arXiv subjects

Cheng Wang

Publications and source records attributed to Cheng Wang.

At least 361 records · Page 20Linked to original sources

arXiv2022

Random matrix description of dynamically backscattered coherent waves propagating in a wide-field-illuminated random medium

The wave propagation in random medium plays a critical role in optics and quantum physics. Multiple scattering of coherent wave in a random medium determines the transport procedure. Brownian motions of the scatterers perturb each propagation trajectory and form dynamic speckle patterns in the backscattered direction. In this study, we applied the random matrix theory (RMT) to investigate the eigenvalue density of the backscattered intensity matrix. We find that the dynamic speckle patterns can be utilized to decouple the singly and multiply backscattered components. The Wishart random matrix of multiple scattering component is well described by the Marcenko-Pastur law, while the single scattering part has low-rank characteristic. We therefore propose a strategy for estimating the first and the second order moments of single and multiple scattering components, respectively, based on the Marcenko-Pastur law and trace analysis. Electric field Monte Carlo simulation and in-vivo experiments demonstrate its potential applications in hidden absorbing object detection and in-vivo blood flow imaging. Our method can be applied to other coherent domain elastic scattering phenomenon for wide-filed propagation of microwave, ultrasound and etc.

physics.optics↗

arXiv2021

Antiferroelectric Smectic Ordering as a Prelude to the Ferroelectric Nematic:Introducing the Smectic $Z_A$ Phase

We have structurally characterized the liquid crystal phase that appears as an intermediate state when a dielectric nematic, having polar disorder of its molecular dipoles, transitions to the almost perfectly polar-ordered ferroelectric nematic. This intermediate phase, which fills a 100-year-old void in the taxonomy of smectics and which we term the "smectic $Z_A$", is antiferroelectric, with the nematic director and polarization oriented parallel to smectic layer planes, and the polarization alternating in sign from layer to layer. The period of this polarization wave ($\sim$180 A) is mesoscopic, corresponding to $\sim$40 molecules side-by-side, indicating that this lamellar structure is collectively stabilized. A Landau free energy, originally formulated to model incommensurate antiferroelectricity in crystals, describes the key features of the nematic-Sm$Z_A$-ferroelectric nematic phase sequence.

cond-mat.soft↗

arXiv2021

Transformer Uncertainty Estimation with Hierarchical Stochastic Attention

Transformers are state-of-the-art in a wide range of NLP tasks and have also been applied to many real-world products. Understanding the reliability and certainty of transformer model predictions is crucial for building trustable machine learning applications, e.g., medical diagnosis. Although many recent transformer extensions have been proposed, the study of the uncertainty estimation of transformer models is under-explored. In this work, we propose a novel way to enable transformers to have the capability of uncertainty estimation and, meanwhile, retain the original predictive performance. This is achieved by learning a hierarchical stochastic self-attention that attends to values and a set of learnable centroids, respectively. Then new attention heads are formed with a mixture of sampled centroids using the Gumbel-Softmax trick. We theoretically show that the self-attention approximation by sampling from a Gumbel distribution is upper bounded. We empirically evaluate our model on two text classification tasks with both in-domain (ID) and out-of-domain (OOD) datasets. The experimental results demonstrate that our approach: (1) achieves the best predictive performance and uncertainty trade-off among compared methods; (2) exhibits very competitive (in most cases, improved) predictive performance on ID datasets; (3) is on par with Monte Carlo dropout and ensemble methods in uncertainty estimation on OOD datasets.

cs.CL↗

arXiv2021

How do the finite-size particles modify the drag in Taylor-Couette turbulent flow

