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Optimal-rate error estimates and a twice decoupled solver for a backward Euler finite element scheme of the Doyle-Fuller-Newman model of lithium-ion batteries

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arXiv 2024年

作者： Xu, Shu Cao, Liqun School of Mathematical Sciences Peking University Beijing100871 China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China State Key Laboratory of Scientific and Engineering Computing Beijing100190 China National Center for Mathematics and Interdisciplinary Sciences Chinese Academy of Sciences Beijing100190 China

We investigate the convergence of a backward Euler finite element discretization applied to a multi-domain and multi-scale elliptic-parabolic system, derived from the Doyle-Fuller-Newman model for lithium-ion batteries. We establish optimal-order error estimates for the solution in the norms l2(H1) and l2(L2(Hrq)), q = 0,1. To improve computational efficiency, we propose a novel solver that accelerates the solution process and controls memory usage. Numerical experiments with realistic battery parameters validate the theoretical error rates and demonstrate the significantly superior performance of the proposed solver over existing solvers. Copyright © 2024, The Authors. All rights reserved.

关键词： Computational efficiency

Adam-family methods for nonsmooth optimization with convergence guarantees

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The Journal of Machine Learning Research

The Journal of Machine Learning Research 2024年第1期25卷 2398-2450页

作者： Nachuan Xiao Xiaoyin Hu Xin Liu Kim-Chuan Toh Institute of Operations Research and Analytics National University of Singapore Singapore School of Computer and Computing Science Hangzhou City University Hangzhou China State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Department of Mathematics and Institute of Operations Research and Analytics National University of Singapore Singapore

In this paper, we present a comprehensive study on the convergence properties of Adam-family methods for nonsmooth optimization, especially in the training of nonsmooth neural networks. We introduce a novel two-timescale framework that adopts a two-timescale updating scheme, and prove its convergence properties under mild assumptions. Our proposed framework encompasses various popular Adam-family methods, providing convergence guarantees for these methods in training nonsmooth neural networks. Furthermore, we develop stochastic subgradient methods that incorporate gradient clipping techniques for training nonsmooth neural networks with heavy-tailed noise. Through our framework, we show that our proposed methods converge even when the evaluation noises are only assumed to be integrable. Extensive numerical experiments demonstrate the high efficiency and robustness of our proposed methods.

关键词： nonsmooth optimization stochastic subgradient methods Adam nonconvex optimization gradient clipping

Blockchain-Assisted Privacy-Preserving and Synchronized key Agreement for VDTNs

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IEEE Transactions on Dependable and Secure computing 2025年

作者： Wang, Chenhao Ming, Yang Liu, Hang Feng, Jie Yang, Mengmeng Xiang, Yang Chang'an University School of Information Engineering Xi'an710064 China Xidian University State Key Laboratory of Integrated Service Networks Xi'an710071 China Commonwealth Scientific and Industrial Research Organization Australia Swinburne University of Technology Department of Computing Technologies VIC3122 Australia

With the continuous development of digitization evolutions, vehicular digital twin networks (VDTNs) facilitate traffic data and optimization results to be exchanged between the vehicle and digital twin as well as shared among a group of digital twins. However, the data exchange and group sharing processes take place in real-time over public communication channels, which suffer from various security and privacy threats. key agreement technologies are promising to enable secure data communications for entities, but the existing key agreement schemes generally fail to fulfill the requirements of synchronization, privacy, and entity management for VDTNs. Therefore, we propose a blockchain-assisted privacy-preserving and synchronized key agreement scheme for VDTNs. In the proposed scheme, the anonymous vehicle and digital twin can negotiate a secret session key in the case of synchronization to achieve secure data exchange. Meanwhile, digital twins are capable of utilizing synchronized state information to dynamically establish a common group encryption key but hold individual decryption keys, which guarantee the security of group sharing. Additionally, the proposed scheme is able to protect identity privacy and manage vehicles and digital twins with the assistance of blockchain and smart contract. The security analysis demonstrates that the proposed scheme provides security and privacy assurances for VDTNs. The performance evaluation indicates that it has excellent expressions in terms of efficiency, practicality, and smart contract consumption. © 2004-2012 IEEE.

