arXiv subjects

Zhi Zhou

Publications and source records attributed to Zhi Zhou.

At least 145 records · Page 8Linked to original sources

arXiv2021

Deep Reinforcement Learning with Spatio-temporal Traffic Forecasting for Data-Driven Base Station Sleep Control

To meet the ever increasing mobile traffic demand in 5G era, base stations (BSs) have been densely deployed in radio access networks (RANs) to increase the network coverage and capacity. However, as the high density of BSs is designed to accommodate peak traffic, it would consume an unnecessarily large amount of energy if BSs are on during off-peak time. To save the energy consumption of cellular networks, an effective way is to deactivate some idle base stations that do not serve any traffic demand. In this paper, we develop a traffic-aware dynamic BS sleep control framework, named DeepBSC, which presents a novel data-driven learning approach to determine the BS active/sleep modes while meeting lower energy consumption and satisfactory Quality of Service (QoS) requirements. Specifically, the traffic demands are predicted by the proposed GS-STN model, which leverages the geographical and semantic spatial-temporal correlations of mobile traffic. With accurate mobile traffic forecasting, the BS sleep control problem is cast as a Markov Decision Process that is solved by Actor-Critic reinforcement learning methods. To reduce the variance of cost estimation in the dynamic environment, we propose a benchmark transformation method that provides robust performance indicator for policy update. To expedite the training process, we adopt a Deep Deterministic Policy Gradient (DDPG) approach, together with an explorer network, which can strengthen the exploration further. Extensive experiments with a real-world dataset corroborate that our proposed framework significantly outperforms the existing methods.

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arXiv2021

Numerical Estimation of a Diffusion Coefficient in Subdiffusion

In this work, we consider the numerical recovery of a spatially dependent diffusion coefficient in a subdiffusion model from distributed observations. The subdiffusion model involves a Caputo fractional derivative of order $α\in(0,1)$ in time. The numerical estimation is based on the regularized output least-squares formulation, with an $H^1(Ω)$ penalty. We prove the well-posedness of the continuous formulation, e.g., existence and stability. Next, we develop a fully discrete scheme based on the Galerkin finite element method in space and backward Euler convolution quadrature in time. We prove the subsequential convergence of the sequence of discrete solutions to a solution of the continuous problem as the discretization parameters (mesh size and time step size) tend to zero. Further, under an additional regularity condition on the exact coefficient, we derive convergence rates in a weighted $L^2(Ω)$ norm for the discrete approximations to the exact coefficient {in the one- and two-dimensional cases}. The analysis relies heavily on suitable nonstandard nonsmooth data error estimates for the direct problem. We provide illustrative numerical results to support the theoretical study.

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arXiv2020

FedHome: Cloud-Edge based Personalized Federated Learning for In-Home Health Monitoring

In-home health monitoring has attracted great attention for the ageing population worldwide. With the abundant user health data accessed by Internet of Things (IoT) devices and recent development in machine learning, smart healthcare has seen many successful stories. However, existing approaches for in-home health monitoring do not pay sufficient attention to user data privacy and thus are far from being ready for large-scale practical deployment. In this paper, we propose FedHome, a novel cloud-edge based federated learning framework for in-home health monitoring, which learns a shared global model in the cloud from multiple homes at the network edges and achieves data privacy protection by keeping user data locally. To cope with the imbalanced and non-IID distribution inherent in user's monitoring data, we design a generative convolutional autoencoder (GCAE), which aims to achieve accurate and personalized health monitoring by refining the model with a generated class-balanced dataset from user's personal data. Besides, GCAE is lightweight to transfer between the cloud and edges, which is useful to reduce the communication cost of federated learning in FedHome. Extensive experiments based on realistic human activity recognition data traces corroborate that FedHome significantly outperforms existing widely-adopted methods.

cs.NI↗

arXiv2020

CoEdge: Cooperative DNN Inference with Adaptive Workload Partitioning over Heterogeneous Edge Devices

Recent advances in artificial intelligence have driven increasing intelligent applications at the network edge, such as smart home, smart factory, and smart city. To deploy computationally intensive Deep Neural Networks (DNNs) on resource-constrained edge devices, traditional approaches have relied on either offloading workload to the remote cloud or optimizing computation at the end device locally. However, the cloud-assisted approaches suffer from the unreliable and delay-significant wide-area network, and the local computing approaches are limited by the constrained computing capability. Towards high-performance edge intelligence, the cooperative execution mechanism offers a new paradigm, which has attracted growing research interest recently. In this paper, we propose CoEdge, a distributed DNN computing system that orchestrates cooperative DNN inference over heterogeneous edge devices. CoEdge utilizes available computation and communication resources at the edge and dynamically partitions the DNN inference workload adaptive to devices' computing capabilities and network conditions. Experimental evaluations based on a realistic prototype show that CoEdge outperforms status-quo approaches in saving energy with close inference latency, achieving up to 25.5%~66.9% energy reduction for four widely-adopted CNN models.

