arXiv subjects

Rui Du

Publications and source records attributed to Rui Du.

32 records · Page 2Linked to original sources

arXiv2022

Mapping evolving population geography in China

China's demographic changes have important global economic and geopolitical implications. Yet, our understanding of such transitions at the micro-spatial scale remains limited due to spatial inconsistency of the census data caused by administrative boundary adjustments. To fill this gap, we manually collected and built a population census panel from 2010 to 2020 at both the county and prefectural-city levels. We show that the massive internal migration drives China's increasing population concentration and regional disparity, resulting in severe population aging in shrinking cities and increasing gender imbalance in growing cities.

econ.GN↗

arXiv2022

Joint Pilot Optimization, Target Detection and Channel Estimation for Integrated Sensing and Communication Systems

Radar sensing will be integrated into the 6G communication system to support various applications. In this integrated sensing and communication system, a radar target may also be a communication channel scatterer. In this case, the radar and communication channels exhibit certain joint burst sparsity. We propose a two-stage joint pilot optimization, target detection and channel estimation scheme to exploit such joint burst sparsity and pilot beamforming gain to enhance detection/estimation performance. In Stage 1, the base station (BS) sends downlink pilots (DP) for initial target search, and the user sends uplink pilots (UP) for channel estimation. Then the BS performs joint target detection and channel estimation based on the reflected DP and received UP signals. In Stage 2, the BS exploits the prior information obtained in Stage 1 to optimize the DP signal to achieve beamforming gain and further refine the performance. A Turbo Sparse Bayesian inference algorithm is proposed for joint target detection and channel estimation in both stages. The pilot optimization problem in Stage 2 is a semi-definite programming with rank-1 constraints. By replacing the rank-1 constraint with a tight and smooth approximation, we propose an efficient pilot optimization algorithm based on the majorization-minimization method. Simulations verify the advantages of the proposed scheme.

cs.IT↗

arXiv2021

A second-order semi-implicit method for the inertial Landau-Lifshitz-Gilbert equation

Recent theoretical and experimental advances show that the inertia of magnetization emerges at sub-picoseconds and contributes to the ultrafast magnetization dynamics which cannot be captured intrinsically by the LLG equation. Therefore, as a generalization, the inertial Landau-Lifshitz-Gilbert (iLLG) equation is proposed to model the ultrafast magnetization dynamics. Mathematically, the LLG equation is a nonlinear system of parabolic type with (possible) degeneracy. However, the iLLG equation is a nonlinear system of mixed hyperbolic-parabolic type with degeneracy, and exhibits more complicated structures. It behaves like a hyperbolic system at the sub-picosecond scale while behaves like a parabolic system at larger timescales. Such hybrid behaviors impose additional difficulties on designing numerical methods for the iLLG equation. In this work, we propose a second-order semi-implicit scheme to solve the iLLG equation. The second temporal derivative of magnetization is approximated by the standard centered difference scheme and the first derivative is approximated by the midpoint scheme involving three time steps. The nonlinear terms are treated semi-implicitly using one-sided interpolation with the second-order accuracy. At each step, the unconditionally unique solvability of the unsymmetric linear system of equations in the proposed method is proved with a detailed discussion on the condition number. Numerically, the second-order accuracy in both time and space is verified. Using the proposed method, the inertial effect of ferromagnetics is observed in micromagnetics simulations at small timescales, in consistency with the hyperbolic property of the model at sub-picoseconds. For long time simulations, the results of the iLLG model are in nice agreements with those of the LLG model, in consistency with the parabolic feature of the iLLG model at larger timescales.

math.NA↗

arXiv2021

FaaSNet: Scalable and Fast Provisioning of Custom Serverless Container Runtimes at Alibaba Cloud Function Compute

Serverless computing, or Function-as-a-Service (FaaS), enables a new way of building and scaling applications by allowing users to deploy fine-grained functions while providing fully-managed resource provisioning and auto-scaling. Custom FaaS container support is gaining traction as it enables better control over OSes, versioning, and tooling for modernizing FaaS applications. However, providing rapid container provisioning introduces non-trivial challenges for FaaS providers, since container provisioning is costly, and real-world FaaS workloads exhibit highly dynamic patterns. In this paper, we design FaaSNet, a highly-scalable middleware system for accelerating FaaS container provisioning. FaaSNet is driven by the workload and infrastructure requirements of the FaaS platform at one of the world's largest cloud providers, Alibaba Cloud Function Compute. FaaSNet enables scalable container provisioning via a lightweight, adaptive function tree (FT) structure. FaaSNet uses an I/O efficient, on-demand fetching mechanism to further reduce provisioning costs at scale. We implement and integrate FaaSNet in Alibaba Cloud Function Compute. Evaluation results show that FaaSNet: (1) finishes provisioning 2500 function containers on 1000 virtual machines in 8.3 seconds, (2) scales 13.4x and 16.3x faster than Alibaba Cloud's current FaaS platform and a state-of-the-art P2P container registry (Kraken), respectively, and (3) sustains a bursty workload using 75.2% less time than an optimized baseline.