关键词： Differential privacy

An Efficient Benders Decomposition Approach for Optimal Large-Scale Network Slicing

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arXiv 2023年

作者： Chen, Wei-Kun Wu, Zheyu Zhang, Rui-Jin Liu, Ya-Feng Dai, Yu-Hong Luo, Zhi-Quan The School of Mathematics and Statistics Beijing Key Laboratory on MCAACI Beijing Institute of Technology Beijing100081 China The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The Shenzhen Research Institute of Big Data The Chinese University of Hong Kong Shenzhen518172 China

This paper considers the network slicing (NS) problem which attempts to map multiple customized virtual network requests to a common shared network infrastructure and allocate network resources to meet diverse service requirements. This paper proposes an efficient customized Benders decomposition algorithm for globally solving the large-scale NP-hard NS problem. The proposed algorithm decomposes the hard NS problem into two relatively easy function placement (FP) and traffic routing (TR) subproblems and iteratively solves them enabling the information feedback between each other, which makes it particularly suitable to solve large-scale problems. Specifically, the FP subproblem is to place service functions into cloud nodes in the network, and solving it can return a function placement strategy based on which the TR subproblem is defined;and the TR subproblem is to find paths connecting two nodes hosting two adjacent functions in the network, and solving it can either verify that the solution of the FP subproblem is an optimal solution of the original problem, or return a valid inequality to the FP subproblem that cuts off the current infeasible solution. The proposed algorithm is guaranteed to find the globally optimal solution of the NS problem. By taking the special structure of the NS problem into consideration, we successfully develop two families of valid inequalities that render the proposed algorithm converge much more quickly and thus much more efficient. Numerical results demonstrate that the proposed valid inequalities effectively accelerate the convergence of the decomposition algorithm, and the proposed algorithm significantly outperforms the existing algorithms in terms of both solution efficiency and quality. Copyright © 2023, The Authors. All rights reserved.

关键词： Resource allocation

Efficient Global Algorithms for Transmit Beamforming Design in ISAC Systems

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arXiv 2024年

作者： Wu, Jiageng Wang, Zhiguo Liu, Ya-Feng Liu, Fan The School of Mathematics Jilin University Changchun130012 China The College of Mathematics Sichuan University Sichuan Chengdu610064 China The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The Department of Electrical and Electronic Engineering Southern University of Science and Technology Shenzhen518055 China

In this paper, we propose a multi-input multi-output transmit beamforming optimization model for joint radar sensing and multi-user communications, where the design of the beamformers is formulated as an optimization problem whose objective is a weighted combination of the sum rate and the Cramér-Rao bound, subject to the transmit power budget. Obtaining the global solution for the formulated nonconvex problem is a challenging task, since the sum-rate maximization problem itself (even without considering the sensing metric) is known to be NP-hard. The main contributions of this paper are threefold. Firstly, we derive an optimal closed-form solution to the formulated problem in the single-user case and the multi-user case where the channel vectors of different users are orthogonal. Secondly, for the general multi-user case, we propose a novel branch and bound (B&B) algorithm based on the McCormick envelope relaxation. The proposed algorithm is guaranteed to find the globally optimal solution to the formulated problem. Thirdly, we design a graph neural network (GNN) based pruning policy to determine irrelevant nodes that can be directly pruned in the proposed B&B algorithm, thereby significantly reducing the number of unnecessary enumerations therein and improving its computational efficiency. Simulation results show the efficiency of the proposed vanilla and GNN-based accelerated B&B algorithms. Copyright © 2024, The Authors. All rights reserved.

关键词： Computational efficiency

On Underdamped Nesterov’s Acceleration

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arXiv 2023年

作者： Chen, Shuo Shi, Bin Yuan, Ya-Xiang State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China University of Chinese Academy of Sciences Beijing100049 China

The high-resolution differential equation framework has been proven to be tailor-made for Nesterov’s accelerated gradient descent method (NAG) and its proximal correspondence — the class of faster iterative shrinkage thresholding algorithms (FISTA). However, the systems of theories is not still complete, since the underdamped case (r γ or the iteration kγ in the mixed term. When the momentum parameter r is 2, the new Lyapunov functions are identical to the previous ones. These new proofs do not only include the convergence rate of the objective value previously obtained according to the low-resolution differential equation framework but also characterize the convergence rate of the minimal gradient norm square. All the convergence rates obtained for the underdamped case are continuously dependent on the parameter r. In addition, it is observed that the high-resolution differential equation approximately simulates the convergence behavior of NAG for the critical case r = −1, while the low-resolution differential equation degenerates to the conservative Newton’s equation. The high-resolution differential equation framework also theoretically characterizes the convergence rates, which are consistent with that obtained for the underdamped case with r = −1. © 2023, CC BY-SA.

关键词： Differential equations

A RIEMANNIAN EXPONENTIAL AUGMENTED LAGRANGIAN METHOD FOR computing THE PROJECTION ROBUST WASSERSTEIN DISTANCE

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arXiv 2022年

作者： Jiang, Bo Liu, Ya-Feng Key Laboratory for NSLSCS of Jiangsu Province School of Mathematical Sciences Nanjing Normal University Nanjing China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

