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Elastic Full Waveform Inversion Based on the Trust Region Strategy

American Journal of Computational Mathematics 2021年第4期11卷 241-266页

作者： Wensheng Zhang Yijun Li 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 School of Mathematical Sciences University of Chinese Academy Sciences Beijing China

In this paper, we investigate the elastic wave full-waveform inversion (FWI) based on the trust region method. The FWI is an optimization problem of minimizing the misfit between the observed data and simulated data. Usually, the line search method is used to update the model parameters iteratively. The line search method generates a search direction first and then finds a suitable step length along the direction. In the trust region method, it defines a trial step length within a certain neighborhood of the current iterate point and then solves a trust region subproblem. The theoretical methods for the trust region FWI with the Newton type method are described. The algorithms for the truncated Newton method with the line search strategy and for the Gauss-Newton method with the trust region strategy are presented. Numerical computations of FWI for the Marmousi model by the L-BFGS method, the Gauss-Newton method and the truncated Newton method are completed. The comparisons between the line search strategy and the trust region strategy are given and show that the trust region method is more efficient than the line search method and both the Gauss-Newton and truncated Newton methods are more accurate than the L-BFGS method.

关键词： Elastic Wave Equations Full-Waveform Inversion Trust Region Strate-gy Line Search Strategy Newton-Type Method Time Domain

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Energy Stable Nodal DG Methods for Maxwell’s Equations of Mixed-Order Form in Nonlinear Optical Media

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Communications on Applied Mathematics and Computation 2024年第1期6卷 30-63页

作者： Maohui Lyu Vrushali A.Bokil Yingda Cheng Fengyan Li State Key Laboratory of Scientific and Engineering Computing(LSEC) Academy of Mathematics and System SciencesChinese Academy of SciencesBeijing100190China Department of Mathematics College of ScienceOregon State UniversityCorvallisOR97331USA Department of Mathematics Michigan State UniversityEast LansingMI48824USA Department of Computational Mathematics Science and EngineeringMichigan State UniversityEast LansingMI48824USA Department of Mathematical Sciences Rensselaer Polytechnic InstituteTroyNY12180USA

In this work,we develop energy stable numerical methods to simulate electromagnetic waves propagating in optical media where the media responses include the linear Lorentz dispersion,the instantaneous nonlinear cubic Kerr response,and the nonlinear delayed Raman molecular vibrational *** the first-order PDE-ODE governing equations considered previously in Bokil et al.(J Comput Phys 350:420–452,2017)and Lyu et al.(J Sci Comput 89:1–42,2021),a model of mixed-order form is adopted here that consists of the first-order PDE part for Maxwell’s equations coupled with the second-order ODE part(i.e.,the auxiliary differential equations)modeling the linear and nonlinear dispersion in the *** main contribution is a new numerical strategy to treat the Kerr and Raman nonlinearities to achieve provable energy stability property within a second-order temporal discretization.A nodal discontinuous Galerkin(DG)method is further applied in space for efficiently handling nonlinear terms at the algebraic level,while preserving the energy stability and achieving high-order *** with d_(E)as the number of the components of the electric field,only a d_(E)×d_(E)nonlinear algebraic system needs to be solved at each interpolation node,and more importantly,all these small nonlinear systems are completely decoupled over one time step,rendering very high parallel *** evaluate the proposed schemes by comparing them with the methods in Bokil et al.(2017)and Lyu et al.(2021)(implemented in nodal form)regarding the accuracy,computational efficiency,and energy stability,by a parallel scalability study,and also through the simulations of the soliton-like wave propagation in one dimension,as well as the spatial-soliton propagation and two-beam interactions modeled by the two-dimensional transverse electric(TE)mode of the equations.

关键词： Maxwell’s equations Kerr and Raman Discontinuous Galerkin method Energy stability

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OPTIMIZATION ON PRODUCT MANIFOLDS UNDER A PRECONDITIONED METRIC

arXiv

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arXiv 2023年

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

Since optimization on Riemannian manifolds relies on the chosen metric, it is appealing to know that how the performance of a Riemannian optimization method varies with different metrics and how to exquisitely construct a metric such that a method can be accelerated. To this end, we propose a general framework for optimization problems on product manifolds endowed with a preconditioned metric, and we develop Riemannian methods under this metric. Generally, the metric is constructed by an operator that aims to approximate the diagonal blocks of the Riemannian Hessian of the cost function. We propose three specific approaches to design the operator: exact block diagonal preconditioning, left and right preconditioning, and Gauss–Newton type preconditioning. Specifically, we tailor new preconditioned metrics and adapt the proposed Riemannian methods to the canonical correlation analysis and the truncated singular value decomposition problems, which provably accelerate the Riemannian methods. Additionally, we adopt the Gauss–Newton type preconditioning to solve the tensor ring completion problem. Numerical results among these applications verify that a delicate metric does accelerate the Riemannian optimization *** Codes 15A69, 65K05, 65F30, 90C30 Copyright © 2023, The Authors. All rights reserved.