cs.NI↗

arXiv2020

Battery Asset Management with Cycle Life Prognosis

Battery Asset Management problem determines the minimum cost replacement schedules for each individual asset in a group of battery assets that operate in parallel. Battery cycle life varies under different operating conditions including temperature, depth of discharge, charge rate, etc., and a battery deteriorates due to usage, which cannot be handled by current asset management models. This paper presents battery cycle life prognosis and its integration with parallel asset management to reduce lifecycle cost of the Battery Energy Storage System (BESS). A nonlinear capacity fade model is incorporated in the parallel asset management model to update battery capacity. Parametric studies have been conducted to explore the influence of different model inputs (e.g. usage rate, unit battery capacity, operating condition and periodical demand) for a five-year time horizon. Experiment results verify the reasonableness of this new framework and suggest that the increase in battery lifetime leads to decrease in lifecycle cost.

eess.SY↗

arXiv2020

Data-Driven Stochastic Optimization for Power Grids Scheduling under High Wind Penetration

To address the environmental concern and improve the economic efficiency, the wind power is rapidly integrated into smart grids. However, the inherent uncertainty of wind energy raises operational challenges. To ensure the cost-efficient, reliable and robust operation, it is critically important to find the optimal decision that can correctly and rigorously hedge against all sources of uncertainty. In this paper, we propose data-driven stochastic unit commitment (SUC) to guide the power grids scheduling. Specifically, given the finite historical data, the posterior predictive distribution is developed to quantify the wind power prediction uncertainty accounting for both inherent stochastic uncertainty of wind power generation and input model estimation error. For complex power grid systems, a finite number of scenarios is used to estimate the expected cost in the planning horizon. To further control the impact of finite sampling error induced by using the sample average approximation (SAA), we propose a parallel computing based optimization solution methodology, which can quickly find the reliable optimal unit commitment decision hedging against various sources of uncertainty. The empirical study over six-bus and 118-bus systems demonstrates that our approach can provide more efficient and robust performance than the existing deterministic and stochastic unit commitment approaches.

eess.SY↗

arXiv2020

Backward difference formula: The energy technique for subdiffusion equation

Based on the equivalence of A-stability and G-stability, the energy technique of the six-step BDF method for the heat equation has been discussed in [Akrivis, Chen, Yu, Zhou, Math. Comp., Revised]. Unfortunately, this theory is hard to extend the time-fractional PDEs. In this work, we consider three types of subdiffusion models, namely single-term, multi-term and distributed order fractional diffusion equations. We present a novel and concise stability analysis of time stepping schemes generated by $k$-step backward difference formula (BDF$k$), for approximately solving the subdiffusion equation. The analysis mainly relies on the energy technique by applying Grenander-Szegö theorem. This kind of argument has been widely used to confirm the stability of various $A$-stable schemes (e.g., $k=1,2$). However, it is not an easy task for the higher-order BDF methods, due to the loss the $A$-stability. The core object of this paper is to fill in this gap.

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arXiv2020

Arbitrarily high-order exponential cut-off methods for preserving maximum principle of parabolic equations

A new class of high-order maximum principle preserving numerical methods is proposed for solving parabolic equations, with application to the semilinear Allen--Cahn equation. The proposed method consists of a $k$th-order multistep exponential integrator in time, and a lumped mass finite element method in space with piecewise $r$th-order polynomials and Gauss--Lobatto quadrature. At every time level, the extra values violating the maximum principle are eliminated at the finite element nodal points by a cut-off operation. The remaining values at the nodal points satisfy the maximum principle and are proved to be convergent with an error bound of $O(τ^k+h^r)$. The accuracy can be made arbitrarily high-order by choosing large $k$ and $r$. Extensive numerical results are provided to illustrate the accuracy of the proposed method and the effectiveness in capturing the pattern of phase-field problems.

math.NA↗

arXiv2020

Error Analysis of Finite Element Approximations of Diffusion Coefficient Identification for Elliptic and Parabolic Problems

In this work, we present a novel error analysis for recovering a spatially dependent diffusion coefficient in an elliptic or parabolic problem. It is based on the standard regularized output least-squares formulation with an $H^1(Ω)$ seminorm penalty, and then discretized using the Galerkin finite element method with conforming piecewise linear finite elements for both state and coefficient, and backward Euler in time in the parabolic case. We derive \textit{a priori} weighted $L^2(Ω)$ estimates where the constants depend only on the given problem data for both elliptic and parabolic cases. Further, these estimates also allow deriving standard $L^2(Ω)$ error estimates, under a positivity condition that can be verified for certain problem data. Numerical experiments are provided to complement the error analysis.

