arXiv subjects

Xing Ji

Publications and source records attributed to Xing Ji.

At least 37 records · Page 2Linked to original sources

arXiv2024

A robustness-enhanced reconstruction based on discontinuity feedback factor for high-order finite volume scheme

In this paper, a robustness-enhanced reconstruction for the high-order finite volume scheme is constructed on the 2-D structured mesh, and both the high-order gas-kinetic scheme(GKS) and the Lax-Friedrichs(L-F) flux solver are considered to verify the validity of this algorithm. The strategy of the successful WENO reconstruction is adopted to select the smooth sub-stencils. However, there are cases where strong discontinuities exist in all sub-stencils of the WENO reconstruction, which leads to a decrease in the robustness. To improve the robustness of the algorithm in discontinuous regions in two-dimensional space, the hybrid reconstruction based on a combination of discontinuity feedback factor(DF) \cite{ji2021gradient} and WENO reconstruction is developed to deal with the possible discontinuities. Numerical results from smooth to extreme cases have been presented and validate that the new finite volume scheme is effective for robustness enhancement and maintains high resolution compared to the WENO scheme.

math.NA↗

arXiv2023

Adaptive wave-particle decomposition in UGKWP method for high-speed flow simulations

With wave-particle decomposition, a unified gas-kinetic wave-particle (UGKWP) method has been developed for the multiscale flow simulations. The UGKWP method captures the transport process in all flow regimes without kinetic solver's constraint on the numerical mesh size and time step being less than the particle mean free path and collision time. In the current UGKWP method, the cell's Knudsen number, defined as the ratio of collision time to numerical time step, is used to distribute the components in the wave-particle decomposition. However, the adaptation of particle in UGKWP is mainly for the capturing of the non-equilibrium transport, and the cell's Knudsen number alone is not enough to identify the non-equilibrium state. For example, in the equilibrium flow regime with a Maxwellian distribution function, even at a large cell's Knudsen number, the flow evolution can be still modelled by the Navier-Stokes solver. Therefore, to further improve the efficiency, an adaptive UGKWP (AUGKWP) method will be developed with the introduction of an additional local flow variable gradient-dependent Knudsen number. As a result, the wave-particle decomposition in UGKWP will be determined by both cell's and gradient's Knudsen numbers, and the particle in UGKWP is solely used to capture the non-equilibrium flow transport. The AUGKWP becomes much more efficient than the previous one with the cell's Knudsen number only in the determination of wave-particle composition. Many numerical tests, including Sod tube, shock structure, flow around a cylinder, flow around a reentry capsule, and an unsteady nozzle plume flow, have been conducted to validate the accuracy and efficiency of AUGKWP. Compared with the original UGKWP, the AUGKWP achieves the same accuracy but has advantages in memory reduction and computational efficiency in the simulation for the flow with the co-existing of multiple regimes.

physics.flu-dyn↗

arXiv2022

A high-order compact gas-kinetic scheme in a rotating coordinate frame and on sliding mesh

This paper extends the high-order compact gas-kinetic scheme (CGKS) to compressible flow simulations on a rotating coordinate frame. The kinetic equation with the inclusion of centrifugal and Coriolis acceleration is used in the construction of the scheme. With the updates of both cell averaged conservative variables and their gradients in the rotating and stationary domains, a third-order compact reconstruction is developed with sliding interface between them. To properly capture shock wave and complicated wave interaction, the HWENO-type non-linear reconstruction and gradient compression factors are incorporated in the scheme. For achieving high-order time accuracy, based on the flux function and its time derivative the multi-stage multi-derivative (MSMD) time stepping method is implemented in the scheme for the fourth-order accuracy with two stages. The CGKS is validated by many test cases from subsonic acoustic wave propagation to the high Mach number shock interaction in a rotating frame. The compact scheme achieves high-order accuracy and remarkable robustness.

physics.comp-ph↗

arXiv2022

High-order Compact Gas-kinetic Schemes for Three-dimensional Flow Simulation on Tetrahedral Mesh

