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作者： Zhou, Hao Zhu, Hengliang Cui, Tao Pan, David Z. Zhou, Dian Zeng, Xuan State Key Laboratory of ASIC and Systems Department of Microelectronics Fudan University Shanghai200433 China State Key Laboratory of Scientific and Engineering Computing National Center for Mathematics and Interdisciplinary Sciences Institute of Computational Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China Department of Electrical and Computer Engineering University of Texas at Austin AustinTX78712 United States Department of Electrical Engineering University of Texas at Dallas RichardsonTX75080 United States

Thermomechanical stress is one of the most important issues in performance and reliability analysis of through silicon via-based 3-D integrated circuits (3-D ICs), where an accurate numerical approach is generally needed to produce stress models and identify weak points in the structure. In this paper, we propose a knowledge-oriented nonuniform (KONU) refinement strategy for 3-D IC stress simulation under the framework of a parallel adaptive finite element method (FEM), and apply it in 3-D IC stress and reliability analysis. Parallel adaptive FEM is promising for solving large-scale problems due to its high accuracy and parallel efficiency. It produces refined meshes based on the a posteriori error analysis, which has the quasi-optimal convergence rate for solving the problem. It has high parallel efficiency, which makes it suitable for handling large and complex structures in 3-D ICs. The KONU refinement strategy developed in this paper can efficiently reduce the number of refinement iterations in parallel adaptive FEM for 3-D IC thermomechanical stress simulation and improves the computational efficiency. It is demonstrated in this paper through several examples that parallel adaptive FEM for thermomechanical stress evaluation can be widely applied in 3-D IC reliability analysis, where accurate stress simulation and modeling is exceptionally important to produce accurate results. © 2018 IEEE.

关键词： Reliability analysis

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Vulnerability of quantum classification to adversarial perturbations

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Physical Review A 2020年第6期101卷 062331-062331页

作者： Nana Liu Peter Wittek Institute of Natural Sciences Shanghai Jiao Tong University Shanghai 200240 China Ministry of Education Key Laboratory in Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai 200240 China University of Michigan-Shanghai Jiao Tong University Joint Institute Shanghai 200240 China Rotman School of Management University of Toronto Toronto Canada M5S 3E6 Creative Destruction Lab Toronto Canada M5S 3E6 Vector Institute for Artificial Intelligence Toronto Canada M5G 1M1 Perimeter Institute for Theoretical Physics Waterloo Canada N2L 2Y5

High-dimensional quantum systems are vital for quantum technologies and are essential in demonstrating practical quantum advantage in quantum computing, simulation, and sensing. Since dimensionality grows exponentially with the number of qubits, the potential power of noisy intermediate-scale quantum devices over classical resources also stems from entangled states in high dimensions. An important family of quantum protocols that can take advantage of high-dimensional Hilbert space is classification tasks. These include quantum machine learning algorithms, witnesses in quantum information processing, and certain decision problems. However, due to counterintuitive geometrical properties emergent in high dimensions, classification problems are vulnerable to adversarial attacks. We demonstrate that the amount of perturbation needed for an adversary to induce a misclassification scales inversely with dimensionality. This is shown to be a fundamental feature independent of the details of the classification protocol. Furthermore, this leads to a tradeoff between the security of the classification algorithm against adversarial attacks and quantum advantages that we expect for high-dimensional problems. In fact, protection against these adversarial attacks requires extra resources that can even scale polynomially with the Hilbert space dimension of the system, which can erase any significant quantum advantage that we might expect from a quantum protocol. This has wide-ranging implications in the use of both near-term and future quantum technologies for classification.

