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A MULTIFIDELITY MONTE CARLO METHOD FOR REALISTIC computational BUDGETS

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arXiv 2022年

作者： Gruber, Anthony Gunzburger, Max Ju, Lili Wang, Zhu Department of Scientific Computing Florida State University 400 Dirac Science Library TallahasseeFL32306 United States Oden Institute for Computational Engineering and Sciences University of Texas at Austin 201 E 24th Street AustinTX78712 United States Department of Mathematics University of South Carolina 1523 Greene Street ColumbiaSC29208 United States

A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing closed-form solution, this method extends the usability of a well known MFMC algorithm, recovering it when the computational budget is large enough. Theoretical results verify that the proposed approach is at least as optimal as its namesake and retains the benefits of multifidelity estimation with minimal assumptions on the budget or amount of available data, providing a notable reduction in variance over simple Monte Carlo *** Codes 62K05, 49M20 Copyright © 2022, The Authors. All rights reserved.

关键词： Monte Carlo methods

A NITSCHE HYBRID MULTISCALE METHOD WITH NON-MATCHING GRIDS

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arXiv 2021年

作者： Ming, Pingbing Song, Siqi LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences No. 55 East Road Zhong-Guan-Cun Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

We propose a Nitsche method for multiscale partial differential equations, which retrieves the macroscopic information and the local microscopic information at one stroke. We prove the convergence of the method for second order elliptic problem with bounded and measurable coefficients. The rate of convergence may be derived for coefficients with further structures such as periodicity and ergodicity. Extensive numerical results confirm the theoretical predictions. Copyright © 2021, The Authors. All rights reserved.

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Verifiable blind quantum computation with identity authentication for different types of clients

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arXiv 2022年

作者： Quan, Junyu Li, Qin Li, Lvzhou School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China School of Computer Science Xiangtan University Xiangtan411105 China Institute of Quantum Computing and Computer Theory School of Computer Science and Engineering Sun Yat-sen University Guangzhou510006 China

Quantum computing has considerable advantages in solving some problems over its classical counterpart. Currently various physical systems are developed to construct quantum computers but it is still challenging and the first use of quantum computers may adopt the cloud style. Blind quantum computing (BQC) provides a solution for clients with limited quantum capabilities to delegate their quantum computation to remote quantum servers while keeping input, output, and even algorithm private. In this paper, we propose three multi-party verifiable blind quantum computing (VBQC) protocols with identity authentication to handle clients with varying quantum capabilities in quantum networks, such as those who can just make measurements, prepare single qubits, or perform a few single-qubit gates. They are client-friendly and flexible since the clients can achieve BQC depending on their own quantum devices and resist both insider outsider attacks in quantum networks. Furthermore, all the three proposed protocols are verifiable, namely that the clients can verify the correctness of their calculations. Copyright © 2022, The Authors. All rights reserved.

关键词： Qubits

Machine learning for elliptic PDEs: Fast rate generalization bound, neural scaling law and minimax optimality

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arXiv 2021年

作者： Lu, Yiping Chen, Haoxuan Lu, Jianfeng Ying, Lexing Blanchet, Jose Institute for Computational and Mathematical Engineering Stanford University StanfordCA United States Department of Computing and Mathematical Sciences Caltech Mathematics Department Duke University United States Department of Mathematics Institute for Computational and Mathematical Engineering Stanford University StanfordCA United States Department of Management Science & Engineering Stanford University StanfordCA United States

In this paper, we study the statistical limits of deep learning techniques for solving elliptic partial differential equations (PDEs) from random samples using the Deep Ritz Method (DRM) and Physics-Informed Neural Networks (PINNs). To simplify the problem, we focus on a prototype elliptic PDE: the Schrödinger equation on a hypercube with zero Dirichlet boundary condition, which has wide application in the quantum-mechanical systems. We establish upper and lower bounds for both methods, which improves upon concurrently developed upper bounds for this problem via a fast rate generalization bound. We discover that the current Deep Ritz Methods is sub-optimal and propose a modified version of it. We also prove that PINN and the modified version of DRM can achieve minimax optimal bounds over Sobolev spaces. Empirically, following recent work which has shown that the deep model accuracy will improve with growing training sets according to a power law, we supply computational experiments to show a similar behavior of dimension dependent power law for deep PDE solvers. © 2021, CC BY.

