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arXiv 2022年

作者： Khorashadizadeh, AmirEhsan Kothari, Konik Salsi, Leonardo Harandi, Ali Aghababaei de Hoop, Maarten Dokmanić, Ivan The Department of Mathematics and Computer Science The University of Basel Basel4001 Switzerland The Department of Electrical and Computer Engineering The University of Illinois at Urbana-Champaign UrbanaIL61801 United States The Department of Electrical Engineering Sharif University of Technology Tehran14399-57131 Iran The Department of Computational and Applied Mathematics Rice University HoustonTX77005 United States

Most deep learning models for computational imaging regress a single reconstructed image. In practice, however, ill-posedness, nonlinearity, model mismatch, and noise often conspire to make such point estimates misleading or insufficient. The Bayesian approach models images and (noisy) measurements as jointly distributed random vectors and aims to approximate the posterior distribution of unknowns. Recent variational inference methods based on conditional normalizing flows are a promising alternative to traditional MCMC methods, but they come with drawbacks: excessive memory and compute demands for moderate to high resolution images and underwhelming performance on hard nonlinear problems. In this work, we propose C-Trumpets-conditional injective flows specifically designed for imaging problems, which greatly diminish these challenges. Injectivity reduces memory footprint and training time while low-dimensional latent space together with architectural innovations like fixed-volume-change layers and skip-connection revnet layers, C-Trumpets outperform regular conditional flow models on a variety of imaging and image restoration tasks, including limited-view CT and nonlinear inverse scattering, with a lower compute and memory budget. C-Trumpets enable fast approximation of point estimates like MMSE or MAP as well as physically-meaningful uncertainty quantification. © 2022, CC BY.

关键词： Image reconstruction

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Novel symmetric numerical methods for solving symmetric mathematical problems

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International Journal of Circuits, Systems and Signal Processing 2021年 15卷 1545-1557页

作者： Ibrahimov, V.R. Mehdiyeva, G.Y.U. Yue, Xiao-Guang Kaabar, Mohammed K.A. Noeiaghdam, Samad Juraev, Davron Aslonqulovich Institute of Control Systems named after Academician A.Huseynov BakuAZ1141 Azerbaijan Computational mathematics Baku State University BakuAZ1148 Azerbaijan Department of Computer Science and Engineering School of Sciences European University Cyprus Nicosia1516 Cyprus Institute of Mathematical Sciences Faculty of Science University of Malaya Kuala Lumpur50603 Malaysia Department of Mathematics and Statistics Washington State University PullmanWA99163 United States Industrial Mathematics Laboratory Baikal School of BRICS Irkutsk National Research Technical University Irkutsk664074 Russia Department of Applied Mathematics and Programming South Ural State University Lenin Prospect 76 Chelyabinsk454080 Russia Department of Natural Science Disciplines Higher Military Aviation School of the Republic of Uzbekistan Karshi City180100 Uzbekistan

—The mathematical model for many problems is arising in different industries of natural science, basically formulated using differential, integral and integro-differential equations. The investigation of these equations is conducted with the help of numerical integration theory. It is commonly known that a class of problems can be solved by applying numerical integration. The construction of the quadrature formula has a direct relation with the computation of definite integrals. The theory of definite integrals is used in geometry, physics, mechanics and in other related subjects of science. In this work, the existence and uniqueness of the solution of above-mentioned equations are investigated. By this way, the domain has been defined in which the solution of these problems is equivalent. All proposed four problems can be solved using one and the same methods. We define some domains in which the solution of one of these problems is also the solution of the other problems. Some stable methods with the degree p © 2021, North Atlantic University Union NAUN. All rights reserved.

关键词： Integrodifferential equations

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Wire Before You Walk

Wire Before You Walk

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Asilomar Conference on Signals, Systems & computers

作者： Tesfa Asmara Dhananjay Bhaskar Ian Adelstein Smita Krishnaswamy Michael Perlmutter Department of Computer Science Pomona College Claremont CA USA Mathematics and Statistics Pomona College Claremont CA USA Department of Genetics Yale School of Medicine New Haven CT USA Department of Mathematics Yale University New Haven CT USA Department of Computer Science Yale University New Haven CT USA Program for Applied Mathematics Yale University New Haven CT USA Computational Biology and Bioinformatics Program Yale University New Haven CT USA Wu Tsai Institute Yale University New Haven CT USA Department of Mathematics Boise State University Boise ID USA

Node embeddings aim to associate a vector to every vertex of a graph which can then be used for downstream tasks such as clustering, classification, or link prediction. Many popular node embeddings such as no $d$ e2vec and DeepWalk are based upon counting which nodes frequently co-occur in random walks of the graph. In this paper, we show that the performance of such algorithms can be improved by rewiring the edges of the graph through a variety of network indices before running DeepWalk. These rewirings effectively give the random walker an inductive bias and increase the accuracy of a logistic regression classifier applied to the node embedding on several benchmark data sets.