Projecting the distance measures onto a low-dimensional space is an efficient way of mitigating the curse of dimensionality in the classical Wasserstein distance using optimal transport. The obtained maximized distance is referred to as projection robust Wasserstein (PRW) distance. In this paper, we equivalently reformulate the computation of the PRW distance as an optimization problem over the Cartesian product of the Stiefel manifold and the Euclidean space with additional nonlinear inequality constraints. We propose a Riemannian exponential augmented Lagrangian method (ReALM) with a global convergence guarantee to solve this problem. Compared with the existing approaches, ReALM can potentially avoid too small penalty parameters. Moreover, we propose a framework of inexact Riemannian gradient descent methods to solve the subproblems in ReALM efficiently. In particular, by using the special structure of the subproblem, we give a practical algorithm named as the inexact Riemannian Barzilai-Borwein method with Sinkhorn iteration (iRBBS). The remarkable features of iRBBS lie in that it performs a flexible number of Sinkhorn iterations to compute an inexact gradient with respect to the projection matrix of the problem and adopts the Barzilai-Borwein stepsize based on the inexact gradient information to improve the performance. We show that iRBBS can return an ǫ-stationary point of the original PRW distance problem within O(ǫ−3) iterations. Extensive numerical results on synthetic and real datasets demonstrate that our proposed ReALM as well as iRBBS outperform the state-of-the-art solvers for computing the PRW *** Codes 65K10, 90C26, 90C47 Copyright © 2022, The Authors. All rights reserved.

关键词： Constrained optimization

ASYMPTOTICS OF LARGE DEVIATIONS OF FINITE DIFFERENCE METHOD FOR STOCHASTIC CAHN-HILLIARD EQUATION

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arXiv 2023年

作者： Jin, Diancong Sheng, Derui School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

In this work, we establish the Freidlin-Wentzell large deviations principle (LDP) of the stochastic Cahn-Hilliard equation with small noise, which implies the one-point LDP. Further, we give the one-point LDP of the spatial finite difference method (FDM) for the stochastic Cahn-Hilliard equation. Our main result is the convergence of the one-point large deviations rate function (LDRF) of the spatial FDM, which is about the asymptotical limit of a parametric variational problem. The main idea for proving the convergence of the LDRF of the spatial FDM is via the Γ-convergence of objective functions, which relies on the qualitative analysis of skeleton equations of the original equation and the numerical method. In order to overcome the difficulty that the drift coefficient is not one-side Lipschitz, we use the equivalent characterization of the skeleton equation of the spatial FDM and the discrete interpolation inequality to obtain the uniform boundedness of the solution to the underlying skeleton equation. This plays an important role in deriving the Γ-convergence of objective functions. Copyright © 2023, The Authors. All rights reserved.

关键词： Finite difference method

Verify All Traffic: Towards Zero-Trust In-Network Intrusion Detection against Multipath Routing

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IEEE Journal on Selected Areas in Communications 2025年第6期43卷 2155-2171页

作者： Zhao, Ziming Li, Zhaoxuan Xie, Xiaofei Liu, Zhipeng Li, Tingting Yu, Jiongchi Zhang, Fan Chen, Binbin School of Software Technology Zhejiang University Ningbo315100 China College of Computer Science and Technology Zhejiang University Hangzhou310027 China ZJU-Hangzhou Global Scientific and Technological Innovation Center 311200 China Key Laboratory of Blockchain and Cyberspace Governance of Zhejiang Province 310027 China Jiaxing Research Institute Zhejiang University 314000 China Zhengzhou Xinda Institute of Advanced Technology Zhengzhou450001 China Singapore State Key Laboratory of Information Security Institute of Information Engineering Chinese Academy of Sciences Beijing100093 China School of Cyber Security UCAS Beijing100049 China School of Computing and Information Systems Singapore Management University Singapore188065 Singapore Advanced Digital Sciences Center Singapore138632 Singapore Singapore University of Technology and Design SingaporeB96049 Singapore

With the popularity of encryption protocols, machine learning (ML)-based traffic analysis technologies have attracted widespread attention. To adapt to modern high-speed bandwidth, recent research is dedicated to advancing zero-trust intrusion detection by offloading feature extraction and model inference into the network dataplane. Especially, with the rise of programmable switches, achieving line-speed ML inference becomes promising. However, existing research only considers a single switch node as a relay to conduct evaluation. This is far from real-world deployments involving multiple switches (given that zero-trust security assumes that threats can originate from anywhere, including within the network), particularly the multi-path routing phenomenon that exists in practice. In this paper, we reveal practical challenges in the context of enabling line-speed model inference in the network dataplane. Furthermore, we propose FCPlane, the forwarding and computing integrated dataplane for zero-trust intrusion detection that aims to enable efficient load balancing while providing reliable traffic analysis results, even against multipath routing. The core idea is to reconcile forwarding and computation to the flowlet level, for which a tailor-made Markov chain model is designed. Based on two public traffic datasets, we evaluate seven state-of-the-art in-network traffic analysis models deployed in four types of topologies (three with multipath routing and one without) to explore performance impact and demonstrate the effectiveness of our proposal. © 1983-2012 IEEE.

关键词： Network intrusion