关键词： Machine learning Quantum algorithms Quantum information processing Quantum protocols

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On the clean numerical simulation(CNS) of chaotic dynamic systems

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Journal of Hydrodynamics 2017年第5期29卷 729-747页

作者：廖世俊 State Key Laboratory of Ocean Engineering Shanghai Jiao Tong UniversityShanghai 200240China MOE Laboratory of Scientific and Engineering Computing Shanghai Jiao Tong UniversityShanghai 200240China School of Naval Architecture Ocean and Civil EngineeringShanghai Jiao Tong UniversityShanghai 200240China

According to Lorenz, chaotic dynamic systems have sensitive dependence on initial conditions（SDIC）, i.e., the butterfly-effect： a tiny difference on initial conditions might lead to huge difference of computer-generated simulations after a long time. Thus, computer-generated chaotic results given by traditional algorithms in double precision are a kind of mixture of ＂true＂（convergent） solution and numerical noises at the same level. Today, this defect can be overcome by means of the ＂clean numerical simulation＂（CNS） with negligible numerical noises in a long enough interval of time. The CNS is based on the Taylor series method at high enough order and data in the multiple precision with large enough number of digits, plus a convergence check using an additional simulation with even smaller numerical noises. In theory, convergent（reliable） chaotic solutions can be obtained in an arbitrary long（but finite） interval of time by means of the CNS. The CNS can reduce numerical noises to such a level even much smaller than micro-level uncertainty of physical quantities that propagation of these physical micro-level uncertainties can be precisely investigated. In this paper, we briefly introduce the basic ideas of the CNS, and its applications in long-term reliable simulations of Lorenz equation, three-body problem and Rayleigh-Bénard turbulent flows. Using the CNS, it is found that a chaotic three-body system with symmetry might disrupt without any external disturbance, say, its symmetry-breaking and system-disruption are ＂self-excited＂, i.e., out-of-nothing. In addition, by means of the CNS, we can provide a rigorous theoretical evidence that the micro-level thermal fluctuation is the origin of macroscopic randomness of turbulent flows. Naturally, much more precise than traditional algorithms in double precision, the CNS can provide us a new way to more accurately investigate chaotic dynamic systems.

关键词： Chaos reliable numerical simulation clean numerical simulation（CNS） three-body problem turbulence origin of randomness

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Structural stability of the transonic shock problem in a divergent three-dimensional axi-symmetric perturbed nozzle

arXiv

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arXiv 2019年

作者： Weng, Shangkun Xie, Chunjing Xin, Zhouping School OfMathematics and Statistics Wuhan University Wuhan Hubei Province430072 China School of Mathematical Sciences Institute of Natural Sciences Ministry of Education Key Laboratory of Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai200240 China Institute of Mathematical Sciences Chinese University of Hong Kong Shatin NT Hong Kong

In this paper, we investigate the structural stability of the transonic shock problem in an axisymmetric perturbed nozzle. The axisymmetric perturbation of supersonic incoming flow including the swirl velocity is also considered. We obtain the existence and uniqueness of the piecewise smooth transonic shock solution in a general 3D axisymmetric De Laval nozzle. Due to the singularity on the axis, a key issue is to find an invertible Lagrange transformation to straighten the stream line. Copyright © 2019, The Authors. All rights reserved.

关键词： Lagrange multipliers

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High Order Mass-Lumping Finite Elements on Simplexes

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高等学校计算数学学报（英文版） 2017年第2期10卷 331-350页

作者： Tao Cui Wei Leng Deng Lin Shichao Ma Linbo Zhang State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of SciencesNo.55 East Zhongguancun Road Beijing 100190 China State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of SciencesNo.55 East Zhongguancun Road Beijing 100190 China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049 China

This paper is concerned with the construction of high order mass-lumping finite elements on simplexes and a program for computing mass-lumping finite elements on triangles and *** polynomial spaces for mass-lumping finite elements,as proposed in the literature,are presented and *** particular,the unisolvence problem of symmetric point-sets for the polynomial spaces used in mass-lumping elements is addressed,and an interesting property of the unisolvent symmetric point-sets is observed and *** its theoretical proof is still lacking,this property seems to be true in general,and it can greatly reduce the number of cases to consider in the computations of mass-lumping elements.A program for computing mass-lumping finite elements on triangles and tetrahedra,derived from the code for computing numerical quadrature rules presented in [7],is *** mass-lumping finite elements on triangles found using this program with higher orders,namely 7,8 and 9,than those available in the literature are reported.

