve the overall average. The Kling-Gupta Efficiency (KGE) and peak flow metrics showed that the Granger-Ramanathan variant “A” (GRA) was similar in performance to the OI method but did not have the drawbacks that OI can typically introduce. The multi-model application can also be further improved by adding more simulations from other hydrological models, whereas the OI method cannot make use of such additional information, thus hitting a performance plateau. This study shows that it is possible to improve regional hydrological model simulations, both for overall flows and peak flows, and on the historical period for both gauged and ungauged basins. This can then be used to better estimate risk in flood frequency analysis and other statistical analyses.

Physics-assisted reduced-order modeling for identifying dominant features of transonic buffet

Transonic buffet is a flow instability phenomenon that arises from the interaction between the shock wave and the separated boundary layer. This flow phenomenon is considered to be highly detrimental during flight and poses a significant risk to the structural strength and fatigue life of aircraft. Up to now, there has been a lack of an accurate, efficient, and intuitive metric to predict buffet and impose a feasible constraint on aerodynamic design. In this paper, a Physics-Assisted Variational Autoencoder is proposed to identify dominant features of transonic buffet, which combines unsupervised reduced-order modeling with additional physical information embedded via a buffet classifier. Specifically, four models with various weights adjusting the contribution of the classifier are trained so as to investigate the impact of buffet information on the latent space. Statistical results reveal that the buffet state can be determined exactly with just one latent space when a proper weight of classifier is chosen. The dominant latent space further reveals a strong relevance with the key flow features located in the boundary layers downstream of shock. Based on this identification, the displacement thickness at 80% chordwise location is proposed as a metric for buffet prediction. This metric achieves an accuracy of 98.5% in buffet state classification, which is more reliable than the existing separation metric used in design. The proposed method integrates the benefits of feature extraction, flow reconstruction, and buffet prediction into a unified framework, demonstrating its potential in low-dimensional representations of high-dimensional flow data and interpreting the “black box” neural network.

Deep-learning-based 3D blood flow reconstruction in transmissive laser speckle imaging.

Transmissive laser speckle imaging (LSI) is useful for monitoring large field-of-view (FOV) blood flow in thick tissues. However, after longer transmissions, the contrast of the transmitted speckle images is more likely to be blurred by multiple scattering, resulting in decreased accuracy and spatial resolution of deep vessels. This study proposes a deep-learning-based strategy for high spatiotemporal resolution three-dimensional (3D) reconstruction from a single transilluminated laser speckle contrast image, providing more structural and functional details without multifocus two-dimensional (2D) imaging or 3D optical imaging with point/line scanning. Based on the correlation transfer equation, a large training dataset is generated by convolving vessel masks with depth-dependent point spread functions (PSF). The UNet and ResNet are used for deblurring and depth estimation. The blood flow in the reconstructed 3D vessels is estimated by a depth-dependent contrast model. The proposed method is evaluated with simulated data and phantom experiments, achieving high-fidelity structural reconstruction with a depth-independent estimation of blood flow. This fast 3D blood flow imaging technique is suitable for real-time monitoring of thick tissue and the diagnosis of vascular diseases.

Evolution of the technique of renoportal anastomosis for patients with complete portal venous occlusion in living donor liver transplantation - a retrospective cohort study.

This study aimed to present our surgical technique and the long-term outcomes of living donor liver transplantations with renoportal anastomosis for patients with complete portal venous occlusion. Renoportal anastomosis (RPA) is a promising technique for portal flow reconstruction during liver transplantation in patients with complete occlusion of the portal vein and extensive splanchnic vein thrombosis. However, reports demonstrating living donor liver transplantations (LDLT) with renoportal anastomosis are rarer than those demonstrating deceased-donor liver transplantation. In this single-center retrospective cohort study, we analyzed the medical records of patients who underwent portal flow reconstruction via RPA with end-to-end anastomosis between the interposition graft and LRV-connected inferior vena cava (VC) cuff. The outcomes included postoperative RPA-related morbidity and patient and allograft survival for patients who underwent LDLT with RPA. Fifteen patients underwent LDLT with portal flow reconstruction via RPA from January 2005 to December 2019. The median follow-up period was 80.7 months (range: 27d-195.2mo). RPA evolved from end-to-end anastomosis in 1 (6.7%) patient to end-to-side anastomoses in the next 6 (40%) patients and finally, to end-to-end anastomoses between the inferior VC cuff connected to the left renal vein (LRV) and interposing vascular grafts in 8 (53.3%) patients. After standardization of the RPA technique from the eighth case in 2011, the incidence rate of RPA-related complications significantly decreased from 42.9% (3/7) to 12.5% (1/8). At the last follow-up, all 11 surviving patients had normal liver function, and 10 patients had patent anastomoses on imaging examination. Our standardized RPA technique using an inferior VC cuff connected to the LRV creates a safe end-to-end RPA.

A Novel Unsupervised Video Anomaly Detection Framework Based on Optical Flow Reconstruction and Erased Frame Prediction.