关键词： Cost functions

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A penalty-free infeasible approach for a class of nonsmooth optimization problems over the Stiefel manifold

arXiv

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arXiv 2021年

作者： Xiao, Nachuan 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 State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences China

Transforming into an exact penalty function model with convex compact constraints yields efficient infeasible approaches for optimization problems with orthogonality constraints. For smooth and 2,1-norm regularized cases, these infeasible approaches adopt simple and orthonormalizationfree updating schemes and show high efficiency in some numerical experiments. However, to avoid orthonormalization while enforcing the feasibility of the final solution, these infeasible approaches introduce a quadratic penalty term,where an inappropriate penalty parameter can lead to numerical inefficiency. Inspired by penalty-free approaches for smooth optimization problems, we proposed a sequential linearized proximal gradient method (SLPG) for a class of optimization problems with orthogonality constraints and nonsmooth regularization term. This approach alternatively takes tangential steps and normal steps to improve the optimality and feasibility respectively. In SLPG, the orthonormalization process is invoked only once at the last step if high precision for feasibility is needed, showing that main iterations in SLPG are orthonormalization-free. Besides, both the tangential steps and normal steps do not involve the penalty parameter, and thus SLPG is penaltyfree and avoids the inefficiency caused by possible inappropriate penalty parameter. We analyze the global convergence properties of SLPG where the tangential steps are inexactly computed. By inexactly computing tangential steps, for smooth cases and 2,1-norm regularized cases, SLPG has a closed-form updating scheme, which leads to cheap tangential steps. Numerical experiments illustrate the advantages of SLPG when compared with existing first-ordermethods. Copyright © 2021, The Authors. All rights reserved.

关键词： Gradient methods

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A Smoothing Levenberg-Marquardt Type Method for NCP

A Smoothing Levenberg-Marquardt Type Method for NCP

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第四届运筹学及其应用国际研讨会

作者： Ju-Liang Zhang State Key Laboratory of Science and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and System SciencesChinese Academy of Sciences

＜正＞In this paper,we convert the nonlinear complementarity problems to an equivalent smooth nonlinear equation system by using smoothing technique. Then we use Levenberg-Marquardt type method to solve the nonlinear equation *** global and local superlinear convergence properties of the method are obtained under very mild ***,the algorithm is locally super-linearly convergent without assumption of strict complementarity of the solutions and uniqueness of the solution of NCP.

关键词： NCP Levenberg-Marquardt method smoothing technique P0 matrix superlinear convergence

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Car-Parinello molecular dynamics simulations of thionitroxide and S-nitrosothiol in the gas phase,methanol,and water——A theoretical study of S-nitrosylation

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中国科学:化学 2012年第10期42卷 1497-1498页

作者： LIANG Juan1,CHENG ShangLi1,HOU JunWei1,XU ZhenHao1,2 & ZHAO Yi-Lei1,2,3* 1 state key laboratory of Microbial Metabolism,School of Life Sciences and Biotechnology,Shanghai Jiao Tong University,Shanghai 200240,China 2 Shanghai Center for Systems Biomedicine,Shanghai Jiao Tong University,Shanghai 200240,China 3 MOE laboratory of scientific and engineering computing,Shanghai Jiao Tong University,Shanghai 200240,China State Key Laboratory of Microbial Metabolism School of Life Sciences and Biotechnology Shanghai Jiao Tong University Shanghai 200240 China Shanghai Center for Systems Biomedicine Shanghai Jiao Tong University Shanghai 200240 China MOE Laboratory of Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai 200240 China

A dilemma about whether thionitroxide radical(RSNHO) or S-nitrosothiol(RSNO) is observed in protein S-nitrosylation has arisen *** illustrate the effect of chemical environment on these structures,this paper presents quantum mechanical molecular dynamics of thionitroxide,and cis-and trans-S-nitrosothiols in the gas phase,methanol,and *** using Car-Parrinello molecular dynamics(CPMD),we have observed that there is free rotation about the S-N bond at 300 K in thionitroxide,but no such rotation is observed for *** C-S-N-O torsion angle distribution in thionitroxide is significantly dependent upon the surrounding environment,leading to either gauche-,cis-,or *** the case of S-nitrosothiol the C-S-N-O plane is twisted slightly by 5°-15° in the cis-isomer,while the periplanar structure is well-retained in the *** calculated results are in agreement with the X-ray crystallographic data of small molecular RSNO ***,for both compounds,the CPMD simulations show that solvation can cause a decrease in the S-N bond ***,the oxygen atom of thionitroxide is found to be a good hydrogen-bond acceptor,forming an oxyanion-hole-like hydrogen bonding network.