关键词： Finite element mass-lumping simplex numerical quadrature multivariate polynomial interpolation unisolvence

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Parallelizable algorithms for optimization problems with orthogonality constraints

arXiv

引用

arXiv 2018年

作者： Gao, Bin Liu, Xin Yuan, Ya-Xiang State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences China

To construct a parallel approach for solving optimization problems with orthogonality constraints is usually regarded as an extremely difficult mission, due to the low scalability of the orthonormalization procedure. However, such demand is particularly huge in some application areas such as materials computation. In this paper, we propose a proximal linearized augmented Lagrangian algorithm (PLAM) for solving optimization problems with orthogonality constraints. Unlike the classical augmented Lagrangian methods, in our algorithm, the prime variables are updated by minimizing a proximal linearized approximation of the augmented Lagrangian function, meanwhile the dual variables are updated by a closed-form expression which holds at any first-order stationary point. The orthonormalization procedure is only invoked once at the last step of the above mentioned algorithm if high-precision feasibility is needed. Consequently, the main parts of the proposed algorithm can be parallelized naturally. We establish global subsequence convergence, worst-case complexity and local convergence rate for PLAM under some mild assumptions. To reduce the sensitivity of the penalty parameter, we put forward a modification of PLAM, which is called parallelizable column-wise block minimization of PLAM (PCAL). Numerical experiments in serial illustrate that the novel updating rule for the Lagrangian multipliers significantly accelerates the convergence of PLAM and makes it comparable with the existent feasible solvers for optimization problems with orthogonality constraints, and the performance of PCAL does not highly rely on the choice of the penalty parameter. Numerical experiments under parallel environment demonstrate that PCAL attains good performance and high scalability in solving discretized Kohn-Sham total energy minimization *** Codes 15A18, 65F15, 65K05, 90C06 Copyright © 2018, The Authors. All rights reserved.

关键词： Linearization

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Efficient verification of continuous-variable quantum states and devices without assuming identical and independent operations

arXiv

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arXiv 2020年

作者： Wu, Ya-Dong Bai, Ge Chiribella, Giulio Liu, Nana QICI Quantum Information and Computation Initiative Department of Computer Science The University of Hong Kong Pokfulam Road Hong Kong The University of Hong Kong Shenzhen Institute of Research and Innovation 5/F Key Laboratory Platform Building No.6 Yuexing 2nd Rd. Nanshan Shenzhen518057 China Department of Computer Science Parks Road OxfordOX1 3QD United Kingdom Perimeter Institute for Theoretical Physics WaterlooONN2L 2Y5 Canada Institute of Natural Sciences Shanghai Jiao Tong University Shanghai200240 China Ministry of Education Key Laboratory in Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai200240 China University of Michigan Shanghai Jiao Tong University Joint Institute Shanghai200240 China

Continuous-variable quantum information, encoded into infinite-dimensional quantum systems, is a promising platform for the realization of many quantum information protocols, including quantum computation, quantum metrology, quantum cryptography, and quantum communication. To successfully demonstrate these protocols, an essential step is the certification of multimode continuous-variable quantum states and quantum devices. This problem is well studied under the assumption that multiple uses of the same device result in identical and independently distributed (i.i.d.) operations. However, in realistic scenarios, identical and independent state preparation and calls to the quantum devices cannot be generally guaranteed. Important instances include adversarial scenarios and instances of time-dependent and correlated noise. In this paper, we propose the first set of reliable protocols for verifying multimode continuous-variable entangled states and devices in these non-i.i.d scenarios. Although not fully universal, these protocols are applicable to Gaussian quantum states, non-Gaussian hypergraph states, as well as amplification, attenuation, and purification of noisy coherent states. Copyright © 2020, The Authors. All rights reserved.