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arXiv2020

When Deep Reinforcement Learning Meets Federated Learning: Intelligent Multi-Timescale Resource Management for Multi-access Edge Computing in 5G Ultra Dense Network

Ultra-dense edge computing (UDEC) has great potential, especially in the 5G era, but it still faces challenges in its current solutions, such as the lack of: i) efficient utilization of multiple 5G resources (e.g., computation, communication, storage and service resources); ii) low overhead offloading decision making and resource allocation strategies; and iii) privacy and security protection schemes. Thus, we first propose an intelligent ultra-dense edge computing (I-UDEC) framework, which integrates blockchain and Artificial Intelligence (AI) into 5G ultra-dense edge computing networks. First, we show the architecture of the framework. Then, in order to achieve real-time and low overhead computation offloading decisions and resource allocation strategies, we design a novel two-timescale deep reinforcement learning (\textit{2Ts-DRL}) approach, consisting of a fast-timescale and a slow-timescale learning process, respectively. The primary objective is to minimize the total offloading delay and network resource usage by jointly optimizing computation offloading, resource allocation and service caching placement. We also leverage federated learning (FL) to train the \textit{2Ts-DRL} model in a distributed manner, aiming to protect the edge devices' data privacy. Simulation results corroborate the effectiveness of both the \textit{2Ts-DRL} and FL in the I-UDEC framework and prove that our proposed algorithm can reduce task execution time up to 31.87%.

cs.NI↗

arXiv2020

An Inverse Potential Problem for Subdiffusion: Stability and Reconstruction

In this work, we study the inverse problem of recovering a potential coefficient in the subdiffusion model, which involves a Djrbashian-Caputo derivative of order $α\in(0,1)$ in time, from the terminal data. We prove that the inverse problem is locally Lipschitz for small terminal time, under certain conditions on the initial data. This result extends the result in Choulli and Yamamoto (1997) for the standard parabolic case to the fractional case. The analysis relies on refined properties of two-parameter Mittag-Leffler functions, e.g., complete monotonicity and asymptotics. Further, we develop an efficient and easy-to-implement algorithm for numerically recovering the coefficient based on (preconditioned) fixed point iteration and Anderson acceleration. The efficiency and accuracy of the algorithm is illustrated with several numerical examples.

math.NA↗

arXiv2020

Numerical Analysis of Backward Subdiffusion Problems

The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time with order $α\in(0,1)$. After using quasi-boundary value method to regularize the "mildly" ill-posed problem, we propose a fully discrete scheme by applying finite element method (FEM) in space and convolution quadrature (CQ) in time. We provide a thorough error analysis of the resulting discrete system in both cases of smooth and nonsmooth data. The analysis relies heavily on smoothing properties of (discrete) solution operators, and nonstandard error estimate for the direct problem in terms of problem data regularity. The theoretical results are useful to balance discretization parameters, regularization parameter and noise level. Numerical examples are presented to illustrate the theoretical results.

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arXiv2020

The energy technique for the six-step BDF method

In combination with the Grenander--Szegö theorem, we observe that a relaxed positivity condition on multipliers, milder than the basic %fundamental requirement of the Nevanlinna--Odeh multipliers that the sum of the absolute values of their components is strictly less than $1$, makes the energy technique applicable to the stability analysis of BDF methods for parabolic equations with selfadjoint elliptic part. This is particularly useful for the six-step BDF method for which no Nevanlinna--Odeh multiplier exists. We introduce multipliers satisfying the positivity property for the six-step BDF method and establish stability of the method for parabolic equations.

