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arXiv 2022年

作者： Canatar, Abdulkadir Peters, Evan Pehlevan, Cengiz Wild, Stefan M. Shaydulin, Ruslan Center for Computational Neuroscience Flatiron Institute New YorkNY10010 United States Department of Physics University of Waterloo WaterlooONN2L 3G1 Canada School of Engineering and Applied Sciences Harvard University CambridgeMA0213 United States Applied Mathematics & Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Global Technology Applied Research JPMorgan Chase New YorkNY10017 United States

Quantum computers are known to provide speedups over classical state-of-the-art machine learning methods in some specialized settings. For example, quantum kernel methods have been shown to provide an exponential speedup on a learning version of the discrete logarithm problem. Understanding the generalization of quantum models is essential to realizing similar speedups on problems of practical interest. Recent results demonstrate that generalization is hindered by the exponential size of the quantum feature space. Although these results suggest that quantum models cannot generalize when the number of qubits is large, in this paper we show that these results rely on overly restrictive assumptions. We consider a wider class of models by varying a hyperparameter that we call quantum kernel bandwidth. We analyze the large-qubit limit and provide explicit formulas for the generalization of a quantum model that can be solved in closed form. Specifically, we show that changing the value of the bandwidth can take a model from provably not being able to generalize to any target function to good generalization for well-aligned targets. Our analysis shows how the bandwidth controls the spectrum of the kernel integral operator and thereby the inductive bias of the model. We demonstrate empirically that our theory correctly predicts how varying the bandwidth affects generalization of quantum models on challenging datasets, including those far outside our theoretical assumptions. We discuss the implications of our results for quantum advantage in machine learning. © 2022, CC BY.

关键词： Bandwidth

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The quenching-activation behavior of the gradient descent dynamics for two-layer neural network models

arXiv

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arXiv 2020年

作者： Ma, Chao Wu, Lei Weinan, E. Department of Mathematics Princeton University Program in Applied and Computational Mathematics Princeton University Institute of Big Data Research

A numerical and phenomenological study of the gradient descent (GD) algorithm for training two-layer neural network models is carried out for different parameter regimes when the target function can be accurately approximated by a relatively small number of neurons. It is found that for Xavier-like initialization, there are two distinctive phases in the dynamic behavior of GD in the under-parametrized regime: An early phase in which the GD dynamics follows closely that of the corresponding random feature model and the neurons are effectively quenched, followed by a late phase in which the neurons are divided into two groups: a group of a few "activated" neurons that dominate the dynamics and a group of background (or "quenched") neurons that support the continued activation and deactivation process. This neural network-like behavior is continued into the mildly over-parametrized regime, where it undergoes a transition to a random feature-like behavior. The quenching-activation process seems to provide a clear mechanism for "implicit regularization". This is qualitatively different from the dynamics associated with the "mean-field" scaling where all neurons participate equally and there does not appear to be qualitative changes when the network parameters are changed. Copyright © 2020, The Authors. All rights reserved.

关键词： Gradient methods

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COVID-19 Infected Lung Computed Tomography Segmentation and Supervised Classification Approach

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Computers, Materials & Continua 2021年第7期68卷 391-407页