cs.DC↗

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

A Survey on Fundamental Limits of Integrated Sensing and Communication

The integrated sensing and communication (ISAC), in which the sensing and communication share the same frequency band and hardware, has emerged as a key technology in future wireless systems. Early works on ISAC have been focused on the design, analysis and optimization of practical ISAC technologies for various ISAC systems. While this line of works are necessary, it is equally important to study the fundamental limits of ISAC in order to understand the gap between the current state-of-the-art technologies and the performance limits, and provide useful insights and guidance for the development of better ISAC technologies that can approach the performance limits. In this paper, we aim to provide a comprehensive survey for the current research progress on the fundamental limits of ISAC. Particularly, we first propose a systematic classification method for both traditional radio sensing (such as radar sensing and wireless localization) and ISAC so that they can be naturally incorporated into a unified framework. Then we summarize the major performance metrics and bounds used in sensing, communications and ISAC, respectively. After that, we present the current research progresses on fundamental limits of each class of the traditional sensing and ISAC systems. Finally, the open problems and future research directions are discussed.

cs.IT↗

arXiv2021

A Gauss-Seidel projection method with the minimal number of updates for stray field in micromagnetic simulations

Magnetization dynamics in magnetic materials is often modeled by the Landau-Lifshitz equation, which is solved numerically in general. In micromagnetic simulations, the computational cost relies heavily on the time-marching scheme and the evaluation of stray field. Explicit marching schemes are efficient but suffer from severe stability constraints, while nonlinear systems of equations have to be solved in implicit schemes though they are unconditionally stable. A better compromise between stability and efficiency is the semi-implicit scheme, such as the Gauss-Seidel projection method (GSPM) and the second-order backward differentiation formula scheme (BDF2). At each marching step, GSPM solves several linear systems of equations with constant coefficients and updates the stray field several times, while BDF2 updates the stray field only once but solves a larger linear system of equations with variable coefficients and a nonsymmetric structure. In this work, we propose a new method, dubbed as GSPM-BDF2, by combing the advantages of both GSPM and BDF2. Like GSPM, this method is first-order accurate in time and second-order accurate in space, and is unconditionally stable with respect to the damping parameter. However, GSPM-BDF2 updates the stray field only once per time step, leading to an efficiency improvement of about $60\%$ than the state-of-the-art GSPM for micromagnetic simulations. For Standard Problem \#4 and \#5 from National Institute of Standards and Technology, GSPM-BDF2 reduces the computational time over the popular software OOMMF by $82\%$ and $96\%$, respectively. Thus, the proposed method provides a more efficient choice for micromagnetic simulations.

math.NA↗

arXiv2020

Enforcing exact boundary and initial conditions in the deep mixed residual method

In theory, boundary and initial conditions are important for the wellposedness of partial differential equations (PDEs). Numerically, these conditions can be enforced exactly in classical numerical methods, such as finite difference method and finite element method. Recent years have witnessed growing interests in solving PDEs by deep neural networks (DNNs), especially in the high-dimensional case. However, in the generic situation, a careful literature review shows that boundary conditions cannot be enforced exactly for DNNs, which inevitably leads to a modeling error. In this work, based on the recently developed deep mixed residual method (MIM), we demonstrate how to make DNNs satisfy boundary and initial conditions automatically in a systematic manner. As a consequence, the loss function in MIM is free of the penalty term and does not have any modeling error. Using numerous examples, including Dirichlet, Neumann, mixed, Robin, and periodic boundary conditions for elliptic equations, and initial conditions for parabolic and hyperbolic equations, we show that enforcing exact boundary and initial conditions not only provides a better approximate solution but also facilitates the training process.

math.NA↗

arXiv2020

A comparison study of deep Galerkin method and deep Ritz method for elliptic problems with different boundary conditions

Recent years have witnessed growing interests in solving partial differential equations by deep neural networks, especially in the high-dimensional case. Unlike classical numerical methods, such as finite difference method and finite element method, the enforcement of boundary conditions in deep neural networks is highly nontrivial. One general strategy is to use the penalty method. In the work, we conduct a comparison study for elliptic problems with four different boundary conditions, i.e., Dirichlet, Neumann, Robin, and periodic boundary conditions, using two representative methods: deep Galerkin method and deep Ritz method. In the former, the PDE residual is minimized in the least-squares sense while the corresponding variational problem is minimized in the latter. Therefore, it is reasonably expected that deep Galerkin method works better for smooth solutions while deep Ritz method works better for low-regularity solutions. However, by a number of examples, we observe that deep Ritz method can outperform deep Galerkin method with a clear dependence of dimensionality even for smooth solutions and deep Galerkin method can also outperform deep Ritz method for low-regularity solutions. Besides, in some cases, when the boundary condition can be implemented in an exact manner, we find that such a strategy not only provides a better approximate solution but also facilitates the training process.