A general framework for the development of high-order compact schemes has been proposed recently. The core steps of the schemes are composed of the following. 1). Based on a kinetic model equation, from a generalized initial distribution of flow variables construct a time-accurate evolution solution of gas distribution function at a cell interface ; 2). Introduce the WENO-type weighting functions into the time-derivative of the cell interface flux function in the multistage multi-derivative time stepping scheme to cope with the possible impingement of a shock wave on a cell interface within a time step; 3). Take moments of interface gas distribution function to obtain the time-accurate flow variables and the corresponding fluxes at the cell interface, and update the cell-averaged flow variables and their gradients inside each control volume; 4). Within the physical domain of dependence of the reconstructed cell, based on the cell-averaged flow variables and their gradients develop compact initial data reconstruction to get initial flow distributions at the beginning of next time step. A compact gas-kinetic scheme (GKS) up to sixth-order accuracy in space and fourth-order in time has been constructed on 2D unstructured mesh before. In this paper, the compact GKS up to fourth-order accuracy on 3D tetrahedral mesh will be further constructed with the focus on the WENO-type initial data reconstruction. Nonlinear weights are designed to achieve high-order accuracy for the smooth Navier-Stokes solution and keep super robustness in 3D computation with strong shock interactions. The fourth-order compact GKS can use a large time step with CFL number $0.6$ in the simulations from subsonic to hypersonic flow. A series of test cases are used to validate the scheme. The high-order compact GKS is ready for 3D applications with complex geometry.

physics.flu-dyn↗

arXiv2021

A p-multigrid compact gas-kinetic scheme for steady-state acceleration

In this paper, the high-order compact gas-kinetic scheme (CGKS) on three-dimensional hybrid unstructured mesh is further developed with the p-multigrid technique for steady-state solution acceleration. The p-multigrid strategy is a two-level algorithm. On the high-order level, the high-order CGKS is used to evolve both cell-averaged conservative flow variables and their gradients under high-order compact initial reconstruction at the beginning of next time step. On the low-order level, starting from the high-order level solution the cell-averaged conservative flow variables is evolved by a first-order scheme, where implicit backward Euler smoother is adopted for accelerating the convergence of steady-state solution. The final iterative updating scheme becomes numerically simple and computationally efficient. The effectiveness of the p-multigrid method is validated in both subsonic and supersonic flow simulations in two- and three-dimensional space with hybrid unstructured mesh. One order of magnitude speedup in the convergence rate has be achieved by the approach in comparison with the explicit counterpart.

physics.comp-ph↗

arXiv2021

Direct Modeling for Computational Fluid Dynamics and the Construction of High-order Compact Scheme for Compressible Flow Simulations

Computational fluid dynamics is a direct modeling of physical laws in a discretized space. The basic physical laws include the mass, momentum and energy conservations, physically consistent transport process, and similar domain of dependence and influence between the physical reality and the numerical representation. Therefore, a physically soundable numerical scheme must be a compact one which involves the closest neighboring cells within the domain of dependence for the solution update under a CFL number $(\sim 1 )$. In the construction of explicit high-order compact scheme, subcell flow distributions or the equivalent degree of freedoms beyond the cell averaged flow variables must be evolved and updated, such as the gradients of the flow variables inside each control volume. The direct modeling of flow evolution under generalized initial condition will be developed in this paper. The direct modeling will provide the updates of flow variables differently on both sides of a cell interface and limit high-order time derivatives of the flux function nonlinearly in case of discontinuity in time, such as a shock wave moving across a cell interface within a time step. The direct modeling unifies the nonlinear limiters in both space for the data reconstruction and time for the time-dependent flux transport. Under the direct modeling framework, as an example, the high-order compact gas-kinetic scheme (GKS) will be constructed. The scheme shows significant improvement in terms of robustness, accuracy, and efficiency in comparison with the previous high-order compact GKS.

physics.flu-dyn↗

arXiv2021

A gradient-compression-based compact high-order gas-kinetic scheme on three-dimensional hybrid unstructured mesh

In this paper, the compact gas-kinetic scheme for compressible flow is extended to hybrid unstructured mesh. Based on both cell-averaged flow variables and their gradients updated from time accurate gas evolution model at cell interfaces, a compact third-order least-square-constrained reconstruction can be obtained on unstructured mesh and a multi-resolution WENO reconstruction is adopted in case of discontinuous solutions. Moreover, a compression factor for the cell-averaged gradients is proposed to take into account the possible discontinuity in flow variables at cell interface, which significantly improves the robustness of the compact scheme for high-speed flow computation on irregular mesh and preserves the accuracy. Numerical tests from incompressible to hypersonic flow are presented to demonstrate the broad applicability of the gradient-compression-based high-order compact scheme.