作者： Aqib Ali Wali Khan Mashwani Samreen Naeem Muhammad Irfan Uddin Wiyada Kumam Poom Kumam Hussam Alrabaiah Farrukh Jamal Christophe Chesneau Department of Computer Science Concordia College BahawalpurBahawalpur63100Pakistan Department of Computer Science&IT Glim Institute of Modern StudiesBahawalpur63100Pakistan Institute of Numerical Sciences Kohat University of Science&TechnologyKohat26000Pakistan Institute of Computing Kohat University of Science and TechnologyKohat26000Pakistan Program in Applied Statistics Department of Mathematics and Computer ScienceFaculty of Science and TechnologyRajamangala University of Technology ThanyaburiThanyaburi12110Thailand Departments of Mathematics Faculty of ScienceCenter of Excellence in Theoretical and Computational Science(TaCS-CoE)&KMUTT Fixed Point Research LaboratoryRoom SCL 802 Fixed Point LaboratoryScience Laboratory BuildingKing Mongkut’s University of Technology Thonburi(KMUTT)Bangkok10140Thailand Department of Medical Research China Medical University HospitalTaichung40402Taiwan College of Engineering Al Ain UniversityAl Ain64141United Arab Emirates Department of Mathematics Tafila Technical UniversityTafila66110Jordan Department of Statistics The Islamia University of BahawalpurBahawalpur63100Pakistan 11Department of MathematicsUniversitéde CaenLMNOCaen14032France

The purpose of this research is the segmentation of lungs computed tomography(CT)scan for the diagnosis of COVID-19 by using machine learning *** dataset contains data from patients who are prone to the *** contains three types of lungs CT images(Normal,Pneumonia,and COVID-19)collected from two different sources;the first one is the Radiology department of Nishtar Hospital Multan and Civil Hospital Bahawalpur,Pakistan,and the second one is a publicly free available medical imaging database known as *** the preprocessing,a novel fuzzy c-mean automated region-growing segmentation approach is deployed to take an automated region of interest(ROIs)and acquire 52 hybrid statistical features for each ***,12 optimized statistical features are selected via the chi-square feature reduction *** the classification,five machine learning classifiers named as deep learning J4,multilayer perceptron,support vector machine,random forest,and naive Bayes are deployed to optimize the hybrid statistical features *** is observed that the deep learning J4 has promising results(sensitivity and specificity:0.987;accuracy:98.67%)among all the deployed *** a complementary study,a statistical work is devoted to the use of a new statistical model to fit the main datasets of COVID-19 collected in Pakistan.

关键词： COVID-19 machine learning fuzzy c-mean deep learning J4

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Bayesian calibration of viscous anisotropic hydrodynamic simulations of heavy-ion collisions

arXiv

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arXiv 2023年

作者： Liyanage, Dananjaya Sürer, Özge Plumlee, Matthew Wild, Stefan M. Heinz, Ulrich Department of Physics The Ohio State University ColumbusOH43210 United States Department of Information Systems and Analytics Miami University OxfordOH45056 United States Northwestern University EvanstonIL60208 United States Industrial Engineering and Management Sciences Department Northwestern University EvanstonIL60208 United States Applied Mathematics & Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States

Due to large pressure gradients at early times, standard hydrodynamic model simulations of relativistic heavy-ion collisions do not become reliable until O(1) fm/c after the collision. To address this one often introduces a pre-hydrodynamic stage that models the early evolution microscopically, typically as a conformal, weakly interacting gas. In such an approach the transition from the pre-hydrodynamic to the hydrodynamic stage is discontinuous, introducing considerable theoretical model ambiguity. Alternatively, fluids with large anisotropic pressure gradients can be handled macroscopically using the recently developed Viscous Anisotropic Hydrodynamics (VAH). In high-energy heavy-ion collisions VAH is applicable already at very early times, and at later times transitions smoothly into conventional second-order viscous hydrodynamics (VH). We present a Bayesian calibration of the VAH model with experimental data for Pb–Pb collisions at the LHC at √sNN = 2.76 TeV. We find that the VAH model has the unique capability of constraining the specific viscosities of the QGP at higher temperatures than other previously used models. © 2023, CC BY.

