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arXiv 2025年

作者： Grichener, Aldana Renzo, Mathieu Kerzendorf, Wolfgang E. Farmer, Rob de Mink, Selma E. Bellinger, Earl Patrick Chan, Chi-Kwan Chen, Nutan Farag, Ebraheem Justham, Stephen Steward Steward Observatory Department of Astronomy University of Arizona 933 North Cherry Avenue TucsonAZ85721 United States Max Planck Institute for Astrophysics Karl-Schwarzschild-Str. 1 Garching85748 Germany Department of Physics Technion Haifa3200003 Israel Department of Computational Mathematics Science and Engineering Michigan State University East LansingMI48824 United States Department of Physics and Astronomy Michigan State University East LansingMI48824 United States Ludwig-Maximilians-Universitat Munchen Geschwister-Scholl-Platz 1 Munchen80539 Germany Department of Astronomy Yale University New HavenCT06511 United States Steward Observatory Department of Astronomy University of Arizona 933 North Cherry Avenue TucsonAZ85721 United States Data Science Institute University of Arizona 1230 N. Cherry Avenue TucsonAZ85721 United States Program in Applied Mathematics University of Arizona 617 North Santa Rita TucsonAZ85721 United States Machine Learning Research Lab Volkswagen AG Munich38440 Germany

One of the main challenges in modeling massive stars to the onset of core collapse is the computational bottleneck of nucleosynthesis during advanced burning stages. The number of isotopes formed requires solving a large set of fully-coupled stiff ordinary differential equations (ODEs), making the simulations computationally intensive and prone to numerical instability. To overcome this barrier, we design a nuclear neural network (NNN) framework with multiple hidden layers to emulate nucleosynthesis calculations and conduct a proof-of-concept to evaluate its performance. The NNN takes the temperature, density and composition of a burning region as input and predicts the resulting isotopic abundances along with the energy generation and loss rates. We generate training sets for initial conditions corresponding to oxygen core depletion and beyond using large nuclear reaction networks, and compare the predictions of the NNNs to results from a commonly used small net. We find that the NNNs improve the accuracy of the electron fraction by 280 − 660 % and the nuclear energy generation by 250 − 750 %, consistently outperforming the small network across all timesteps. They also achieve significantly better predictions of neutrino losses on relatively short timescales, with improvements ranging from 100 − 106 %. While further work is needed to enhance their accuracy and applicability to different stellar conditions, integrating NNN trained models into stellar evolution codes is promising for facilitating large-scale generation of core-collapse supernova (CCSN) progenitors with higher physical fidelity. © 2025, CC BY.

关键词： Nucleosynthesis

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TSP cuts which do not conform to the template paradigm 5th

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5th International Conference on Mobile Agents, MA 2001

作者： Applegate, David Bixby, Robert Chvátal, Vašek Cook, William Algorithms and Optimization Department AT and T Labs – Research Florham ParkNJ07932 United States Computational and Applied Mathematics Rice University HoustonTX77005 United States Department of Computer Science Rutgers University PiscatawayNJ08854 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

ISBN: (纸本)3540428771

The first computer implementation of the Dantzig-Fulkerson- Johnson cutting-plane method for solving the traveling salesman problem, written by Martin, used subtour inequalities as well as cutting planes of Gomory’s type. The practice of looking for and using cuts that match prescribed templates in conjunction with Gomory cuts was continued in computer codes of Miliotis, Land, and Fleischmann. Gr¨otschel, Padberg, and Hong advocated a different policy, where the template paradigm is the only source of cuts;furthermore, they argued for drawing the templates exclusively from the set of linear inequalities that induce facets of the TSP polytope. These policies were adopted in the work of Crowder and Padberg, in the work of Gr¨otschel and Holland, and in the work of Padberg and Rinaldi;their computer codes produced the most impressive computational TSP successes of the nineteen eighties. Eventually, the template paradigm became the standard frame of reference for cutting planes in the TSP. The purpose of this paper is to describe a technique for finding cuts that disdains all understanding of the TSP polytope and bashes on regardless of all prescribed templates. Combining this technique with the traditional template approach was a crucial step in our solutions of a 13,509-city TSP instance and a 15,112-city TSP instance. © Springer-Verlag Berlin Heidelberg 2001.