math.NA↗

arXiv2021

Unified gas-kinetic wave-particle methods VI: Disperse dilute gas-particle multiphase flow

In this paper, a unified gas-kinetic wave-particle scheme (UGKWP) for the disperse dilute gas-particle multiphase flow is proposed. The gas phase is always in the hydrodynamic regime. However, the particle phase covers different flow regimes from particle trajectory crossing to the hydrodynamic wave interaction with the variation of local particle phase Knudsen number. The UGKWP is an appropriate method for the capturing of the multiscale transport mechanism in the particle phase through its coupled wave-particle formulation. In the regime with intensive particle collision, the evolution of solid particle will be followed by the analytic wave with quasi-equilibrium distribution; while in the rarefied regime the non-equilibrium particle phase will be captured through particle tracking and collision, which plays a decisive role in recovering particle trajectory crossing behavior. The gas-kinetic scheme (GKS) is employed for the simulation of gas flow. In the highly collision regime for the particles, no particles will be sampled in UGKWP and the wave formulation for solid particle with the hydrodynamic gas phase will reduce the system to the two-fluid Eulerian model. On the other hand, in the collisionless regime for the solid particle, the free transport of solid particle will be followed in UGKWP, and coupled system will return to the Eulerian-Lagrangian formulation for the gas and particle. The scheme will be tested for in all flow regimes, which include the non-equilibrium particle trajectory crossing, the particle concentration under different Knudsen number, and the dispersion of particle flow with the variation of Stokes number. A experiment of shock-induced particle bed fluidization is simulated and the results are compared with experimental measurements. These numerical solutions validate suitability of the proposed scheme for the simulation of gas-particle multiphase flow.

physics.comp-ph↗

arXiv2021

Two-step multi-resolution reconstruction-based compact gas-kinetic scheme on tetrahedral mesh

In this paper, a third-order compact gas-kinetic scheme (GKS) on unstructured tetrahedral mesh is constructed for the compressible Euler and Navier-Stokes solutions. The time-dependent gas distribution function at a cell interface is used to calculate the fluxes for the updating the cell-averaged flow variables and to evaluate the time accurate cell-averaged flow variables as well for evolving the cell-averaged gradients of flow variables. With the accurate evolution model for both flow variables and their slopes, the quality of the scheme depends closely on the accuracy and reliability of the initial reconstruction of flow variables. The reconstruction scheme becomes more challenge on tetrahedral mesh, where the conventional second-order unlimited least-square reconstruction can make the scheme be linearly unstable when using cell-averaged conservative variables alone with von Neumann neighbors. Benefiting from the evolved cell-averaged slopes, on tetrahedral mesh the GKS is linearly stable from a compact third-order smooth reconstruction with a large CFL number. In order to further increase the robustness of the high-order compact GKS for capturing discontinuous solution, a new two-step multi-resolution weighted essentially non-oscillatory (WENO) reconstruction will be proposed. The novelty of the reconstruction includes the following. Firstly, it releases the stability issue from a second-order compact reconstruction through the introduction of a pre-reconstruction step. Secondly, in the third-order non-linear reconstruction, only one more large stencil is added beside those in the second-order one, which significantly simplifies the high-order reconstruction. The proposed third-order scheme shows good robustness in high speed flow computation and favorable mesh adaptability in cases with complex geometry.

physics.comp-ph↗

arXiv2020

A compact high-order gas-kinetic scheme on unstructured mesh for acoustic and shock wave computations

In this paper an even higher-order compact GKS up to sixth order of accuracy will be constructed for the shock and acoustic wave computation on unstructured mesh. The compactness is defined by the physical domain of dependence for an unstructured triangular cell, which may involve the closest neighbors of neighboring cells. The compactness and high-order accuracy of the scheme are coming from the consistency between the high-order initial reconstruction and the high-order gas evolution model under GKS framework. The high-order evolution solution at a cell interface provides not only a time-accurate flux function, but also the time-evolving flow variables. Therefore, the cell-averaged flow variables and their gradients can be explicitly updated at the next time level from the moments of the same time-dependent gas distribution function. Based on the cell averages and cell-averaged derivatives, both linear and nonlinear high-order reconstruction can be obtained for macroscopic flow variables in the evaluation of local equilibrium and non-equilibrium states. The current nonlinear reconstruction is a combination of WENO and ENO methodology. The initial piecewise discontinuous reconstruction is used for the determination non-equilibrium state and an evolved smooth reconstruction for the equilibrium state. The evolution model in gas-kinetic scheme is based on a relaxation process from non-equilibrium to equilibrium state. The accuracy, efficiency, and robustness of the scheme have been validated. The main conclusion of the paper is that beyond the first-order Riemann solver, the use of high-order gas evolution model seems necessary in the development of high-order schemes.