Reconstruction-based and prediction-based approaches are widely used for video anomaly detection (VAD) in smart city surveillance applications. However, neither of these approaches can effectively utilize the rich contextual information that exists in videos, which makes it difficult to accurately perceive anomalous activities. In this paper, we exploit the idea of a training model based on the "Cloze Test" strategy in natural language processing (NLP) and introduce a novel unsupervised learning framework to encode both motion and appearance information at an object level. Specifically, to store the normal modes of video activity reconstructions, we first design an optical stream memory network with skip connections. Secondly, we build a space-time cube (STC) for use as the basic processing unit of the model and erase a patch in the STC to form the frame to be reconstructed. This enables a so-called "incomplete event (IE)" to be completed. On this basis, a conditional autoencoder is utilized to capture the high correspondence between optical flow and STC. The model predicts erased patches in IEs based on the context of the front and back frames. Finally, we employ a generating adversarial network (GAN)-based training method to improve the performance of VAD. By distinguishing the predicted erased optical flow and erased video frame, the anomaly detection results are shown to be more reliable with our proposed method which can help reconstruct the original video in IE. Comparative experiments conducted on the benchmark UCSD Ped2, CUHK Avenue, and ShanghaiTech datasets demonstrate AUROC scores reaching 97.7%, 89.7%, and 75.8%, respectively.

Tensor-based flow reconstruction from optimally located sensor measurements

Reconstructing high-resolution flow fields from sparse measurements is a major challenge in fluid dynamics. Existing methods often vectorize the flow by stacking different spatial directions on top of each other, hence confounding the information encoded in different dimensions. Here, we introduce a tensor-based sensor placement and flow reconstruction method which retains and exploits the inherent multidimensionality of the flow. We derive estimates for the flow reconstruction error, storage requirements and computational cost of our method. We show, with examples, that our tensor-based method is significantly more accurate than similar vectorized methods. Furthermore, the variance of the error is smaller when using our tensor-based method. While the computational cost of our method is comparable to similar vectorized methods, it reduces the storage cost by several orders of magnitude. The reduced storage cost becomes even more pronounced as the dimension of the flow increases. We demonstrate the efficacy of our method on three examples: a chaotic Kolmogorov flow, in situ and satellite measurements of the global sea surface temperature and three-dimensional unsteady simulated flow around a marine research vessel.

Reconstructing the Unsaturated Flow Equation From Sparse and Noisy Data: Leveraging the Synergy of Group Sparsity and Physics‐Informed Deep Learning

AbstractData‐driven scientific discovery methods have been developed and applied to discover governing equations from data, involving the attempt to discover the unsaturated flow equation in soils from data. However, an important but unresolved problem is how to reconstruct the unsaturated flow equation from highly noisy and scarce discrete data. In this study, we present a new deep‐learning framework: DeepGS (deep‐learning‐based group sparsity framework), that leverages the synergy of group sparsity and physics‐informed deep learning (PIDL) to reconstruct the latent governing equation for unsaturated flow. In particular, we design a strategy that decomposes the identification of the unsaturated flow equation into two tasks: the determination of the partial differential equation structure and the reconstruction of the nonlinear coefficients. The tasks can be seamlessly handled by group sparse regression and the PIDL approach. Through the training, it realizes the simultaneous reconstruction of soil moisture dynamics and unsaturated flow governing equation. A series of comprehensive numerical experiments are conducted to determine the optimal architecture and test its performance. The results show the efficacy and robustness of DeepGS, which significantly outperform previous methods. We also conclude that accurately reconstructing soil moisture dynamics and spatiotemporal derivatives from noisy and scarce data play a critical role in governing equation discovery. This study further demonstrates the potential of discovering the governing equation for unsaturated flow from data in more complex scenarios, where rich and accurate soil moisture observations are generally intractable to access.

Super-resolution reconstruction of turbulent flows with a transformer-based deep learning framework

Details of flow field are highly relevant to understand the mechanism of turbulence, but obtaining high-resolution turbulence often requires enormous computing resources. Although the super-resolution reconstruction of turbulent flow fields is an efficient way to obtain the details, the traditional interpolation methods are difficult to reconstruct small-scale structures, and the results are too smooth. In this paper, based on the transformer backbone architecture, we present a super-resolution transformer for turbulence to reconstruct turbulent flow fields with high quality. It is supervised and has a broader perceptual field for better extraction of deep-level features. The model is applied to forced isotropic turbulence and turbulent channel flow dataset, and the reconstructed instantaneous flow fields are comprehensively compared and analyzed. The results show that SRTT can recover the turbulent flow fields with high spatial resolution and capture small-scale details. It can obtain either the isotropic or the anisotropic turbulent properties even in complex flow configurations.