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Machine Learning for the Physics of Climate

arXiv

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arXiv 2024年

作者： Bracco, Annalisa Brajart, Julien Dijkstra, Henk A. Hassanzadeh, Pedram Lessing, Christian Monteleoni, Claire School of Earth and Atmospheric Sciences Georgia Institute of Technology AtlantaGA United States Bergen Norway Institute for Marine and Atmospheric Research Utrecht University Utrecht Netherlands Department of Geophysical Sciences Commitee on Computational and Applied Mathematics University of Chicago IL United States Reading United Kingdom INRIA Paris France Computer Science Department University of Colorado Boulder BoulderCO United States

An exponential growth in computing power, which has brought more sophisticated and higher resolution simulations of the climate system, and an exponential increase in observations since the first weather satellite was put in orbit, are revolutionizing climate science. Big data and associated algorithms, coalesced under the field of Machine Learning (ML), offer the opportunity to study the physics of the climate system in ways, and with an amount of detail, infeasible few years ago. The inference provided by ML has allowed to ask causal questions and improve prediction skills beyond classical barriers. Furthermore, when paired with modeling experiments or robust research in model parameterizations, ML is accelerating computations, increasing accuracy and allowing for generating very large ensembles at a fraction of the cost. In light of the urgency imposed by climate change and the rapidly growing role of ML, we review its broader accomplishments in climate physics. Decades long standing problems in observational data reconstruction, representation of sub-grid scale phenomena and climate (and weather) prediction are being tackled with new and justified optimism. Ultimately, this review aims at providing a perspective on the benefits and major challenges of exploiting ML in studying complex systems. © 2024, CC BY.

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Linear Combination of Hamiltonian Simulation for Nonunitary Dynamics with Optimal State Preparation Cost

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Physical Review Letters 2023年第15期131卷 150603-150603页

作者： Dong An Jin-Peng Liu Lin Lin Joint Center for Quantum Information and Computer Science University of Maryland College Park Maryland 20742 USA Department of Mathematics University of California Berkeley California 94720 USA Simons Institute for the Theory of Computing University of California Berkeley California 94720 USA Center for Theoretical Physics Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA Lawrence Berkeley National Laboratory Applied Mathematics and Computational Research Division Berkeley California 94720 USA Challenge Institute for Quantum Computation University of California Berkeley California 94720 USA

We propose a simple method for simulating a general class of nonunitary dynamics as a linear combination of Hamiltonian simulation (LCHS) problems. LCHS does not rely on converting the problem into a dilated linear system problem or on the spectral mapping theorem. The latter is the mathematical foundation of many quantum algorithms for solving a wide variety of tasks involving nonunitary processes, such as the quantum singular value transformation. The LCHS method can achieve optimal cost in terms of state preparation. We also demonstrate an application for open quantum dynamics simulation using the complex absorbing potential method with near-optimal dependence on all parameters.

关键词： Open quantum systems Quantum algorithms Quantum algorithms & computation Quantum simulation Differential equations

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AMG Preconditioners based on Parallel Hybrid Coarsening and Multi-objective Graph Matching

AMG Preconditioners based on Parallel Hybrid Coarsening and ...

