检索结果-内蒙古大学图书馆

An Iterative Thresholding Method for the Minimum Compliance Problem

Communications in Computational Physics 2023年第4期33卷 1189-1216页

作者： Luyu Cen Wei Hu Dong Wang Xiaoping Wang Department of Mathematics Hong Kong University of Science and TechnologyClear Water BayKowloonHong KongChina The Program in Applied and Computational Mathematics Princeton UniversityPrincetonNew JerseyUSA School of Science and Engineering The Chinese University of Hong KongShenzhenGuangdong 518172China Shenzhen International Center for Industrial and Applied Mathematics Shenzhen Research Institute of Big DataGuangdong 518172China

In this paper,we propose a simple energy decaying iterative thresholding algorithm to solve the two-phase minimum compliance *** material domain is implicitly represented by its characteristic function,and the problem is formulated into a minimization problem by the principle of minimum complementary *** prove that the energy is decreasing in each *** effective continuation schemes are proposed to avoid trapping into the local *** results on 2D isotropic linear material demonstrate the effectiveness of the proposed methods.

关键词： Minimum compliance convolution thresholding linear elasticity

来源：评论

学校读者我要写书评

暂无评论

Bernstein Operational Matrix with Error Analysis for Solving High Order Delay Differential Equations

引用

International Journal of applied and Computational mathematics 2017年第3期3卷 1749-1762页

作者： Bataineh, A. Isik, O. Aloushoush, N. Shawagfeh, N. Department of Mathematics Faculty of Science Al-Balqa’ Applied University Al Salt 19117 Jordan Elementary Mathematics Education Program Faculty of Education Mugla Sitki Kocman University Mugla 48000 Turkey Department of Mathematics Faculty of Science University of Jordan Amman Jordan

In this paper, we propose a numerical method based on Bernstein polynomials and their operational matrices for solving both linear and non-linear delay differential equations (DDEs). The Bernstein operational matrices for differentiation and delay functions are introduced. The aim is to reduce the DDEs to a set of algebraic equations. Moreover If the exact solution is polynomial, then the exact solution set will be obtained. Even the exact solution is unknown, an upper bound based on the regularity of the exact solution will be obtained. By using the residual correction procedure and the error analysis of the four- and five-order Runge–Kutta method (RK45) the absolute errors may be estimated and the approximate solution can be corrected. Some examples are given to demonstrate the validity and applicability of the new method and a comparison is made with the existing results. © 2016, Springer India Pvt. Ltd.

关键词： Bernstein polynomials Delay differential equation Nonlinearity Operational matrix of differentiation

来源：评论

学校读者我要写书评

暂无评论

Nuclear Neural Networks: Emulating Late Burning Stages in Core Collapse Supernova Progenitors

arXiv

引用

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

来源：评论

学校读者我要写书评

暂无评论

Solving Algebraic Riccati Equations via Proper Orthogonal Decomposition

引用

IFAC Proceedings Volumes 2014年第3期47卷 7767-7772页

作者： Boris Kramer Department of Mathematics Interdisciplinary Center for Applied Mathematics Virginia Tech Blacksburg VA 24061 USA

In this paper we present a method to solve algebraic Riccati equations by employing a projection method based on Proper Orthogonal Decomposition. The method only requires simulations of linear systems to compute the solution of a Lyapunov equation. The leading singular vectors are then used to construct a projector which is employed to produce a reduced order system. We compare this approach to an extended Krylov subspace method and a standard Gramian based method.

关键词：

来源：评论

学校读者我要写书评

暂无评论

Stability of pairwise social dilemma games: Destructive agents, constructive agents, and their joint effects

引用

Physical Review E 2024年第3期110卷 034307页

作者： Khadija Khatun Chen Shen Lei Shi Jun Tanimoto Interdisciplinary Graduate School of Engineering Sciences Department of Applied Mathematics Faculty of Engineering Sciences School of Statistics and Mathematics

Destructive agents, who opt out of the game and indiscriminately harm others, paradoxically foster cooperation, representing an intriguing variant of the voluntary participation strategy. Yet, their impact on cooperation remains inadequately understood, particularly in the context of pairwise social dilemma games and in comparison to their counterparts, constructive agents, who opt out of the game but indiscriminately benefit others. Furthermore, little is known about the combined effects of both agent types on cooperation dynamics. Using replicator dynamics in infinite and well-mixed populations, we find that contrary to their role in facilitating cooperation in multiplayer games, destructive agents fail to encourage cooperation in pairwise social dilemmas. Instead, they replace defection in the prisoners' dilemma and stag-hunt games. Similarly, in the chicken game, they can destabilize or replace the mixed equilibrium of cooperation and defection, undermining cooperation in the harmony (trivial) game. Conversely, constructive agents, when their payoffs exceed their contributions to opponents, can exhibit effects similar to destructive agents. However, if their payoffs are lower, while they destabilize defection in prisoners' dilemma and stag-hunt games, they do not disrupt the cooperation equilibrium in harmony games and have a negligible impact on the coexistence of cooperation in chicken games. The combination of destructive and constructive agents does not facilitate cooperation, but instead generates complex evolutionary dynamics, including bistable, tristable, and quadstable states, with outcomes contingent on their relative payoffs and game types. These results, taken together, enhance our understanding of the impact of the voluntary participation mechanism on cooperation, contributing to a more comprehensive understanding of its influence.

关键词： Game theory models

来源：评论

学校读者我要写书评

暂无评论

Learning representation and control in continuous Markov decision processes

Learning representation and control in continuous Markov dec...

