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检索条件"机构=Department of Mathematics&Program in Applied and Computational Mathematics"
814 条 记 录,以下是151-160 订阅
CHAOTIC TRANSPORT IN 2-DIMENSIONAL AND 3-DIMENSIONAL FLOW PAST A CYLINDER
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PHYSICS OF FLUIDS A-FLUID DYNAMICS 1991年 第5期3卷 1051-1062页
作者: BATCHO, P KARNIADAKIS, GE Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 Department of Mechanical and Aerospace Engineering Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544
The response of transport measures (Nusselt number, drag and lift force) for two- and three-dimensional flow past a heated cylinder reaching a chaotic state is investigated numerically using a spectral element discret...
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Probabilistic Theory of Mean Field Games with Applications I  1
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丛书名: Probability Theory and Stochastic Modelling
2018年
作者: René Carmona François Delarue
Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illust... 详细信息
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AN OPTIMAL SCHEDULED LEARNING RATE FOR A RANDOMIZED KACZMARZ ALGORITHM
arXiv
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arXiv 2022年
作者: Marshall, Nicholas F. Mickelin, Oscar Department of Mathematics Oregon State University United States Program in Applied and Computational Mathematics Princeton University United States
We study how the learning rate affects the performance of a relaxed randomized Kaczmarz algorithm for solving Ax ≈ b + Ε, where Ax = b is a consistent linear system and Ε has independent mean zero random entries. W... 详细信息
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A Priori Estimates of the Population Risk for Residual Networks
arXiv
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arXiv 2019年
作者: Weinan, E. Ma, Chao Wang, Qingcan Department of Mathematics Princeton University Program in Applied and Computational Mathematics Princeton University Beijing Institute of Big Data Research
Optimal a priori estimates are derived for the population risk, also known as the generalization error, of a regularized residual network model. An important part of the regularized model is the usage of a new path no... 详细信息
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A Comparative Analysis of Optimization and Generalization Properties of Two-layer Neural Network and Random Feature Models Under Gradient Descent Dynamics
arXiv
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arXiv 2019年
作者: Weinan, E. Ma, Chao Wu, Lei Department of Mathematics Princeton University Program in Applied and Computational Mathematics Princeton University Beijing Institute of Big Data Research
A fairly comprehensive analysis is presented for the gradient descent dynamics for training two-layer neural network models in the situation when the parameters in both layers are updated. General initialization schem... 详细信息
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Ordered and disordered stealthy hyperuniform point patterns across spatial dimensions
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Physical Review Research 2024年 第3期6卷 033260页
作者: Peter K. Morse Paul J. Steinhardt Salvatore Torquato Department of Chemistry Department of Physics Princeton Institute of Materials Princeton Center for Theoretical Science Program in Applied and Computational Mathematics
In previous work [Phys. Rev. X 5, 021020 (2015)] it was shown that stealthy hyperuniform systems can be regarded as hard spheres in Fourier space in the sense that the structure factor is exactly zero in a spherical r... 详细信息
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Machine learning from a continuous viewpoint
arXiv
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arXiv 2019年
作者: Weinan, E. Ma, Chao Wu, Lei Department of Mathematics Princeton University Program in Applied and Computational Mathematics Princeton University Beijing Institute of Big Data Research
We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, very much in the spirit of classical numerical analysis and statistical physics.... 详细信息
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Analysis of the gradient descent algorithm for a deep neural network model with skip-connections
arXiv
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arXiv 2019年
作者: Weinan, E. Ma, Chao Wang, Qingcan Wu, Lei Department of Mathematics Princeton University Program in Applied and Computational Mathematics Princeton University Beijing Institute of Big Data Research
The behavior of the gradient descent (GD) algorithm is analyzed for a deep neural network model with skip-connections. It is proved that in the over-parametrized regime, for a suitable initialization, with high probab... 详细信息
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Inertial Hegselmann-Krause systems
Inertial Hegselmann-Krause systems
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American Control Conference (ACC)
作者: Bernard Chazelle Chu Wang Department of Computer Science Princeton University Program in Applied and Computational Mathematics Princeton University
We derive an energy bound for inertial Hegselmann-Krause (HK) systems, which we define as a variant of the classic HK model in which the agents can change their weights arbitrarily at each step. We use the bound to pr... 详细信息
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Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
Strong and weak divergence in finite time of Euler's method ...
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作者: Hutzenthaler, Martin Jentzen, Arnulf Kloeden, Peter E. LMU Biozentrum Department Biologie II University of Munich 82152 Planegg-Martinsried Germany Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544-1000 United States Institute for Mathematics Goethe University Frankfurt am Main 60054 Frankfurt am Main Germany
The stochastic Euler scheme is known to converge to the exact solution of a stochastic differential equation (SDE) with globally Lipschitz continuous drift and diffusion coefficients. Recent results extend this conver... 详细信息
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