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arXiv2020

Leveraging the Power of Prediction: Predictive Service Placement for Latency-Sensitive Mobile Edge Computing

Mobile edge computing (MEC) is emerging to support delay-sensitive 5G applications at the edge of mobile networks. When a user moves erratically among multiple MEC nodes, the challenge of how to dynamically migrate its service to maintain service performance (i.e., user-perceived latency) arises. However, frequent service migration can significantly increase operational cost, incurring the conflict between improving performance and reducing cost. To address these mis-aligned objectives, this paper studies the performance optimization of mobile edge service placement under the constraint of long-term cost budget. It is challenging because the budget involves the future uncertain information (e.g., user mobility). To overcome this difficulty, we devote to leveraging the power of prediction and advocate predictive service placement with predicted near-future information. By using two-timescale Lyapunov optimization method, we propose a T-slot predictive service placement (PSP) algorithm to incorporate the prediction of user mobility based on a frame-based design. We characterize the performance bounds of PSP in terms of cost-delay trade-off theoretically. Furthermore, we propose a new weight adjustment scheme for the queue in each frame named PSP-WU to exploit the historical queue information, which greatly reduces the length of queue while improving the quality of user-perceived latency. Rigorous theoretical analysis and extensive evaluations using realistic data traces demonstrate the superior performance of the proposed predictive schemes.

cs.NI↗

arXiv2020

Incomplete Iterative Solution of the Subdiffusion Problem

In this work, we develop an efficient incomplete iterative scheme for the numerical solution of the subdiffusion model involving a Caputo derivative of order $α\in(0,1)$ in time. It is based on piecewise linear Galerkin finite element method in space and backward Euler convolution quadrature in time and solves one linear algebraic system inexactly by an iterative algorithm at each time step. We present theoretical results for both smooth and nonsmooth solutions, using novel weighted estimates of the time-stepping scheme. The analysis indicates that with the number of iterations at each time level chosen properly, the error estimates are nearly identical with that for the exact linear solver, and the theoretical findings provide guidelines on the choice. Illustrative numerical results are presented to complement the theoretical analysis.

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arXiv2020

HFEL: Joint Edge Association and Resource Allocation for Cost-Efficient Hierarchical Federated Edge Learning

Federated Learning (FL) has been proposed as an appealing approach to handle data privacy issue of mobile devices compared to conventional machine learning at the remote cloud with raw user data uploading. By leveraging edge servers as intermediaries to perform partial model aggregation in proximity and relieve core network transmission overhead, it enables great potentials in low-latency and energy-efficient FL. Hence we introduce a novel Hierarchical Federated Edge Learning (HFEL) framework in which model aggregation is partially migrated to edge servers from the cloud. We further formulate a joint computation and communication resource allocation and edge association problem for device users under HFEL framework to achieve global cost minimization. To solve the problem, we propose an efficient resource scheduling algorithm in the HFEL framework. It can be decomposed into two subproblems: \emph{resource allocation} given a scheduled set of devices for each edge server and \emph{edge association} of device users across all the edge servers. With the optimal policy of the convex resource allocation subproblem for a set of devices under a single edge server, an efficient edge association strategy can be achieved through iterative global cost reduction adjustment process, which is shown to converge to a stable system point. Extensive performance evaluations demonstrate that our HFEL framework outperforms the proposed benchmarks in global cost saving and achieves better training performance compared to conventional federated learning.

cs.DC↗

arXiv2020

Subdiffusion with Time-Dependent Coefficients: Improved Regularity and Second-Order Time Stepping

This article concerns second-order time discretization of subdiffusion equations with time-dependent diffusion coefficients. High-order differentiability and regularity estimates are established for subdiffusion equations with time-dependent coefficients. Using these regularity results and a perturbation argument of freezing the diffusion coefficient, we prove that the convolution quadrature generated by the second-order backward differentiation formula, with proper correction at the first time step, can achieve second-order convergence for both nonsmooth initial data and incompatible source term. Numerical experiments are consistent with the theoretical results.

math.NA↗

arXiv2020

Numerical methods for nonlocal and fractional models

Partial differential equations (PDEs) are used, with huge success, to model phenomena arising across all scientific and engineering disciplines. However, across an equally wide swath, there exist situations in which PDE models fail to adequately model observed phenomena or are not the best available model for that purpose. On the other hand, in many situations, nonlocal models that account for interaction occurring at a distance have been shown to more faithfully and effectively model observed phenomena that involve possible singularities and other anomalies. In this article, we consider a generic nonlocal model, beginning with a short review of its definition, the properties of its solution, its mathematical analysis, and specific concrete examples. We then provide extensive discussions about numerical methods, including finite element, finite difference, and spectral methods, for determining approximate solutions of the nonlocal models considered. In that discussion, we pay particular attention to a special class of nonlocal models that are the most widely studied in the literature, namely those involving fractional derivatives. The article ends with brief considerations of several modeling and algorithmic extensions which serve to show the wide applicability of nonlocal modeling.

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