We experimentally investigate the drag modification by neutrally buoyant finite-size particles with various aspect ratios in a Taylor-Couette (TC) turbulent flow. The current Reynolds number, $Re$, ranges from $6.5\times10^3$ to $2.6\times10^4$, and the particle volume fraction, $Φ$, is up to $10\%$. Particles with three kinds of aspect ratio, $λ$, are used: $λ=1/3$ (oblate), $λ=1$ (spherical) and $λ=3$ (prolate). Unlike the case of bubbly TC flow, we find that the suspended finite-size particles increase the drag of the TC system regardless of their aspect ratios. In addition, the normalized friction coefficient, $c_{f,Φ}/c_{f,Φ=0}$, decreases with increasing $Re$, the reason could be that in the current low volume fractions the turbulent stress becomes dominant at higher $Re$. As $Re$ increases, the particles distribute more evenly in the entire system, which results from both the greater turbulence intensity and the more pronounced finite-size effects of the particles at higher $Re$. Moreover, it is found that the variation of the particle aspect ratios leads to different particle collective effects. The suspended spherical particles, which tend to cluster near the walls and form a particle layer, significantly affect the boundary layer and result in maximum drag modification. The minimal drag modification is found in the oblate case, where the particles preferentially cluster in the bulk region, and thus the particle layer is absent. Based on the optical measurement results, it can be concluded that, in the low volume fraction ranges ($Φ=0.5\%$ and $Φ= 2\%$ here), the larger drag modification is connected to the near-wall particle clustering. The present findings suggest that the particle shape plays a significant role in drag modification.

physics.flu-dyn↗

arXiv2021

Monocular 3D Object Detection: An Extrinsic Parameter Free Approach

Monocular 3D object detection is an important task in autonomous driving. It can be easily intractable where there exists ego-car pose change w.r.t. ground plane. This is common due to the slight fluctuation of road smoothness and slope. Due to the lack of insight in industrial application, existing methods on open datasets neglect the camera pose information, which inevitably results in the detector being susceptible to camera extrinsic parameters. The perturbation of objects is very popular in most autonomous driving cases for industrial products. To this end, we propose a novel method to capture camera pose to formulate the detector free from extrinsic perturbation. Specifically, the proposed framework predicts camera extrinsic parameters by detecting vanishing point and horizon change. A converter is designed to rectify perturbative features in the latent space. By doing so, our 3D detector works independent of the extrinsic parameter variations and produces accurate results in realistic cases, e.g., potholed and uneven roads, where almost all existing monocular detectors fail to handle. Experiments demonstrate our method yields the best performance compared with the other state-of-the-arts by a large margin on both KITTI 3D and nuScenes datasets.

cs.CV↗

arXiv2021

Extracting single- and multiple-scattering components in laser speckle contrast imaging of tissue blood flow

Random matrix theory provides new insights into multiple scattering in random media. In a recent study, we demonstrated the statistical separation of single- and multiple-scattering components based on a Wishart random matrix. The first- and second-order moments were estimated through a Wishart random matrix constructed using dynamically-backscattered speckle images. In this study, this new strategy was applied to laser speckle contrast imaging (LSCI) of in-vivo blood flow. The random matrix-based method was adapted and parameterized using electric field Monte Carlo simulations and in-vitro blood flow phantom experiments. The new method was further applied in in-vivo experiments, demonstrating the benefits of separating the single- and multiple-scattering components, and was compared with the traditional temporal LASCA method. More specifically, the new method captures stimulus-induced functional changes in blood flow and tissue perfusion in the superficial and deeper layers. The new method extends the ability of LSCI to image functional and pathological changes.

physics.med-ph↗

arXiv2021

Convergence Analysis of A Second-order Accurate, Linear Numerical Scheme for The Landau-Lifshitz Equation with Large Damping Parameters

A second order accurate, linear numerical method is analyzed for the Landau-Lifshitz equation with large damping parameters. This equation describes the dynamics of magnetization, with a non-convexity constraint of unit length of the magnetization. The numerical method is based on the second-order backward differentiation formula in time, combined with an implicit treatment of the linear diffusion term and explicit extrapolation for the nonlinear terms. Afterward, a projection step is applied to normalize the numerical solution at a point-wise level. This numerical scheme has shown extensive advantages in the practical computations for the physical model with large damping parameters, which comes from the fact that only a linear system with constant coefficients (independent of both time and the updated magnetization) needs to be solved at each time step, and has greatly improved the numerical efficiency. Meanwhile, a theoretical analysis for this linear numerical scheme has not been available. In this paper, we provide a rigorous error estimate of the numerical scheme, in the discrete $\ell^{\infty}(0,T; \ell^2) \cap \ell^2(0,T; H_h^1)$ norm, under suitable regularity assumptions and reasonable ratio between the time step-size and the spatial mesh-size. In particular, the projection operation is nonlinear, and a stability estimate for the projection step turns out to be highly challenging. Such a stability estimate is derived in details, which will play an essential role in the convergence analysis for the numerical scheme, if the damping parameter is greater than 3.