math.NA↗

arXiv2020

Comparison of the performance of high-order schemes based on the gas-kinetic and HLLC fluxes

In this paper, a comparison of the performance of two high-order finite volume methods based on the gas-kinetic scheme (GKS) and HLLC fluxes is carried out in structured rectangular mesh. For both schemes, the fifth-order WENO-AO reconstruction is adopted to achieve a high-order spatial accuracy. In terms of temporal discretization, a two-stage fourth-order (S2O4) time marching strategy is adopted for WENO5-AO-GKS scheme, and the fourth-order Runge-Kutta (RK4) method is employed for WENO5-AO-HLLC scheme. For the viscous flow computation, the GKS includes both inviscid and viscous fluxes in the evolution of a single cell interface gas distribution function. While for the WENO5-AO-HLLC scheme, the inviscid flux is provided by HLLC Riemann solver, and the viscous flux is discretized by a sixth-order central difference method. Based on the tests of forward Mach step and viscous shock tube, both schemes show outstanding shock capturing property. From the Titarev-Toro and double shear layer tests, WENO5-AO-GKS scheme seems to have a better resolution than WENO5-AO-HLLC scheme. Both schemes show excellent robustness in extreme cases, such as the Le Blanc problem. From the cases of the Noh problem and the compressible isotropic turbulence, WENO5-AO-GKS scheme shows favorite robustness. In the compressible isotropic turbulence and three-dimensional Taylor-Green vortex problems, WENO-AO-GKS can use a CFL number up to 0.5, instead of 0.3 for WENO5-AO-HLLC. In terms of computational efficiency, WENO5-AO-HLLC scheme is about 27% more expensive than WENO5-AO-GKS scheme in the two-dimensional viscous flow problems, but is about 15% faster in the three-dimensional case. Due to the multi-dimensionality, WENO5-AO-GKS scheme performs better than WENO5-AO-HLLC scheme in the laminar boundary layer and the double shear layer test.

physics.comp-ph↗

arXiv2020

A three-dimensional compact high-order gas-kinetic scheme on structured mesh

In this paper, a third-order compact gas-kinetic scheme is firstly proposed for three-dimensional computation for the compressible Euler and Navier-Stokes solutions. The scheme achieves its compactness due to the time-dependent gas distribution function in GKS, which provides not only the fluxes but also the time accurate flow variables in the next time level at a cell interface. As a result, the cell averaged first-order spatial derivatives of flow variables can be obtained naturally through the Gauss's theorem. Then, a third-order compact reconstruction involving the cell averaged values and their first-order spatial derivatives can be achieved. The trilinear interpolation is used to treat possible non-coplanar elements on general hexahedral mesh. The constrained least-square technique is applied to improve the accuracy in the smooth case. To deal with both smooth and discontinuous flows, a new HWENO reconstruction is designed in the current scheme by following the ideas in Zhu, 2018. No identification of troubled cells is needed in the current scheme. In contrast to the Riemann solver-based method, the compact scheme can achieve a third-order temporal accuracy with the two-stage two-derivative temporal discretization, instead of the three-stage Runge-Kutta method. Overall, the proposed scheme inherits the high accuracy and efficiency of the previous ones in two-dimensional case. The desired third-order accuracy can be obtained with curved boundary. The robustness of the scheme has been validated through many cases, including strong shocks in both inviscid and viscous flow computations. Quantitative comparisons for both smooth and discontinuous cases show that the current third-order scheme can give competitive results against the fifth-order non-compact GKS under the same mesh. A large CFL number around 0.5 can be used in the present scheme.

physics.comp-ph↗

arXiv2020

An acoustic and shock wave capturing compact high-order gas-kinetic scheme with spectral-like resolution