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Euromicro Conference on Parallel, Distributed and Network-Based Processing

作者： Pasqua D'Ambra Fabio Durastante S M Ferdous Salvatore Filippone Mahantesh Halappanavar Alex Pothen National Research Council (CNR) Institute for Applied Computing “M. Picone” (IAC) Napoli Italy Department of Mathematics University of Pisa Pisa Italy Pacific Northwest National Laboratory Physical and Computational Sciences Richland WA USA Dept. of Civil and Computer Engineering University of Rome Tor-Vergata Rome Italy Computer Science Department Purdue University West Lafayette IN USA

We describe preliminary results from a multi-objective graph matching algorithm, in the coarsening step of an aggregation-based Algebraic MultiGrid (AMG) preconditioner, for solving large and sparse linear systems of equations on high-end parallel computers. We have two objectives. First, we wish to improve the convergence behavior of the AMG method when applied to highly anisotropic problems. Second, we wish to extend the parallel package PSCToolkit to exploit multi-threaded parallelism at the node level on multi-core processors. Our matching proposal balances the need to simultaneously compute high weights and large cardinalities by a new formulation of the weighted matching problem combining both these objectives using a parameter $\lambda$ . We compute the matching by a parallel $2/3-\varepsilon$ -approximation algorithm for maximum weight matchings. Results with the new matching algorithm show that for a suitable choice of the parameter $\lambda$ we compute effective preconditioners in the presence of anisotropy, i.e., smaller solve times, setup times, iterations counts, and operator complexity.

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High-speed and low-power molecular dynamics processing unit(MDPU)with ab initio accuracy

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npj computational Materials 2024年第1期10卷 559-568页

作者： Pinghui Mo Yujia Zhang Zhuoying Zhao Hanhan Sun Junhua Li Dawei Guan Xi Ding Xin Zhang Bo Chen Mengchao Shi Duo Zhang Denghui Lu Yinan Wang Jianxing Huang Fei Liu Xinyu Li Mohan Chen Jun Cheng Bin Liang Weinan E Jiayu Dai Linfeng Zhang Han Wang Jie Liu College of Integrated Circuits Hunan UniversityChangsha410082P.R.China College of Electrical and Information Engineering Hunan UniversityChangsha410082P.R.China College of Computer National University of Defense TechnologyChangsha410073P.R.China Department of Physics National University of Defense TechnologyChangsha410073P.R.China DP Technology 100080 BeijingP.R.China AI for Science Institute 100080 BeijingP.R.China Academy for Advanced Interdisciplinary Studies Peking University100871 BeijingP.R.China HEDPS CAPTCollege of EngineeringPeking University100871 BeijingP.R.China School of Mathematical Science Peking University100871 BeijingP.R.China State Key Laboratory of Physical Chemistry of Solid Surfaces iChEMCollege of Chemistry and Chemical EngineeringXiamen UniversityXiamen361005P.R.China School of Integrated Circuits Peking University100871 BeijingP.R.China Center for Machine Learning Research Peking University100871 BeijingP.R.China Institute of Applied Physics and Computational Mathematics 100088 BeijingP.R.China Greater Bay Area Institute for Innovation Hunan UniversityGuangzhou511300P.R.China Department of Electrical and Computer Engineering University of WashingtonSeattleWA98195USA

Molecular dynamics(MD)is an indispensable atomistic-scale computational tool widely-used in various *** the past decades,nearly all ab initio MD and machine-learning MD have been based on the general-purpose central/graphics processing units(CPU/GPU),which are well-known to suffer from their intrinsic“memory wall”and“power wall”***,nowadays MD calculations with ab initio accuracy are extremely time-consuming and power-consuming,imposing serious restrictions on the MD simulation size and *** solve this problem,here we propose a special-purpose MD processing unit(MDPU),which could reduce MD time and power consumption by about 103 times(109 times)compared to state-of-the-art machine-learningMD(ab initio MD)based on CPU/GPU,while keeping ab initio *** significantly-enhanced performance,the proposed MDPU may pave a way for the accurate atomistic-scale analysis of large-size and/or longduration problems which were impossible/impractical to compute before.

关键词： consuming power MDP

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Viscous Shock Wave to an Inflow Problem for Compressible Viscous Gas with Large Density Oscillations

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Acta Mathematicae Applicatae Sinica 2019年第1期35卷 129-157页

作者： Dong-fen BIAN Li-li FAN Lin HE Hui-jiang ZHAO School of Mathematics and Statistics Beijing Institute of Technology School of Mathematics and Computer Science Wuhan Polytechnic University Institute of Applied Mathematics Academy of Mathematics and Systems Science The Chinese Academy of Sciences School of Mathematics and Statistics Wuhan University Computational Science Hubei Key Laboratory Wuhan University