关键词： quantum mechanical molecular dynamics S-nitrosylation thionitroxide S-nitrosothiol solvent effect

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Flexible alignment of images using B-spline reparameterization and L2-gradient flows

Flexible alignment of images using B-spline reparameterizati...

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Congress on Image and Signal Processing, CISP

作者： Guoliang Xu Yanmei Zheng State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics Chinese Academy and Sciences Beijing China

In this paper, we present a new flexible alignment method to align two or more similar images. By minimizing an energy functional measuring the difference of the initial image and target image, a L 2 -gradient flow is derived. The flow is integrated by a finite element method in the spatial direction and a semi-implicit Euler scheme in the temporal direction. The experimental results show that the proposed method is efficient, effective and capable of capturing large variation of the initial and the target images.

关键词： Spline Image registration Linear systems Correlation Equations

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Adaptive energy-preserving algorithms for guiding center system

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Plasma Science and Technology 2023年第4期25卷 11-22页

作者：朱贝贝刘健张嘉炜祝爱卿唐贻发 Department of Applied Mathematics School of Mathematics and PhysicsUniversity of Science and Technology BeijingBeijing 100083Peopleʼs Republic of China School of Nuclear Science and Technology University of Science and Technology of ChinaHefei 230026Peopleʼs Republic of China Advanced algorithm Joint Lab Shandong Computer Science CenterQilu University of TechnologyJinan 250014Peopleʼs Republic of China The State Key Laboratory of Scientific and Engineering Computing The Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190Peopleʼs Republic of China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049Peopleʼs Republic of China

We develop two types of adaptive energy preserving algorithms based on the averaged vector field for the guiding center dynamics,which plays a key role in magnetized *** adaptive scheme is applied to the Gauss Legendre’s quadrature rules and time stepsize respectively to overcome the energy drift problem in traditional energy-preserving *** new adaptive algorithms are second order,and their algebraic order is carefully *** results show that the global energy errors are bounded to the machine precision over long time using these adaptive algorithms without massive extra computation cost.

关键词： guiding center system energy-preserving methods adaptive energy conservation

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Moiré cavity quantum electrodynamics

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Science Advances 2025年第21期11卷 eadv8115页

作者： Wang, Yu-Tong Ye, Qi-Hang Yan, Jun-Yong Qiao, Yufei Liu, Yu-Xin Ye, Yong-Zheng Chen, Chen Cheng, Xiao-Tian Li, Chen-Hui Zhang, Zi-Jian Huang, Cheng-Nian Meng, Yun Zou, Kai Zhan, Wen-Kang Zhao, Chao Hu, Xiaolong Tee, Clarence Augustine T.H. Sha, Wei E.I. Huang, Zhixiang Liu, Huiyun Jin, Chao-Yuan Ying, Lei Liu, Feng State Key Laboratory of Extreme Photonics and Instrumentation College of Information Science and Electronic Engineering Zhejiang University Hangzhou310027 China School of Physics Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control Zhejiang University Hangzhou310027 China International Joint Innovation Center Zhejiang University Haining314400 China School of Precision Instrument and Optoelectronic Engineering Tianjin University Tianjin300072 China Key Laboratory of Optoelectronic Information Science and Technology Ministry of Education Tianjin300072 China Laboratory of Solid State Optoelectronics Information Technology Institute of Semiconductors Chinese Academy of Sciences Beijing100083 China College of Materials Science and Opto-Electronic Technology University of Chinese Academy of Science Beijing101804 China College of Physics and Electrical Information Engineering Zhejiang Normal University Hangzhou310058 China Key Laboratory of Intelligent Computing and Signal Processing Ministry of Education Anhui University Hefei230039 China Department of Electronic and Electrical Engineering University College London LondonWC1E 7JE United Kingdom ZJU-Hangzhou Global Scientific and Technological Innovation Center Zhejiang University Zhejiang Hangzhou311200 China