math.NA↗

arXiv2021

Oscillatory Fourier Neural Network: A Compact and Efficient Architecture for Sequential Processing

Tremendous progress has been made in sequential processing with the recent advances in recurrent neural networks. However, recurrent architectures face the challenge of exploding/vanishing gradients during training, and require significant computational resources to execute back-propagation through time. Moreover, large models are typically needed for executing complex sequential tasks. To address these challenges, we propose a novel neuron model that has cosine activation with a time varying component for sequential processing. The proposed neuron provides an efficient building block for projecting sequential inputs into spectral domain, which helps to retain long-term dependencies with minimal extra model parameters and computation. A new type of recurrent network architecture, named Oscillatory Fourier Neural Network, based on the proposed neuron is presented and applied to various types of sequential tasks. We demonstrate that recurrent neural network with the proposed neuron model is mathematically equivalent to a simplified form of discrete Fourier transform applied onto periodical activation. In particular, the computationally intensive back-propagation through time in training is eliminated, leading to faster training while achieving the state of the art inference accuracy in a diverse group of sequential tasks. For instance, applying the proposed model to sentiment analysis on IMDB review dataset reaches 89.4% test accuracy within 5 epochs, accompanied by over 35x reduction in the model size compared to LSTM. The proposed novel RNN architecture is well poised for intelligent sequential processing in resource constrained hardware.

cs.NE↗

arXiv2021

ConTIG: Continuous Representation Learning on Temporal Interaction Graphs

Representation learning on temporal interaction graphs (TIG) is to model complex networks with the dynamic evolution of interactions arising in a broad spectrum of problems. Existing dynamic embedding methods on TIG discretely update node embeddings merely when an interaction occurs. They fail to capture the continuous dynamic evolution of embedding trajectories of nodes. In this paper, we propose a two-module framework named ConTIG, a continuous representation method that captures the continuous dynamic evolution of node embedding trajectories. With two essential modules, our model exploit three-fold factors in dynamic networks which include latest interaction, neighbor features and inherent characteristics. In the first update module, we employ a continuous inference block to learn the nodes' state trajectories by learning from time-adjacent interaction patterns between node pairs using ordinary differential equations. In the second transform module, we introduce a self-attention mechanism to predict future node embeddings by aggregating historical temporal interaction information. Experiments results demonstrate the superiority of ConTIG on temporal link prediction, temporal node recommendation and dynamic node classification tasks compared with a range of state-of-the-art baselines, especially for long-interval interactions prediction.

cs.SI↗

arXiv2021

HiTMap: A Hierarchical Topological Map Representation for Navigation in Unknown Environments

The ability to autonomously navigate in unknown environments is important for mobile robots. The map is the core component to achieve this. Most map representations rely on drift-free state estimation and provide a global metric map to navigate. However, in large-scale real-world applications, it's hard to prohibit drifts and compose a globally consistent map quickly. In this paper, a novel representation named, HiTMap, is proposed to enhance the existing map representations. The central idea is to adopt a submap-based hierarchical topology rather than a global metric map so that only a local metric map is maintained for obstacle avoidance which ensures the lightweight of the representation. To guide the robots navigate into unknown spaces, frontiers are detected and attached to the map as an attribute. We also develop a path planning module to evaluate the feasibility and efficiency of our map representation. The system is validated in a simulation environment and a demonstration in the real world is conducted. In addition, the HiTMap is made available open-source.

cs.RO↗

arXiv2021

Storage and Transmission Capacity Requirements of a Remote Solar Power Generation System

Large solar power stations usually locate in remote areas and connect to the main grid via a long transmission line. Energy storage unit is deployed locally with the solar plant to smooth its output. Capacities of the grid-connection transmission line and the energy storage unit have a significant impact on the utilization rate of solar energy, as well as the investment cost. This paper characterizes the feasible set of capacity parameters under a given solar spillage rate and a fixed investment budget. A linear programming based projection algorithm is proposed to obtain such a feasible set, offering valuable references for system planning and policy making.

eess.SY↗

arXiv2021

A second-order accurate, operator splitting scheme for reaction-diffusion systems in an energetic variational formulation