关键词： Traveling salesman problem

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Local order metrics for many-particle systems across length scales

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Physical Review Research 2024年第3期6卷 033262页

作者： Charles Emmett Maher Salvatore Torquato Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics

Formulating order metrics that sensitively quantify the degree of order/disorder in many-particle systems in d-dimensional Euclidean space Rd across length scales is an outstanding challenge in physics, chemistry, and materials science. Since an infinite set of n-particle correlation functions is required to fully characterize a system, one must settle for a reduced set of structural information, in practice. We initiate a program to use the local number variance σN2(R) associated with a spherical sampling window of radius R (which encodes pair correlations) and an integral measure derived from it ΣN(Ri,Rj) that depends on two specified radial distances Ri and Rj. Across the first three space dimensions (d=1,2,3), we find these metrics can sensitively describe and categorize the degree of order/disorder of 41 different models of antihyperuniform, nonhyperuniform, disordered hyperuniform, and ordered hyperuniform many-particle systems at a specified length scale R. Using our local variance metrics, we demonstrate the importance of assessing order/disorder with respect to a specific value of R. These local order metrics could also aid in the inverse design of structures with prescribed length-scale-specific degrees of order/disorder that yield desired physical properties. In future work, it would be fruitful to explore the use of higher-order moments of the number of points within a spherical window of radius R [S. Torquato et al., Phys. Rev. X 11, 021028 (2021)] to devise even more sensitive order metrics.

关键词： Classical statistical mechanics

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Accelerating the complex Hessenberg QR algorithm with the csx600 floating-point coprocessor

Accelerating the complex Hessenberg QR algorithm with the cs...

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19th IASTED International Conference on Parallel and Distributed Computing and Systems

作者： Yamamoto, Yusaku Miyata, Takafumi Nakamura, Yoshimasa Dept. of Computational Science and Engineering Graduate School of Engineering Nagoya University Nagoya 464-8603 Japan Dept. of Applied Mathematics and Physics Graduate School of Informatics Kyoto University/ JST SORST Kyoto 606-8501 Japan

ISBN: (纸本)9780889867048

In this paper, we show how to speed up the Hessenberg QR algorithm for computing the eigenvalues of a dense complex nonsymmetric matrix using the CSX600 floating-point coprocessor. Our approach is based on the small-bulge multishift QR algorithm proposed by Braman et al. This algorithm can perform a major part of the computation in the form of matrix multiplication and is therefore very suited to high performance architectures. However, to exploit the potential of the CSX600, the number of shifts must be increased to more than two hundred. In that case, the parts other than matrix multiplication begin to occupy a considerable percentage of the execution time, thereby limiting the speedup. To solve this problem, we focus on two most time-consuming parts in the algorithm except for matrix multiplication: accumulation of bulge-chasing transformations and solution of a decoupled small eigenproblem. We reconstruct the former as a recursive algorithm and apply a blocking technique to the latter. This enables these parts to be computed also using matrix multiplication. As a result of these optimizations, we obtained up to 3.8 times speedup with the CSX600 processor over a 3.2GHz Xeon processor when computing the eigenvalues of a 12,000 × 12,000 complex Hessenberg matrix.

关键词： Coprocessor

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Modelling of Motion of a Volvox Colony using Many-Body System and Its Qualitative Comparison with Observations 9

Modelling of Motion of a Volvox Colony using Many-Body Syste...