关键词： Quantum optics

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On the origin of intrinsic randomness of Rayleigh-Benard turbulence

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Science China(Physics,Mechanics & Astronomy) 2017年第1期60卷 42-54页

作者： ZhiLiang Lin LiPo Wang ShiJun Liao School of Naval Architecture Ocean and Civil Engineering Shanghai Jiaotong University Shanghai 200240 China UM-SJTU Joint Institute Shanghai Jiaotong University Shanghai 200240 China Ministry-of-Education Key Laboratory in Scientific and Engineering Computing Shanghai 200240 China

It is of broad interest to understand how the evolution of non-equilibrium systems can be triggered and the role played by external perturbations. A famous example is the origin of randomness in the laminar-turbulence transition, which is raised in the pipe flow experiment by Reynolds as a century old unresolved problem. Although there exist different hypotheses, it is widely believed that the randomness is "intrinsic", which, however, remains as an open question to be verified. Simulating the modeled RayleighB′enard convection system by means of the so-called clean numerical simulation(CNS) with negligible numerical noises that are smaller even than thermal fluctuation, we verify that turbulence can be self-excited from the inherent thermal fluctuation without any external disturbances, i.e. out of nothing. This reveals a relationship between microscopic physical uncertainty and macroscopic randomness. It is found that in physics the system nonlinearity functions as a channel for randomness information,and energy as well, to transport microscopic uncertainty toward large scales. Such scenario can generally be helpful to understand the various relevant phenomena. In methodology, compared with direct numerical simulation(DNS), CNS opens a new direction to investigate turbulent flows with largely improved accuracy and reliability.

关键词： turbulence chaos thermal fluctuation clean numerical simulation

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An Adaptive Lagrangian Algorithm for Optimal Portfolio Deleveraging with Cross-Impact

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Journal of Systems Science & Complexity 2017年第5期30卷 1121-1135页

作者： XU Fengmin SUN Min DAI Yuhong School of Economics and Finance Xi'an Jiaotong UniversityXi'an 710049China School of Mathematics and Statistics Xi'an Jiaotong UniversityXi'an 710049China The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Science//Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

This paper considers the problem of optimal portfolio deleveraging, which is a crucial problem in finance. Taking the permanent and temporary price cross-impact into account, the authors establish a quadratic program with box constraints and a singly quadratic constraint. Under some assumptions, the authors give an optimal trading priority and show that the optimal solution must be achieved when the quadratic constraint is active. Further, the authors propose an adaptive Lagrangian algorithm for the model, where a piecewise quadratic root-finding method is used to find the Lagrangian multiplier. The convergence of the algorithm is established. The authors also present some numerical results, which show the usefulness of the algorithm and validate the optimal trading priority.

关键词： Adaptive Lagrangian algorithm deleveraging price cross-impact

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Anisotropic spectral manifold wavelet descriptor for deformable shape analysis and matching 26

Anisotropic spectral manifold wavelet descriptor for deforma...

引用

26th Pacific Conference on Computer Graphics and Applications, Pacific Graphics 2018

作者： Li, Qinsong Liu, Shengjun Hu, Ling Liu, Xinru Institute of Engineering Modeling and Scientific Computing Central South University Hunan Changsha410083 China School of Mathematics and Computational Science Hunan First Normal University Hunan Changsha410205 China State Key Laboratory of High Performance Manufacturing Complex Central South University Hunan Changsha410083 China

ISBN: (纸本)9783038680734

In this paper, we present a novel framework termed Anisotropic Spectral Manifold Wavelet Transform (ASMWT) for shape analysis. ASMWT comprehensively analyzes the signals from multiple directions on local manifold regions of the shape with a series of low-pass and band-pass frequency filters in each direction. Using the ASMWT coefficients of a very simple function, we efficiently construct a localizable and discriminative multiscale point descriptor, named as the Anisotropic Spectral Manifold Wavelet Descriptor (ASMWD). Since the filters used in our descriptor are direction-sensitive and able to robustly reconstruct the signals with a finite number of scales, it makes our descriptor be intrinsic-symmetry unambiguous, compact as well as efficient. The extensive experimental results demonstrate that our method achieves significant performance than several state-of-the-art methods when applied in vertex-wise shape matching. © 2018 The Author(s).

关键词： Wavelet transforms

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