A second-order accurate in time, positivity-preserving, and unconditionally energy stable operator splitting numerical scheme is proposed and analyzed for the system of reaction-diffusion equations with detailed balance. The scheme is designed based on an energetic variational formulation, in which the reaction part is reformulated in terms of the reaction trajectory, and both the reaction and diffusion parts dissipate the same free energy. At the reaction stage, the reaction trajectory equation is approximated by a second-order Crank-Nicolson type method. The unique solvability, positivity-preserving, and energy-stability are established based on a convexity analysis. In the diffusion stage, an exact integrator is applied if the diffusion coefficients are constant, and a Crank-Nicolson type scheme is applied if the diffusion process becomes nonlinear. In either case, both the positivity-preserving property and energy stability could be theoretically established. Moreover, a combination of the numerical algorithms at both stages by the Strang splitting approach leads to a second-order accurate, structure-preserving scheme for the original reaction-diffusion system. Numerical experiments are presented, which demonstrate the accuracy of the proposed scheme.

math.NA↗

arXiv2021

Detecting Mitosis against Domain Shift using a Fused Detector and Deep Ensemble Classification Model for MIDOG Challenge

Mitotic figure count is an important marker of tumor proliferation and has been shown to be associated with patients' prognosis. Deep learning based mitotic figure detection methods have been utilized to automatically locate the cell in mitosis using hematoxylin \& eosin (H\&E) stained images. However, the model performance deteriorates due to the large variation of color tone and intensity in H\&E images. In this work, we proposed a two stage mitotic figure detection framework by fusing a detector and a deep ensemble classification model. To alleviate the impact of color variation in H\&E images, we utilize both stain normalization and data augmentation, aiding model to learn color irrelevant features. The proposed model obtains an F1 score of 0.7550 on the preliminary testing set released by the MIDOG challenge.

cs.CV↗

arXiv2021

Early Stages of Flame Propagation in Tubes with No-slip Walls and the Mechanism of Tulip Flame Formation

The early stages of flames propagation in tubes with no-slip walls and the inversion of the flame front from a convex shape directed towards unburned gas to a concave shape with a cusp directed to the burned gas, known as a tulip flame, was investigated for closed and half-open tubes by solving the fully compressible reactive Navier-Stokes equations with a one-step Arrhenius chemical model for the highly reactive hydrogen/air and slowly reacting methane/air mixtures. The development of the tulip flame in hydrogen/air obtained in simulations with a one-step Arrhenius model was compared with simulations using a detailed chemical model. It is shown that the inversion of the flame front and the onset of the tulip flame occurs due to rarefaction waves generated by the decelerating flame when its surface was reduced due to extinguishing of the rear parts of the flame skirt at the sidewalls. The rarefaction waves reduce the flow velocity ahead of the flame, creating an uneven velocity profile, which facilitate the flame front inversion. In the case of a flame propagating in a tube with both ends closed, the compression wave reflected from the tube end opposite to the ignition end, also contribute to the inversion of the flame front. In the case of fast flames and a relatively short tube with both closed ends, the rarefaction waves may invert the flow velocities in the unburned gas towards the propagating flame. The tulip flame formation mechanism is a purely gas-dynamic phenomenon not associated with flame instabilities or vortex motion, in agreement with the conclusion obtained in recent experimental studies [1].

physics.flu-dyn↗

arXiv2021

Optimal error estimates of a second-order projection finite element method for magnetohydrodynamic equations

In this paper, we propose and analyze a temporally second-order accurate, fully discrete finite element method for the magnetohydrodynamic (MHD) equations. A modified Crank--Nicolson method is used to discretize the model and appropriate semi-implicit treatments are applied to the fluid convection term and two coupling terms. These semi-implicit approximations result in a linear system with variable coefficients for which the unique solvability can be proved theoretically. In addition, we use a decoupling projection method of the Van Kan type \cite{vankan1986} in the Stokes solver, which computes the intermediate velocity field based on the gradient of the pressure from the previous time level, and enforces the incompressibility constraint via the Helmholtz decomposition of the intermediate velocity field. The energy stability of the scheme is theoretically proved, in which the decoupled Stokes solver needs to be analyzed in details. Optimal-order convergence of $\mathcal{O} (τ^2+h^{r+1})$ in the discrete $L^\infty(0,T;L^2)$ norm is proved for the proposed decoupled projection finite element scheme, where $τ$ and $h$ are the time stepsize and spatial mesh size, respectively, and $r$ is the degree of the finite elements. Existing error estimates of second-order projection methods of the Van Kan type \cite{vankan1986} were only established in the discrete $L^2(0,T;L^2)$ norm for the Navier--Stokes equations. Numerical examples are provided to illustrate the theoretical results.