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9th Asian Physics Symposium 2021, APS 2021

作者： Dini, Septian Ulan Nurafni, Sevi Fairuza, Achmad Zacky Taufik, Intan Master Program in Physics Faculty of Mathematics and Natural Science InstitutTeknologi Bandung Bandung40132 Indonesia Master Program in Computational Science Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung Bandung40132 Indonesia Master Program in Nanotechnology Graduate School Institut Teknologi Bandung Bandung40132 Indonesia School of Life Science and Technology Institut Teknologi Bandung40132 Indonesia

Approximately 500-60,000 volvox cells constructed a colony with a spherical or elliptical hollow form. Each cell can use its flagella to move. For a colony of hundred cells to perform a direct motion, there must be a coordination of the flagella. In this work, we assume that the cells already form the spherical colony and can perform some simple motion types, i.e., translational (TRAN), roll (ROLL), spin (SPIN), and superposition of the motions, and neglect detail of each flagellum. It is possible to map each cell in the colony using angular positions with a constant radius R and different θ _i and φ_i, where i = 1, 2,..., N with N is the number of cells constructing a colony. The center of the colony is R = (x, y, z). The TRAN mode can be obtained, wherex(t) = x(0) + vxt, y(t) = y(0) + vyt, z(t) = z(0) +vzt, ROLLmode with θ(t) = ω(0) + ωθt and SPIN with φ(t) = ω(0) + ωφt. Through the available observation video, the model of volvox colony motion is also shown to have a qualitative agreement. © Published under licence by IOP Publishing Ltd.

关键词： Cells

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Demystifying Disagreement-on-the-Line in High Dimensions 40

Demystifying Disagreement-on-the-Line in High Dimensions

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40th International Conference on Machine Learning, ICML 2023

作者： Lee, Donghwan Moniri, Behrad Huang, Xinmeng Dobriban, Edgar Hassani, Hamed Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania PA United States Department of Electrical and Systems Engineering University of Pennsylvania PA United States Department of Statistics and Data Science University of Pennsylvania PA United States

Evaluating the performance of machine learning models under distribution shifts is challenging, especially when we only have unlabeled data from the shifted (target) domain, along with labeled data from the original (source) domain. Recent work suggests that the notion of disagreement, the degree to which two models trained with different randomness differ on the same input, is a key to tackling this problem. Experimentally, disagreement and prediction error have been shown to be strongly connected, which has been used to estimate model performance. Experiments have led to the discovery of the disagreement-on-the-line phenomenon, whereby the classification error under the target domain is often a linear function of the classification error under the source domain;and whenever this property holds, disagreement under the source and target domain follow the same linear relation. In this work, we develop a theoretical foundation for analyzing disagreement in high-dimensional random features regression;and study under what conditions the disagreement-on-the-line phenomenon occurs in our setting. Experiments on CIFAR-10-C, Tiny ImageNet-C, and Camelyon17 are consistent with our theory and support the universality of the theoretical findings. © 2023 Proceedings of Machine Learning Research. All rights reserved.

关键词： Errors

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Semi-analytical finite element method applied for characterizing micropolar fibrous composites

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applied mathematics and Mechanics(English Edition) 2024年第12期45卷 2147-2164页

作者： J.A.OTERO Y.ESPINOSA-ALMEYDA R.RODRIGUEZ-RAMOS J.MERODIO School of Engineering and Sciences Monterrey Institute of TechnologyEstado de Mexico 52926Mexico Institute of Engineering and Technology Autonomous University of Ciudad JuarezCiudad JuarezChihuahua 32310Mexico Postgraduate Program in Computational Modeling in Science and Technology Federal Fluminense UniversityRıo de Janeiro 27255-125Brazil Faculty of Mathematics and Computer Science University of HavanaLa Habana 10400Cuba Department of Mathematics Applied to ICT School of Informatics Systems EngineeringTechnical University of MadridMadrid 28031Spain

A semi-analytical finite element method(SAFEM),based on the two-scale asymptotic homogenization method(AHM)and the finite element method(FEM),is implemented to obtain the effective properties of two-phase fiber-reinforced composites(FRCs).The fibers are periodically distributed and unidirectionally aligned in a homogeneous *** framework addresses the static linear elastic micropolar problem through partial differential equations,subject to boundary conditions and perfect interface contact *** mathematical formulation of the local problems and the effective coefficients are presented by the *** local problems obtained from the AHM are solved by the FEM,which is denoted as the *** numerical results are provided,and the accuracy of the solutions is analyzed,indicating that the formulas and results obtained with the SAFEM may serve as the reference points for validating the outcomes of experimental and numerical computations.