Quantum emitters are a key component in photonic quantum technologies. Enhancing single-photon emission by engineering their photonic environment is essential for improving overall efficiency in quantum information processing. However, this enhancement is often limited by the need for ultraprecise emitter placement within conventional photonic cavities. Inspired by the fascinating physics of moiré pattern, we propose a multilayer moiré photonic crystal with a robust isolated flatband. Theoretical analysis reveals that, with nearly infinite photonic density of states, the moiré cavity simultaneously has a high Purcell factor and large tolerance over the emitter’s position, breaking the constraints of conventional cavities. We then experimentally demonstrate various cavity quantum electrodynamic phenomena with a quantum dot in moiré cavity. A large tuning range (up to 40-fold) of quantum dot’s radiative lifetime is achieved through strong Purcell enhancement and inhibition effects. Our findings open the door for moiré flatband cavity–enhanced quantum light sources and quantum nodes for the quantum internet. Copyright © 2025 The Authors, some rights reserved.

关键词： Quantum electronics

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The Quantum Internet (Technical Version)

arXiv

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arXiv 2025年

作者： Rohde, Peter P. Huang, Zixin Ouyang, Yingkai Huang, He-Liang Su, Zu-En Devitt, Simon Ramakrishnan, Rohit Mantri, Atul Tan, Si-Hui Liu, Nana Harrison, Scott Radhakrishnan, Chandrashekar Brennen, Gavin K. Baragiola, Ben Q. Dowling, Jonathan P. Byrnes, Tim Munro, William J. Centre for Quantum Software and Information Faculty of Engineering and Information Technology University of Technology Sydney SydneyNSW Australia Hearne Institute for Theoretical Physics Louisiana State University Baton Rouge United States School of Mathematical and Physical Sciences Macquarie University NSW2109 Australia School of Mathematical and Physical Sciences University of Sheffield SheffieldS3 7RH United Kingdom Henan Key Laboratory of Quantum Information and Cryptography Henan Zhengzhou450000 China Hefei National Laboratory for Physical Sciences at Microscale Department of Modern Physics University of Science & Technology of China Hefei China CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information & Quantum Physics University of Science & Technology of China Hefei China CAS-Alibaba Quantum Computing Laboratory Shanghai China InstituteQ Aalto University Espoo02150 Finland Indian Institute of Science Bangalore India Singapore University of Technology & Design Singapore Centre for Quantum Technologies National University of Singapore Singapore Horizon Quantum Ireland 24 Fitzwilliam Place Dublin 2 D02 T296 Ireland Institute of Natural Sciences Shanghai Jiao Tong University Shanghai200240 China School of Mathematical Sciences Shanghai Jiao Tong University Shanghai200240 China Ministry of Education Key Laboratory in Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai200240 China Shanghai Artificial Intelligence Laboratory Shanghai China University of Michigan Shanghai Jiao Tong University Joint Institute Shanghai200240 China Leibniz Institute for Research & Information in Education Frankfurt am Main Germany Department of Computer Science and Engineering NYU Shanghai 567 West Yangsi Road Shanghai200124 China Centre of Excellence in Engineered Quantum Systems Macquarie University NSW Australia Centre for Quantum Computation and Communication Technology School of Science RMIT University VIC

The desire to share and unite remote digital assets motivated the development of the classical internet, the enabler of the entire 21st century economy and our modern way of life. As we enter the quantum era, it is to be expected there will be a similar demand for networking quantum assets, motivating a global quantum internet for bringing together the world's quantum resources, leveraging off their exponential trajectory in capability. We present models for quantum networking, how they might be applied in the future, and the implications they will have. Socially, economically, politically and geostrategically, the upcoming era of quantum supremacy will be as significant for the 21st century as the transistor was for the 20th. The inherently different scaling in the computational power of quantum computers fundamentally changes the dynamics of how they will operate in the future. Given their high expected initial cost, a client/server model for outsourcing computation will be essential for enabling the accessibility and proliferation of this technology, and ensuring its economic viability. We therefore anticipate the emergence of cloud quantum computing, a model for outsourcing quantum computations to the network. We argue that economic efficiency will mandate that all future quantum computers be united into a single global virtual quantum computer, offering exponentially more power to all network participants than if they were to keep their resources to themselves. This model for the allocation of computational resources is uniquely quantum, with no classical analogue, completely altering the economic landscape for the future of computation. Given the sensitivity of much of the data to which future quantum computers are going to foreseeably be applied, protocols for encrypted quantum computation will be essential - the outsourcing of computations that neither an eavesdropper nor even the server performing the computation can spy upon. This will enable new models fo

关键词： Outsourcing

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