math.NA↗

arXiv2021

Federated Learning with Fair Averaging

Fairness has emerged as a critical problem in federated learning (FL). In this work, we identify a cause of unfairness in FL -- conflicting gradients with large differences in the magnitudes. To address this issue, we propose the federated fair averaging (FedFV) algorithm to mitigate potential conflicts among clients before averaging their gradients. We first use the cosine similarity to detect gradient conflicts, and then iteratively eliminate such conflicts by modifying both the direction and the magnitude of the gradients. We further show the theoretical foundation of FedFV to mitigate the issue conflicting gradients and converge to Pareto stationary solutions. Extensive experiments on a suite of federated datasets confirm that FedFV compares favorably against state-of-the-art methods in terms of fairness, accuracy and efficiency. The source code is available at https://github.com/WwZzz/easyFL.

cs.LG↗

arXiv2021

Advantages of a semi-implicit scheme over a fully implicit scheme for Landau-Lifshitz-Gilbert equation

Magnetization dynamics in magnetic materials is modeled by the Landau-Lifshitz-Gilbert (LLG) equation. In the LLG equation, the length of magnetization is conserved and the system energy is dissipative. Implicit and semi-implicit schemes have been used in micromagnetics simulations due to their unconditional numerical stability. In more details, implicit schemes preserve the properties of the LLG equation, but solve a nonlinear system of equations per time step. In contrast, semi-implicit schemes only solve a linear system of equations, while additional operations are needed to preserve the length of magnetization. It still remains unclear which one shall be used if both implicit and semi-implicit schemes are available. In this work, using the implicit Crank-Nicolson (ICN) scheme as a benchmark, we propose to make this implicit scheme semi-implicit. It can be proved that both schemes are second-order accurate in space and time. For the unique solvability of nonlinear systems of equations in the ICN scheme, we require that the temporal step size scales quadratically with the spatial mesh size. It is numerically verified that the convergence of the nonlinear solver becomes slower for larger temporal step size and multiple magnetization profiles are obtained for different initial guesses. The linear systems of equations in the semi-implicit CN (SICN) scheme are unconditionally uniquely solvable, and the condition that the temporal step size scales linearly with the spatial mesh size is needed in the convergence of the SICN scheme. In terms of numerical efficiency, the SICN scheme achieves the same accuracy as the ICN scheme with less computational time. Based on these results, we conclude that a semi-implicit scheme is superior to its implicit analog both theoretically and numerically, and we recommend the semi-implicit scheme in micromagnetics simulations if both methods are available.

physics.comp-ph↗

arXiv2021

Error estimate of a decoupled numerical scheme for the Cahn-Hilliard-Stokes-Darcy system

We analyze a fully discrete finite element numerical scheme for the Cahn-Hilliard-Stokes-Darcy system that models two-phase flows in coupled free flow and porous media. To avoid a well-known difficulty associated with the coupling between the Cahn-Hilliard equation and the fluid motion, we make use of the operator-splitting in the numerical scheme, so that these two solvers are decoupled, which in turn would greatly improve the computational efficiency. The unique solvability and the energy stability have been proved in~\cite{CHW2017}. In this work, we carry out a detailed convergence analysis and error estimate for the fully discrete finite element scheme, so that the optimal rate convergence order is established in the energy norm, i.e.,, in the $\ell^\infty (0, T; H^1) \cap \ell^2 (0, T; H^2)$ norm for the phase variables, as well as in the $\ell^\infty (0, T; H^1) \cap \ell^2 (0, T; H^2)$ norm for the velocity variable. Such an energy norm error estimate leads to a cancellation of a nonlinear error term associated with the convection part, which turns out to be a key step to pass through the analysis. In addition, a discrete $\ell^2 (0;T; H^3)$ bound of the numerical solution for the phase variables plays an important role in the error estimate, which is accomplished via a discrete version of Gagliardo-Nirenberg inequality in the finite element setting.

math.NA↗