In this paper, a compact high-order gas-kinetic scheme (GKS) with spectral resolution will be presented and used in the simulation of acoustic and shock waves. For accurate simulation, the numerical scheme is required to have excellent dissipation-dispersion preserving property, while the wave modes, propagation characteristics, and wave speed of the numerical solution should be kept as close as possible to the exact solution of governing equations. For compressible flow simulation with shocks, the numerical scheme has to be equipped with proper numerical dissipation to make a crispy transition in the shock layer. Based on the high-order gas evolution model, the GKS provides a time accurate solution at a cell interface, from which both time accurate flux function and the time evolving flow variables can be obtained. The GKS updates explicitly both cell-averaged conservative flow variables and the cell-averaged gradients by applying Gauss-theorem along the boundary of the control volume. Based on the cell-averaged flow variables and cell-averaged gradients, a reconstruction with compact stencil can be obtained. With the same stencil of a second-order scheme, a reconstruction up to 8th-order spacial accuracy can be constructed, which include the nonlinear and linear reconstruction for the non-equilibrium and equilibrium states respectively. The GKS unifies the nonlinear and linear reconstruction through a time evolution process at a cell interface from the non-equilibrium state to an equilibrium one. In the region between these two limits, the contribution from nonlinear and linear reconstructions depends on the weighting functions of $\exp(-Δt/τ)$ and $(1-\exp(-Δt /τ))$, where $Δt$ is the time step and $τ$ is the particle collision time, which is enhanced in the shock region. As a result, both shock and acoustic wave can be captured accurately in GKS.

physics.comp-ph↗

arXiv2019

Performance Enhancement for High-order Gas-kinetic Scheme Based on WENO-adaptive-order Reconstruction

High-order gas-kinetic scheme (HGKS) has been well-developed in the past years. Abundant numerical tests including hypersonic flow, turbulence, and aeroacoustic problems, have been used to validate its accuracy, efficiency, and robustness. However, there are still rooms for its further improvement. Firstly, the reconstruction in the previous scheme mainly achieves a third-order accuracy for the initial non-equilibrium states. At the same time, the equilibrium state in space and time in HGKS has to be reconstructed separately. Secondly, it is complicated to get reconstructed data at Gaussian points from the WENO-type method in high dimensions. For HGKS, besides the point-wise values at the Gaussian points it also requires the slopes in both normal and tangential directions of a cell interface. Thirdly, there exists visible spurious overshoot/undershoot at weak discontinuities from the previous HGKS with the standard WENO reconstruction. In order to overcome these difficulties, in this paper we use an improved reconstruction for HGKS. The WENO with adaptive order (WENO-AO) method is implemented for reconstruction.A whole polynomial inside each cell is provided in WENO-AO reconstruction. The HGKS becomes simpler than the previous one with the direct implementation of cell interface values and their slopes from WENO-AO. The additional reconstruction of equilibrium state at the beginning of each time step can be avoided as well by dynamically merging the reconstructed non-equilibrium slopes. The new HGKS essentially releases or totally removes the above existing problems in previous HGKS. The accuracy of the scheme from 1D to 3D from the new HGKS can recover the theoretical order of accuracy of the WENO reconstruction.In the two- and three-dimensional simulations, the new HGKS shows better robustness and efficiency than the previous scheme in all test cases.

physics.comp-ph↗

arXiv2019

A HWENO Reconstruction Based High-order Compact Gas-kinetic Scheme on Unstructured Meshes

As an extension of previous fourth-order compact gas kinetic scheme (GKS) on structured meshes (Ji et al. 2018), this work is about the development of a third-order compact GKS on unstructured meshes for the compressible Euler and Navier-Stokes solutions. Based on the time accurate high-order gas-kinetic evolution solution at a cell interface, the time dependent gas distribution function in GKS provides not only the flux function and its time derivative at a cell interface, but also the time accurate flow variables there at next time level. As a result, besides updating the conservative flow variables inside each control volume through the interface fluxes, the cell averaged first-order spatial derivatives of flow variables in the cell can be also obtained using the updated flow variables at the cell interfaces around that cell through the divergence theorem. Therefore, with the flow variables and their first-order spatial derivatives inside each cell, the Hermite WENO (HWENO) techniques can be naturally implemented for the compact high-order reconstruction at the beginning of a new time step. Following the reconstruction method in (Zhu et al. 2018), a new HWENO reconstruction on triangular meshes is designed in the current scheme. Combined with a two-stage temporal discretization and second-order gas-kinetic flux function, a third-order spatial and temporal accuracy in the current compact scheme can be achieved. Accurate solutions can be obtained for both inviscid and viscous flows without sensitive dependence on the quality of triangular meshes. The robustness of the scheme has been validated as well through the cases with strong shocks in the hypersonic viscous flow simulations.