关键词： Optimization

Measuring kinetic inductance and superfluid stiffness of two-dimensional superconductors using high-quality transmission-line resonators

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Physical Review Research 2024年第4期6卷 043245-043245页

作者： Mary Kreidel Xuanjing Chu Jesse Balgley Abhinandan Antony Nishchhal Verma Julian Ingham Leonardo Ranzani Raquel Queiroz Robert M. Westervelt School of Engineering and Applied Sciences Harvard University Cambridge Massachusetts 02138 USA Department of Applied Physics and Applied Mathematics Columbia University New York New York 10027 USA Department of Mechanical Engineering Columbia University New York New York 10027 USA Department of Physics Columbia University New York New York 10027 USA RTX BBN Technologies Quantum Engineering and Computing Group Cambridge Massachusetts 02138 USA Center for Computational Quantum Physics Flatiron Institute New York New York 10010 USA Department of Physics Harvard University Cambridge Massachusetts 02138 USA

The discovery of van der Waals superconductors in recent years has generated a lot of excitement for their potentially novel pairing mechanisms. However, their typical atomic-scale thickness and micrometer-scale lateral dimensions impose severe challenges to investigations of pairing symmetry by conventional methods. We demonstrate an improved technique that employs high-quality-factor superconducting resonators to measure the kinetic inductance—up to one part per million—and loss of a van der Waals superconductor. We analyze the equivalent circuit model to extract the kinetic inductance, superfluid stiffness, penetration depth, and ratio of imaginary and real parts of the complex conductivity. We validate the technique by measuring aluminum and finding excellent agreement in both the zero-temperature superconducting gap as well as the complex conductivity data when compared with BCS theory. We then demonstrate the utility of the technique by measuring the kinetic inductance of multilayered niobium diselenide and discuss the limits to the accuracy of our technique when the transition temperature of the sample, NbSe2 at 7.06 K, approaches our Nb probe resonator at 8.59 K. Our method will be useful for practitioners in the growing fields of superconducting physics, materials science, and quantum sensing, as a means of characterizing superconducting circuit components and studying pairing mechanisms of the novel superconducting states which arise in layered two-dimensional materials and heterostructures.

关键词： Quantum circuits Superconducting order parameter Superconductivity 2-dimensional systems Van der Waals systems Methods in superconductivity Microwave techniques

Influence of Material Parameter Variability on the Predicted Coronary Artery Biomechanical Environment via Uncertainty Quantification

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arXiv 2024年

作者： Berggren, Caleb C. Jiang, David Wang, Y.F. Jack Bergquist, Jake A. Rupp, Lindsay C. Liu, Zexin MacLeod, Rob S. Narayan, Akil Timmins, Lucas H. Department of Biomedical Engineering University of Utah Salt Lake CityUT United States Scientific Computing and Imaging Institute University of Utah Salt Lake CityUT United States Nora Eccles Cardiovascular Research and Training Institute University of Utah Salt Lake CityUT United States Department of Mathematics University of Utah Salt Lake CityUT United States School of Engineering Medicine Texas A&M University HoustonTX United States Department of Biomedical Engineering Texas A&M University College StationTX United States

Central to the clinical adoption of patient-specific modeling strategies is demonstrating that simulation results are reliable and safe. Indeed, simulation frameworks must be robust to uncertainty in model input(s), and levels of confidence should accompany results. In this study, we applied a coupled uncertainty quantification-finite element (FE) framework to understand the impact of uncertainty in vascular material properties on variability in predicted stresses. Univariate probability distributions were fit to material parameters derived from layer-specific mechanical behavior testing of human coronary tissue. Parameters were assumed to be probabilistically independent, allowing for efficient parameter ensemble sampling. In an idealized coronary artery geometry, a forward FE model for each parameter ensemble was created to predict tissue stresses under physiologic loading. An emulator was constructed within the UncertainSCI software using polynomial chaos techniques, and statistics and sensitivities were directly computed. Results demonstrated that material parameter uncertainty propagates to variability in predicted stresses across the vessel wall, with the largest dispersions in stress within the adventitial layer. Variability in stress was most sensitive to uncertainties in the anisotropic component of the strain energy function. Moreover, unary and binary interactions within the adventitial layer were the main contributors to stress variance, and the leading factor in stress variability was uncertainty in the stress-like material parameter that describes the contribution of the embedded fibers to the overall artery stiffness. Results from a patient-specific coronary model confirmed many of these findings. Collectively, these data highlight the impact of material property variation on uncertainty in predicted artery stresses and present a pipeline to explore and characterize forward model uncertainty in computational biomechanics. © 2024, CC BY.