This paper is concerned with the inflow problem for one-dimensional compressible Navier-Stokes equations. For such a problem, Huang, Matsumura, and Shi showed in [4] that there exists viscous shock wave solution to the inflow problem and both the boundary layer solution, the viscous shock wave, and their superposition are time-asymptotically nonlinear stable provided that both the initial perturbation and the boundary velocity are assumed to be sufficiently small. The main purpose of this paper is to show that similar stability results still hold for a class of large initial perturbation which can allow the initial density to have large oscillations. The proofs are given by an elementary energy method and our main idea is to use the smallness of the strength of the viscous shock wave and the boundary velocity to control the possible growth of the solutions induced by the nonlinearity of the compressible Navier-Stokes equations and the inflow boundary *** key point in our analysis is to deduce the desired uniform positive lower and upper bounds on the density.

关键词： compressible Navier-Stokes equations inflow problem viscous shock wave large density oscillations

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Constant-time Quantum Algorithm for Homology Detection of Closed Curves

Constant-time Quantum Algorithm for Homology Detection of Cl...

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Optica Quantum 2.0 Conference and Exhibition, Quantum 2.0

作者： Nghiem, Nhat A. David Gu, Xianfeng Wei, Tzu-Chieh Department of Physics and Astronomy State University of New York at Stony Brook Stony BrookNY11794-3800 United States Department of Computer Science State University of New York at Stony Brook Stony BrookNY11794 United States Department of Applied Mathematics & Statistics State University of New York at Stony Brook Stony BrookNY11794 United States C. N. Yang Institute for Theoretical Physics State University of New York at Stony Brook Stony BrookNY11794-3840 United States Institute for Advanced Computational Science State University of New York at Stony Brook Stony BrookNY11794-5250 United States

Given an oracle that could query the inclusion of edges on a closed curve, we give a constant-time (single query usage) quantum algorithm that determines whether or not that curve is homologous to zero on a two-dimens... 详细信息

ISBN: (纸本)9781957171272

关键词： Biomedical imaging Machine learning Machine vision Phase estimation Quantum computation Sensor networks

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Ro-vibrational quenching calculations of C−2 in collision with H2

arXiv

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arXiv 2024年

作者： Giri, Kousik Mant, Barry Gianturco, Franco A. Wester, Roland Franz, Jan Biswas, Rupayan Lourderaj, Upakarasamy Sathyamurthy, Narayanasami Department of Computational Sciences Central University of Punjab Punjab Bathinda151401 India Institüt für Ionenphysik und Angewandte Physik Universität Innsbruck Technikerstr. 25 Innsbruck6020 Austria Institute of Physics and Applied Computer Science Faculty of Applied Physics and Mathematics Gdańsk University of Technology ul. Narutowicza 11/12 Gdańsk80-233 Poland Bhubaneswar OCC of Homi Bhabha National Institute Odisha Khurda752050 India Indian Institute of Science Education and Research SAS Nagar Punjab Mohali140306 India

The molecular anion C−2 has been of interest in the last few years as a candidate for laser cooling due to its electronic structure and favourable branching ratios to the ground electronic and vibrational state. Molecular hydrogen has been used by the Wester group in Innsbruck as a buffer gas to cool the molecule’s internal ro-vibrational motion. In the present work, we generate a new, five dimensional (5D) interaction potential for the system by considering the H2 as a rigid rotor and the C−2 as a rotating-vibrating diatomic molecule. We thereafter calculate the cross sections and rate coefficients for ro-vibrational inelastic collisions of C−2 with both para- and ortho-H2 on this new 5D ab initio potential energy surface using quantum scattering theory for the dynamics. The rates for vibrational quenching are obtained over the range of temperatures which covers the single value measured by the experiments. A comparison is also made with the earlier results using a simpler 3D interaction potential. Furthermore, para-H2 is found to be more efficient than ortho-H2 (with or without undergoing rotational excitation) in cooling C−2. The rate coefficients for cooling the anions has been computed by appropriately weighting the ortho- and para-H2 and compared with the available experimental result at 20 K. When the vibrational de-excitation rate coefficients are taken to be the ones not causing any concurrent rotational excitations in the final C−2 anions, the properly averaged results are found to get smaller and to become very close to the experimental measurements. The implications of these new results for laser cooling of C−2 are analyzed and discussed. © 2024, CC BY.

关键词： Molecules

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