关键词： Hydrodynamics

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A new result for the local well-posedness of the Camassa-Holm type equations in critial Besov spaces (Equation presented)

arXiv

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arXiv 2021年

作者： Ye, Weikui Yin, Zhaoyang Guo, Yingying Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing100088 China Department of Mathematics Sun Yat-Sen University Guangzhou510275 China School of Mathematics and Big Data Foshan University Foshan528000 China

For the famous Camassa-Holm equation, the well-posedness in (Equation presented) with 1 ≤ p ≤ 2 and the ill-posedness in (Equation presented) with (Equation presented) had been studied in [23,24,31]. That is to say,... 详细信息

关键词： Banach spaces

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First-principles determination of the phonon-point defect scattering and thermal transport due to fission products in ThO2

arXiv

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arXiv 2023年

作者： Malakkal, Linu Katre, Ankita Zhou, Shuxiang Jiang, Chao Hurley, David H. Marianetti, Chris A. Khafizov, Marat Computational Mechanics and Materials Department Idaho National Laboratory Idaho FallsID83415 United States Department of Scientific Computing Modeling and Simulation SP Pune University Pune411007 India Idaho National Laboratory Idaho FallsID83415 United States Department of Applied Physics and Applied Mathematics Columbia University 500 West 120th Street New YorkNY10027 United States Department of Mechanical and Aerospace Engineering The Ohio State University 201 West 19th Ave ColumbusOH43210 United States

This work presents the first-principles calculations of the lattice thermal conductivity degradation due to point defects in thorium dioxide using an iterative solution of the Peirels-Boltzmann transport equation. We have used the non-perturbative Green's function methodology to compute the phononpoint defect scattering rates that consider the local distortion around the point defect, including the mass difference changes, interatomic force constants, and structural relaxation near the point defects. The point defects considered in this work include the vacancy of thorium (VTh) and oxygen (VO), substitutions of helium (HeTh), krypton (KrTh), zirconium (ZrTh), iodine (ITh) and xenon (XeTh) in the thorium site, and the three different configurations of the Schottky defects. The results of the phonon-defect scattering rate reveal that, among all the considered intrinsic defects, the thorium vacancy and helium substitution in the thorium site scatter the phonon most due to the substantial changes in the force constant and structural distortions. The scattering of phonons due to the substitutional defects unveils that the zirconium atom scatters phonons the least, followed by xenon, iodine, krypton, and helium. This is contrary to the intuition that the scattering strength follows HeTh > KrTh > ZrTh > ITh > XeTh based on the mass difference. This striking difference in the zirconium phonon scattering is due to the local chemical environment changes. Zirconium is an electropositive element with valency similar to thorium and, therefore, can bond with the oxygen atoms, thus creating less force constant variance compared to iodine, an electronegative element, and the noble gases helium, xenon, and krypton. These results can serve as a benchmark for analytical models and help the engineering-scale modeling effort for nuclear design. © 2023, CC BY.

关键词： Boltzmann equation

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Exclusion Volumes of Convex Bodies in High Space Dimensions: Applications to Virial Coefficients and Continuum Percolation

arXiv

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arXiv 2022年

作者： Torquato, Salvatore Jiao, Yang Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Institute of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Materials Science and Engineering Arizona State University TempeAZ85287 United States Department of Physics Arizona State University TempeAZ85287 United States

Using the concepts of mixed volumes and quermassintegrals of convex geometry, we derive an exact formula for the exclusion volume vex(K) for a general convex body K that applies in any space dimension. While our main interests concern the rotationally-averaged exclusion volume of a convex body with respect to another convex body, we also describe some results for the exclusion volumes for convex bodies with the same orientation. We show that the sphere minimizes the dimensionless exclusion volume vex(K)/v(K) among all convex bodies, whether randomly oriented or uniformly oriented, for any d, where v(K) is the volume of K. When the bodies have the same orientation, the simplex maximizes the dimensionless exclusion volume for any d with a large-d asymptotic scaling behavior of 22d/d3/2, which is to be contrasted with the corresponding scaling of 2d for the sphere. We present explicit formulas for quermassintegrals W0(K), . . ., Wd(K) for many different nonspherical convex bodies, including cubes, parallelepipeds, regular simplices, cross-polytopes, cylinders, spherocylinders, ellipsoids as well as lower-dimensional bodies, such as hyperplates and line segments. These results are utilized to determine the rotationally-averaged exclusion volume vex(K) for these convex-body shapes for dimensions 2 through 12. While the sphere is the shape possessing the minimal dimensionless exclusion volume, we show that, among the convex bodies considered that are sufficiently compact, the simplex possesses the maximal vex(K)/v(K) with a scaling behavior of 21.6618...d. Subsequently, we apply these results to determine the corresponding second virial coefficient B2(K) of the aforementioned hard hyperparticles. Our results are also applied to compute estimates of the continuum percolation threshold ηc derived previously by the authors for systems of identical overlapping convex bodies. We conjecture that overlapping spheres possess the maximal value of ηc among all identical nonzero-vol