关键词： Uncertainty analysis

An efficient quadratic programming relaxation based algorithm for large-scale MIMO detection

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arXiv 2020年

作者： Zhao, Ping-Fan Li, Qing-Na Chen, Wei-Kun Liu, Ya-Feng School of Mathematics and Statistics Beijing Institute of Technology Beijing China School of Mathematics and Statistics Beijing Key Laboratory on MCAACI Beijing Institute of Technology Beijing 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

Multiple-input multiple-output (MIMO) detection is a fundamental problem in wireless communications and it is strongly NP-hard in general. Massive MIMO has been recognized as a key technology in the fifth generation (5G) and beyond communication networks, which on one hand can significantly improve the communication performance, and on the other hand poses new challenges of solving the corresponding optimization problems due to the large problem size. While various efficient algorithms such as semidefinite relaxation (SDR) based approaches have been proposed for solving the small-scale MIMO detection problem, they are not suitable to solve the large-scale MIMO detection problem due to their high computational complexities. In this paper, we propose an efficient sparse quadratic programming (SQP) relaxation based algorithm for solving the large-scale MIMO detection problem. In particular, we first reformulate the MIMO detection problem as an SQP problem. By dropping the sparse constraint, the resulting relaxation problem shares the same global minimizer with the SQP problem. In sharp contrast to the SDRs for the MIMO detection problem, our relaxation does not contain any (positive semidefinite) matrix variable and the numbers of variables and constraints in our relaxation are significantly less than those in the SDRs, which makes it particularly suitable for the large-scale problem. Then we propose a projected Newton based quadratic penalty method to solve the relaxation problem, which is guaranteed to converge to the vector of transmitted signals under reasonable conditions. By extensive numerical experiments, when applied to solve small-scale problems, the proposed algorithm is demonstrated to be competitive with the state-of-the-art approaches in terms of detection accuracy and solution efficiency;when applied to solve large-scale problems, the proposed algorithm achieves better detection performance than a recently proposed generalized power *** Codes 90C2

关键词： Quadratic programming

Interface Faceting-Defaceting Mediated by Disconnections

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arXiv 2022年

作者： Qiu, Caihao Salvalaglio, Marco Srolovitz, David J. Han, Jian Department of Materials Science and Engineering City University of Hong Kong Hong Kong Institute of Scientific Computing TU Dresden Dresden01062 Germany Dresden Center for Computational Materials Science TU Dresden Dresden01062 Germany Department of Mechanical Engineering The University of Hong Kong Pokfulam Road Hong Kong Shenzhen China

An intrinsic feature of nearly all internal interfaces in crystalline systems (homo- and hetero-phase) is the presence of disconnections (topological line defects constrained to the interface that have both step and dislocation character). Disconnections play a major role in determining interface thermodynamics and kinetics. We demonstrate that elastic interactions between disconnections lead to a thermodynamic, first-order, finite-temperature, faceting-defaceting transition, in agreement with experiments. These elastic interactions strongly modify equilibrium interface morphologies (compared with those solely determined by anisotropic surface energy) as well as the kinetics and morphologies of migrating interfaces. We demonstrate these phenomena through numerical simulations based upon a general, continuum disconnection-based model for interface thermodynamics and kinetics applied to embedded particles/grains, steady-state interface migration geometries, and nominally flat interfaces. Copyright © 2022, The Authors. All rights reserved.

关键词： Thermodynamics

On the Power of Gradual Network Alignment Using Dual-Perception Similarities

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arXiv 2022年

作者： Park, Jin-Duk Tran, Cong Shin, Won-Yong Cao, Xin The School of Mathematics and Computing Computational Science and Engineering Yonsei University Seoul03722 Korea Republic of The Faculty of Information Technology Posts and Telecommunications Institute of Technology Hanoi100000 Viet Nam Pohang37673 Korea Republic of The School of Computer Science and Engineering The University of New South Wales Sydney2052 Australia

Network alignment (NA) is the task of finding the correspondence of nodes between two networks based on the network structure and node attributes. Our study is motivated by the fact that, since most of existing NA methods have attempted to discover all node pairs at once, they do not harness information enriched through interim discovery of node correspondences to more accurately find the next correspondences during the node matching. To tackle this challenge, we propose Grad-Align, a new NA method that gradually discovers node pairs by making full use of node pairs exhibiting strong consistency, which are easy to be discovered in the early stage of gradual matching. Specifically, Grad-Align first generates node embeddings of the two networks based on graph neural networks along with our layer-wise reconstruction loss, a loss built upon capturing the first-order and higher-order neighborhood structures. Then, nodes are gradually aligned by computing dual-perception similarity measures including the multi-layer embedding similarity as well as the Tversky similarity, an asymmetric set similarity using the Tversky index applicable to networks with different scales. Additionally, we incorporate an edge augmentation module into Grad-Align to reinforce the structural consistency. Through comprehensive experiments using real-world and synthetic datasets, we empirically demonstrate that Grad-Align consistently outperforms state-of-the-art NA methods. © 2022, CC BY.

关键词： Embeddings