Flow Reconstruction Around a Surface-Mounted Prism from Sparse Velocity and/or Scalar Measurements Using a Combination of POD and a Data-Driven Estimator

A data-driven algorithm is proposed for flow reconstruction from sparse velocity and/or scalar measurements. The algorithm is applied to the flow around a two-dimensional, wall-mounted, square prism. To reduce the problem dimensionality, snapshots of flow and scalar fields are processed to derive POD modes and their time coefficients. Then a system identification algorithm is employed to build a reduced order, linear, dynamical system for the flow and scalar dynamics. Optimal estimation theory is subsequently applied to derive a Kalman estimator to predict the time coefficients of the POD modes from sparse measurements. Analysis of the flow and scalar spectra demonstrate that the flow field leaves its footprint on the scalar, thus extracting velocity from scalar concentration measurements is meaningful. The results show that remarkably good reconstruction of the flow statistics (Reynolds stresses) and instantaneous flow patterns can be obtained using a very small number of sensors (even a single scalar sensor yields very satisfactory results for the case considered). The Kalman estimator derived at one condition is able to reconstruct with acceptable accuracy the flow fields at two nearby off-design conditions. Further work is needed to assess the performance of the algorithm in more complex, three-dimensional, flows.

Simulation of Particle Trajectories in Gas Turbine Components and Assessment of Unsteady Effects Using an Efficient Eulerian-Lagrangian Technique

In recent years, CFD has proven to be a very useful asset to help with predicting complex flows in a wide range of situations, including multiphase and gas-particle flows. On this track, numerical modelling of particle-laden flows in multistage turbomachinery has become an important step in helping to analyse the behaviour of a discrete phase in gas turbines. Furthermore, unsteady effects due, for example, to rotor–stator interaction may have an effect on trajectories and capture efficiencies of the discrete phase. Unfortunately, computational times for transient simulations can be exceedingly high, especially if a discrete-phase needs also to be simulated. For this reason, this work reports a new method for the efficient and accurate simulation of particle-laden flows in gas turbine engines components. The Harmonic Balance Method is exploited to gain orders of magnitude speedup exploiting the idea that once the flow field has been embedded in the spectral basis, it can be reconstructed at any desired time. In this way, not only can the computational time needed to reach convergence of the flow field be dramatically reduced, but there is also no need to keep simulating the flow field during particle tracking. On the contrary, the continuous phase field can be retrieved at any desired time through flow reconstruction. This technique is conceptually simple, but, to the authors’ knowledge, has never been applied so far in particle-laden flow simulations and represents a novelty in the field. First, the implementation of the method is described, and details are given on how phase-lagged boundary conditions can be applied to flow and particles to further speed up the calculation. Then, some relevant case studies are presented to highlight the performance of the method.

An analysis of reconstruction noise from undersampled 4D flow MRI

Novel Magnetic Resonance (MR) imaging modalities can quantify hemodynamics but require long acquisition times, precluding its widespread use for early diagnosis of cardiovascular disease. To reduce acquisition times, flow reconstruction from undersampled data is routinely performed.Reconstructed anatomical and hemodynamic images may present visual artifacts. While some artifacts are reconstruction errors, and a consequence of undersampling, others are due to measurement noise or the random choice of samples. A reconstructed image becomes thus a random variable: its bias leads to systematic reconstruction errors, whereas its fluctuations may induce spatial correlations that may be misconstrued for visual information or that may carry to quantities of interest computed from the image. Although the former has been studied in the literature, the latter has not received as much attention.In this study, we investigate the theoretical properties of the random perturbations arising from the reconstruction process. To our knowledge, this is the first study on this topic. We perform numerical experiments on simulated flow, on aortic phantom flow, and on aortic flow. These show that the correlation length remains limited to two to three pixels when a Gaussian undersampling pattern is combined with ℓ1-norm minimization methods. The correlation length may increase significantly for other undersampling patterns, higher undersampling factors (i.e., higher than 8× compression), and other reconstruction methods. Our findings suggest that the reconstruction method has a large impact on the correlation. As reconstruction methods are routinely used in practice, the impact of these random perturbations in practical applications merits further study.

Local estimation of quasi-geostrophic flows in Earth’s core

SUMMARYThe inference of fluid motion below the core–mantle boundary from geomagnetic observations presents a highly non-unique inverse problem. We propose a new method that provides a unique local estimate of the velocity field, assuming quasi-geostrophic flow in the core interior (which implies equatorial mirror symmetry) and negligible magnetic diffusion. These assumptions remove the theoretical underdetermination, enabling us to invert for the flow at each point of a spherical grid representing the core surface. The unreliable reconstruction of small-scale flows, which arises because only large-scale observations are available, is mitigated by smoothing the locally estimated velocity field using a Gaussian process regression. Application of this method to synthetic data provided by a state-of-the-art geodynamo simulation suggests that using this approach, the large-scale flow pattern of the core surface flow can be well reconstructed, while the flow amplitude tends to be underestimated. We compare these results with a core flow inversion using a Bayesian framework that incorporates statistics from numerical geodynamo models as prior information. We find that whether the latter method provides a more accurate recovery of the reference flow than the local estimation depends heavily on how realistic/relevant the chosen prior information is. Application to real geomagnetic data shows that both methods are able to reproduce the main features found in previous core flow studies.