关键词： Spheres

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PPDONet: Deep Operator Networks for Fast Prediction of Steady-State Solutions in Disk-Planet Systems

arXiv

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arXiv 2023年

作者： Mao, Shunyuan Dong, Ruobing Lu, Lu Yi, Kwang Moo Wang, Sifan Perdikaris, Paris Department of Physics and Astronomy University of Victoria VictoriaBCV8P 5C2 Canada Department of Chemical and Biomolecular Engineering University of Pennsylvania PhiladelphiaPA19104 United States Department of Computer Science University of British Columbia VancouverBCV6T 1Z4 Canada Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA19104 United States Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania PhiladelphiaPA19104 United States

We develop a tool, which we name Protoplanetary Disk Operator Network (PPDONet), that can predict the solution of disk-planet interactions in protoplanetary disks in real-time. We base our tool on Deep Operator Networks (DeepONets), a class of neural networks capable of learning non-linear operators to represent deterministic and stochastic differential equations. With PPDONet we map three scalar parameters in a disk-planet system - the Shakura & Sunyaev viscosity α, the disk aspect ratio h0, and the planet-star mass ratio q - to steady-state solutions of the disk surface density, radial velocity, and azimuthal velocity. We demonstrate the accuracy of the PPDONet solutions using a comprehensive set of tests. Our tool is able to predict the outcome of disk-planet interaction for one system in less than a second on a laptop. A public implementation of PPDONet is available at https://***/smao-astro/PPDONet. Copyright © 2023, The Authors. All rights reserved.

关键词： Open source software

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Hybrid Auxiliary Field Quantum Monte Carlo for Molecular Systems

arXiv

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arXiv 2022年

作者： Chen, Yixiao Zhang, Linfeng Weinan, E. Car, Roberto Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States AI for Science Institute Beijing100080 China DP Technology Beijing100080 China Center for Machine Learning Research School of Mathematical Sciences Peking University Beijing100084 China Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States

We propose a quantum Monte Carlo approach to solve the many-body Schrödinger equation for the electronic ground state. The method combines optimization from variational Monte Carlo and propagation from auxiliary field quantum Monte Carlo, in a way that significantly alleviates the sign problem. In application to molecular systems, we obtain highly accurate results for configurations dominated by either dynamic or static electronic correlation. Copyright © 2022, The Authors. All rights reserved.

关键词： Monte Carlo methods

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Uniform resolvent estimates for critical magnetic Schrödinger operators in 2D

arXiv

引用

arXiv 2021年

作者： Fanelli, Luca Zhang, Junyong Zheng, Jiqiang Ikerbasque Universidad del País Vasco Departamento de Matemáticas Bilbao Spain Department of Mathematics Beijing Institute of Technology Beijing100081 China Institute of Applied Physics and Computational Mathematics Beijing100088 China

We study the Lp−Lq-type uniform resolvent estimates for 2D-Schrödinger operators in scaling-critical magnetic fields, involving the Aharonov-Bohm model as a main example. As an application, we prove localization estimates for the eigenvalue of some non self-adjoint zero-order perturbations of the magnetic Hamiltonian. © 2021, CC BY.

关键词： Magnetism

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