math.NA↗

arXiv2019

Quasi-Monte Carlo sampling for machine-learning partial differential equations

Solving partial differential equations in high dimensions by deep neural network has brought significant attentions in recent years. In many scenarios, the loss function is defined as an integral over a high-dimensional domain. Monte-Carlo method, together with the deep neural network, is used to overcome the curse of dimensionality, while classical methods fail. Often, a deep neural network outperforms classical numerical methods in terms of both accuracy and efficiency. In this paper, we propose to use quasi-Monte Carlo sampling, instead of Monte-Carlo method to approximate the loss function. To demonstrate the idea, we conduct numerical experiments in the framework of deep Ritz method proposed by Weinan E and Bing Yu. For the same accuracy requirement, it is observed that quasi-Monte Carlo sampling reduces the size of training data set by more than two orders of magnitude compared to that of MC method. Under some assumptions, we prove that quasi-Monte Carlo sampling together with the deep neural network generates a convergent series with rate proportional to the approximation accuracy of quasi-Monte Carlo method for numerical integration. Numerically the fitted convergence rate is a bit smaller, but the proposed approach always outperforms Monte Carlo method. It is worth mentioning that the convergence analysis is generic whenever a loss function is approximated by the quasi-Monte Carlo method, although observations here are based on deep Ritz method.

math.NA↗

arXiv2019

Numerical methods for antiferromagnetics

Compared with ferromagnetic counterparts, antiferromagnetic materials are considered as the future of spintronic applications since these materials are robust against the magnetic perturbation, produce no stray field, and display ultrafast dynamics. There are (at least) two sets of magnetic moments in antiferromagnets (with magnetization of the same magnitude but antiparallel directions) and ferrimagnets (with magnetization of the different magnitude). The coupled dynamics for the bipartite collinear antiferromagnets is modeled by a coupled system of Landau-Lifshitz-Gilbert equations with an additional term originated from the antiferromagnetic exchange, which leads to femtosecond magnetization dynamics. In this paper, we develop three Gauss-Seidel projection methods for micromagnetics simulation in antiferromagnets and ferrimagnets. They are first-order accurate in time and second-order in space, and only solve linear systems of equations with constant coefficients at each step. Femtosecond dynamics, Néel wall structure, and phase transition in presence of an external magnetic field for antiferromagnets are provided with the femtosecond stepsize.

cs.CE↗

arXiv2019

Two improved Gauss-Seidel projection methods for Landau-Lifshitz-Gilbert equation

In this paper, we present two improved Gauss-Seidel projection methods with unconditional stability. The first method updates the gyromagnetic term and the damping term simultaneously and follows by a projection step. The second method introduces two sets of approximate solutions, where we update the gyromagnetic term and the damping term simultaneously for one set of approximate solutions and apply the projection step to the other set of approximate solutions in an alternating manner. Compared to the original Gauss-Seidel projection method which has to solve heat equations $7$ times at each time step, the improved methods solve heat equations $5$ times and $3$ times, respectively. First-order accuracy in time and second-order accuracy in space are verified by examples in both 1D and 3D. In addition, unconditional stability with respect to both the grid size and the damping parameter is confirmed numerically. Application of both methods to a realistic material is also presented with hysteresis loops and magnetization profiles. Compared with the original method, the recorded running times suggest that savings of both methods are about $2/7$ and $4/7$ for the same accuracy requirement, respectively.

math.NA↗

arXiv2018

A lattice Boltzmann model for two-phase flow in porous media

In this paper, a lattice Boltzmann (LB) model with double distribution functions is proposed for two-phase flow in porous media where one distribution function is used for pressure governed by the Poisson equation, and the other is applied for saturation evolution described by the convection-diffusion equation with a source term. We first performed a Chapman-Enskog analysis, and show that the macroscopic nonlinear equations for pressure and saturation can be recovered correctly from present LB model. Then in the framework of LB method, we develop a local scheme for pressure gradient or equivalently velocity, which may be more efficient than the nonlocal second-order finite-difference schemes. We also perform some numerical simulations, and the results show that the developed LB model and local scheme for velocity are accurate and also have a second-order convergence rate in space. Finally, compared to the available pore-scale LB models for two-phase flow in porous media, the present LB model has more potential in the study of the large-scale problems.

physics.comp-ph↗

arXiv2014

A FETI-DP preconditioner of discontinuous Galerkin method for multiscale problems in high constrast media

In this paper we consider second order elliptic partial differential equations with highly varying (heterogeneous) coefficients on a two-dimensional region. The problems are discretized by a composite finite element (FE) and discontinuous Galerkin (DG) Method. The fine grids are in general nonmatching across the subdomain boundaries, and the subdomain partitioning does not need to resolve the jumps in the coefficient. A FETI-DP preconditioner is proposed and analyzed to solve the resulting linear system. Numerical results are presented to support our theory.

math.NA↗