physics.comp-ph↗

arXiv2019

Compact Higher-order Gas-kinetic Schemes with Spectral-like Resolution for Compressible Flow Simulations

In this paper, a class of compact higher-order gas-kinetic schemes (GKS) with spectral resolution will be presented. Based on the high-order gas evolution model in GKS, both the interface flux function and conservative flow variables can be evaluated explicitly from the time-accurate gas distribution function. As a result, inside each control volume both the cell-averaged flow variables and their cell-averaged gradients can be updated within each time step. The flow variable update and slope update are coming from the same physical solution at the cell interface. Different from many other approaches, such as HWENO, there are no additional governing equations in GKS for the slopes or equivalent degrees of freedom independently inside each cell. For nonlinear gas dynamic evolution, the above compact linear reconstruction from the symmetric stencil can be divided into sub-stencils and apply a biased nonlinear WENO-Z reconstruction. In GKS, the time evolution solution of the gas distribution function at a cell interface covers a physical process from an initial non-equilibrium state to a final equilibrium one. The GKS evolution models unifies the nonlinear and linear reconstructions in gas evolution process for the determination of a time-dependent gas distribution function. This dynamically adaptive model helps to solve a long lasting problem in the development of high-order schemes about the choices of the linear and nonlinear reconstructions. Compared with discontinuous Galerkin (DG) scheme, the current compact GKS uses the same local and compact stencil, achieves the 6th-order and 8th-order accuracy, uses a much larger time step with CFL number $\geq 0.3$, and gets accurate solutions in both shock and smooth regions without introducing trouble cell and additional limiting process. At the same time, the current scheme solves the Navier-Stokes equations.

physics.comp-ph↗

arXiv2018

Orthogonal Deep Features Decomposition for Age-Invariant Face Recognition

As facial appearance is subject to significant intra-class variations caused by the aging process over time, age-invariant face recognition (AIFR) remains a major challenge in face recognition community. To reduce the intra-class discrepancy caused by the aging, in this paper we propose a novel approach (namely, Orthogonal Embedding CNNs, or OE-CNNs) to learn the age-invariant deep face features. Specifically, we decompose deep face features into two orthogonal components to represent age-related and identity-related features. As a result, identity-related features that are robust to aging are then used for AIFR. Besides, for complementing the existing cross-age datasets and advancing the research in this field, we construct a brand-new large-scale Cross-Age Face dataset (CAF). Extensive experiments conducted on the three public domain face aging datasets (MORPH Album 2, CACD-VS and FG-NET) have shown the effectiveness of the proposed approach and the value of the constructed CAF dataset on AIFR. Benchmarking our algorithm on one of the most popular general face recognition (GFR) dataset LFW additionally demonstrates the comparable generalization performance on GFR.

cs.CV↗

arXiv2018

CosFace: Large Margin Cosine Loss for Deep Face Recognition

Face recognition has made extraordinary progress owing to the advancement of deep convolutional neural networks (CNNs). The central task of face recognition, including face verification and identification, involves face feature discrimination. However, the traditional softmax loss of deep CNNs usually lacks the power of discrimination. To address this problem, recently several loss functions such as center loss, large margin softmax loss, and angular softmax loss have been proposed. All these improved losses share the same idea: maximizing inter-class variance and minimizing intra-class variance. In this paper, we propose a novel loss function, namely large margin cosine loss (LMCL), to realize this idea from a different perspective. More specifically, we reformulate the softmax loss as a cosine loss by $L_2$ normalizing both features and weight vectors to remove radial variations, based on which a cosine margin term is introduced to further maximize the decision margin in the angular space. As a result, minimum intra-class variance and maximum inter-class variance are achieved by virtue of normalization and cosine decision margin maximization. We refer to our model trained with LMCL as CosFace. Extensive experimental evaluations are conducted on the most popular public-domain face recognition datasets such as MegaFace Challenge, Youtube Faces (YTF) and Labeled Face in the Wild (LFW). We achieve the state-of-the-art performance on these benchmarks, which confirms the effectiveness of our proposed approach.

cs.CV↗