引用

21st National Conference on Artificial Intelligence and the 18th Innovative Applications of Artificial Intelligence Conference, AAAI-06/IAAI-06

作者： Mahadevan, Sridhar Maggioni, Mauro Ferguson, Kimberly Osentoski, Sarah Department of Computer Science University of Massachusetts 140 Governor's Drive Amherst MA 01003 Program in Applied Mathematics Department of Mathematics Yale University New Haven CT 06510

ISBN: (纸本)1577352815

This paper presents a novel framework for simultaneously learning representation and control in continuous Markov decision processes. Our approach builds on the framework of proto-value functions, in which the underlying representation or basis functions are automatically derived from a spectral analysis of the state space manifold. The proto-value functions correspond to the eigenfunctions of the graph Laplacian. We describe an approach to extend the eigenfunctions to novel states using the Nyström extension. A least-squares policy iteration method is used to learn the control policy, where the underlying subspace for approximating the value function is spanned by the learned proto-value functions. A detailed set of experiments is presented using classic benchmark tasks, including the inverted pendulum and the mountain car, showing the sensitivity in performance to various parameters, and including comparisons with a parametric radial basis function method. Copyright © 2006, American Association for Artificial Intelligence (***). All rights reserved.

关键词： Knowledge representation

来源：评论

学校读者我要写书评

暂无评论

Renormalization theory for eddy diffusivity in turbulent transport

引用

Physical Review Letters 1992年第20期68卷 3028-3028页

作者： Marco Avellaneda Andrew J. Majda Department of Mathematics Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544

We examine the derivation of eddy-diffusivity equations for transport of passive scalars in a turbulent velocity field. Our main contention is that, in the long-time–large-distance limit, the eddy-diffusivity equations can take very different forms according to the statistical properties of the subgrid velocity, and that these equations depend very sensitively on the interplay between spatial and temporal velocity fluctuations. Such crossovers can be represented in a ‘‘phase diagram’’ involving two relevant statistical parameters. Strikingly, the Kolmogorov-Obukhov statistical theory is shown to lie on a phase-transition boundary.

关键词：

来源：评论

学校读者我要写书评

暂无评论

Coarse-grained spectral projection: A deep learning assisted approach to quantum unitary dynamics

引用

Physical Review B 2021年第2期103卷 024304-024304页

作者： Pinchen Xie Weinan E Department of Mathematics and Program in Applied and Computational Mathematics Princeton University New Jersey 08544 USA

We propose the coarse-grained spectral projection method (CGSP), a deep learning assisted approach for tackling quantum unitary dynamic problems with an emphasis on quench dynamics. We show that CGSP can extract spectral components of many-body quantum states systematically with a sophisticated neural network quantum ansatz. CGSP fully exploits the linear unitary nature of the quantum dynamics and is potentially superior to other quantum Monte Carlo methods for ergodic dynamics. Preliminary numerical results on one-dimensional XXZ models with periodic boundary conditions are carried out to demonstrate the practicality of CGSP.

关键词： Quantum quench Quantum statistical mechanics Nonequilibrium lattice models Machine learning Monte Carlo methods

来源：评论

学校读者我要写书评

暂无评论

Value function approximation with diffusion wavelets and Laplacian eigenfunctions

Value function approximation with diffusion wavelets and Lap...

引用

2005 Annual Conference on Neural Information Processing Systems, NIPS 2005

作者： Mahadevan, Sridhar Maggioni, Mauro Department of Computer Science University of Massachusetts Amherst MA 01003 United States Program in Applied Mathematics Department of Mathematics Yale University New Haven CT 06511 United States

ISBN: (纸本)9780262232531

We investigate the problem of automatically constructing efficient representations or basis functions for approximating value functions based on analyzing the structure and topology of the state space. In particular, two novel approaches to value function approximation are explored based on automatically constructing basis functions on state spaces that can be represented as graphs or manifolds: one approach uses the eigenfunctions of the Laplacian, in effect performing a global Fourier analysis on the graph;the second approach is based on diffusion wavelets, which generalize classical wavelets to graphs using multiscale dilations induced by powers of a diffusion operator or random walk on the graph. Together, these approaches form the foundation of a new generation of methods for solving large Markov decision processes, in which the underlying representation and policies are simultaneously learned.

关键词： Diffusion

来源：评论

学校读者我要写书评

暂无评论

Optimization of second order spatially distributed systems with multiple interconnected actuator/sensor pairs

引用

IFAC-PapersOnLine 2016年第18期49卷 476-481页

作者： Demetriou, Michael A. Fahroo, Fariba Aerospace Engineering Program Mechanical Engineering Department Worcester Polytechnic Institute WorcesterMA01609 United States Department of Applied Mathematics Naval Postgraduate School MontereyCA93943 United States

This work considers the economic aspects in control implementation of second order spatially distributed systems. By opting to use multiple actuator/sensor pairs with limited capacity, instead of a single actuator/sensor pair with higher price and larger capacity, this work provides a first view into the economic, computational and communication aspects. Considering a large number of actuator/sensor pairs and the a priori defined controller architecture of static output feedback along with the collocation assumption of the actuators and sensors, the resulting closed-loop system is expressed in terms of a static output feedback gain matrix that defines the communication amongst the actuator/sensor pairs. The design problem is then to find the values of the static feedback gain matrix in order to optimize a performance measure. Using the energy of the second order infinite dimensional system as the performance measure, the resulting optimization is expressed in terms of the solution to a parameterized operator Lyapunov equation. Simulation studies of the wave PDE in one spatial dimension for different communication topologies, reveal the effects of communication on the performance of the closed loop system. © 2016

关键词： Actuators Closed loop systems Feedback control Lyapunov functions Spatial distribution Actuator/sensor Communication topologies Controller architectures Distributed parameter systems Infinite dimensional system Second order systemss Spatially distributed system Static output feedback

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：