关键词： semi-analytical approach fiber-reinforced composite(FRC) effective property finite element method(FEM) asymptotic homogenization method(AHM) micropolar elasticity

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A Theory of Non-Linear Feature Learning with One Gradient Step in Two-Layer Neural Networks 41

A Theory of Non-Linear Feature Learning with One Gradient St...

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41st International Conference on Machine Learning, ICML 2024

作者： Moniri, Behrad Lee, Donghwan Hassani, Hamed Dobriban, Edgar Department of Electrical and Systems Engineering University of Pennsylvania PA United States Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania PA United States Department of Statistics and Data Science University of Pennsylvania PA United States

Feature learning is thought to be one of the fundamental reasons for the success of deep neural networks. It is rigorously known that in two-layer fully-connected neural networks under certain conditions, one step of gradient descent on the first layer can lead to feature learning;characterized by the appearance of a separated rank-one component-spike-in the spectrum of the feature matrix. However, with a constant gradient descent step size, this spike only carries information from the linear component of the target function and therefore learning non-linear components is impossible. We show that with a learning rate that grows with the sample size, such training in fact introduces multiple rank-one components, each corresponding to a specific polynomial feature. We further prove that the limiting large-dimensional and large sample training and test errors of the updated neural networks are fully characterized by these spikes. By precisely analyzing the improvement in the training and test errors, we demonstrate that these non-linear features can enhance learning. Copyright 2024 by the author(s)

关键词： Adversarial machine learning

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Positron-Impact Excitation of Hydrogen Atoms in Debye Plasmas

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Chinese Physics Letters 2010年第1期27卷 111-114页

作者：张松斌祁月盈屈一至陈向军王建国 Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics University of Science and Technology of China Hefei 230026 Key Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics PO Box 8009 Beijing 100088 School of Electrical Engineering Jiaxing University Jiaxing 314001 College of Material Sciences and Optoelectronic Technology Graduate School of the Chinese Academy of Sciences PO Box 4588 Beijing 100049

The positron-impact excitation of hydrogen atoms embedded in plasma environments is investigated using the close-coupling approximation from the low to intermediate energy region without including any positronium formation channel, and the excitation cross sections for 1s→2s, 1s→2p and 2s→2p processes are calculated in a wide Debye parameter range. The screening interactions, described by the Debye-Hückel model, decrease the coupling matrix elements, resulting in the reduction of the excitation cross sections from a few percent to one magnitude of ten. This will alter remarkably the spectroscopy of hydrogen in intensity and position, which should be considered in the simulation and diagnostics under some specific plasma conditions.

关键词： Chinese climate network complex systems small world community

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Solving optimal feedback control of Chinese population dynamics by viscosity solution approach

Solving optimal feedback control of Chinese population dynam...

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作者： Sun, Bing Guo, Bao-Zhu Institute of Systems Science Academy of Mathematics and System Sciences Beijing 100080 China Graduate School Chinese Academy of Sciences Beijing 100039 China School of Computational and Applied Mathematics University of the Witwatersrand Private 3 Wits 2050 Johannesburg South Africa

ISBN: (纸本)008045108X

in this paper, the optimal birth feedback control of a McKendrick type age-structured population dynamic system based on the Chinese population dynamics is considered. Adopt the dynamic programming approach, to obtain the Hamilton-Jacobi-Bellman equation and prove that the value function is its viscosity solution. By the derived classical verification theorem, the optimal birth feedback control is found explicitly. A finite difference scheme is designed to solving numerically the optimal birth feedback control. Under the same constraint, by comparing with different controls, the validity of the optimality of the obtained control is verified numerically. Copyright © 2005 IFAC.

关键词： Dynamic programming

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