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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231-240 订阅
Active learning of uniformly accurate inter-atomic potentials for materials simulation
arXiv
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arXiv 2018年
作者: Zhang, Linfeng Lin, De-Ye Wang, Han Car, Roberto Weinan, E. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Institute of Applied Physics and Computational Mathematics Huayuan Road 6 Beijing100088 China CAEP Software Center for High Performance Numerical Simulation Huayuan Road 6 Beijing100088 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Huayuan Road 6 Beijing100088 China Department of Chemistry Department of Physics Program in Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Beijing Institute of Big Data Research Beijing100871 China
An active learning procedure called Deep Potential Generator (DP-GEN) is proposed for the construction of accurate and transferable machine learning-based models of the potential energy surface (PES) for the molecular... 详细信息
来源: 评论
ON A LINEARIZATION OF QUADRATIC WASSERSTEIN DISTANCE
arXiv
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arXiv 2022年
作者: Greengard, Philip Hoskins, Jeremy G. Marshall, Nicholas F. Singer, Amit Department of Statistics Columbia University United States Department of Statistics University of Chicago United States Program in Applied and Computational Mathematics The Department of Mathematics Princeton University United States
This paper studies the problem of computing a linear approximation of quadratic Wasserstein distance W2. In particular, we compute an approximation of the negative homogeneous weighted Sobolev norm whose connection to... 详细信息
来源: 评论
Generalization error of GAN from the discriminator's perspective
arXiv
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arXiv 2021年
作者: Yang, Hongkang Weinan, E. Program in Applied and Computational Mathematics Princeton University United States Department of Mathematics Princeton University United States Beijing Institute of Big Data Research China
The generative adversarial network (GAN) is a well-known model for learning high-dimensional distributions, but the mechanism for its generalization ability is not understood. In particular, GAN is vulnerable to the m... 详细信息
来源: 评论
Manifold learning with arbitrary norms
arXiv
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arXiv 2020年
作者: Kileel, Joe Moscovich, Amit Zelesko, Nathan Singer, Amit Department of Mathematics Oden Institute University of Texas at Austin United States Department of Statistics and Operations Research Tel-Aviv University Israel Department of Mathematics Brown University United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University
Manifold learning methods play a prominent role in nonlinear dimensionality reduction and other tasks involving high-dimensional data sets with low intrinsic dimensionality. Many of these methods are graph-based: they... 详细信息
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Complexity measures for neural networks with general activation functions using path-based norms
arXiv
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arXiv 2020年
作者: Li, Zhong Ma, Chao Wu, Lei School of Mathematical Sciences Peking University China Department of Mathematics Stanford University United States Program in Applied and Computational Mathematics Princeton University United States
A simple approach is proposed to obtain complexity controls for neural networks with general activation functions. The approach is motivated by approximating the general activation functions with one-dimensional ReLU ... 详细信息
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The barron space and the flow-induced function spaces for neural network models
arXiv
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arXiv 2019年
作者: Weinan, E. Ma, Chao Wu, Lei Department of Mathematics Princeton University United States Program in Applied and Computational Mathematics Princeton University United States Beijing Institute of Big Data Research China
One of the key issues in the analysis of machine learning models is to identify the appropriate function space and norm for the model. This is the set of functions endowed with a quantity which can control the approxi... 详细信息
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Local and global strong solutions for SQG in bounded domains
arXiv
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arXiv 2017年
作者: Constantin, Peter Nguyen, Huy Quang DEPARTMENT OF MATHEMATICS PRINCETON UNIVERSITY PRINCETONNJ08544 United States PROGRAM IN APPLIED AND COMPUTATIONAL MATHEMATICS PRINCETON UNIVERSITY PRINCETONNJ08544 United States
We prove local well-posedness for the inviscid surface quasigeostrophic (SQG) equation in bounded domains of R2. When fractional Dirichlet Laplacian dissipation is added, global existence of strong solutions is obtain...
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On quasisymmetric plasma equilibria sustained by small force
arXiv
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arXiv 2020年
作者: Constantin, Peter Drivas, Theodore D. Ginsberg, Daniel Department of Mathematics Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States
We construct smooth, non-symmetric plasma equilibria which possess closed, nested flux surfaces and solve the Magnetohydrostatic (steady three-dimensional incompressible Euler) equations with a small force. The soluti... 详细信息
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Chaotic behavior of interacting elliptical instability modes
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The Physics of Fluids 1988年 第1期31卷 6-8页
作者: Carl S. Hellberg Steven A. Orszag Department of Physics Princeton University Princeton New Jersey 08544 Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544
A three‐mode projection of the Navier–Stokes equations for nonlinear perturbations to an elliptical vortex is studied numerically. It is found that, as the Reynolds number increases, the perturbations undergo a sequ...
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Domain Formation in the Plasma Membrane: Roles of Nonequilibrium Lipid Transport and Membrane Proteins
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Physical Review Letters 2008年 第17期100卷 178102-178102页
作者: Jun Fan Maria Sammalkorpi Mikko Haataja Department of Mechanical and Aerospace Engineering Princeton Institute for the Science and Technology of Materials (PRISM) and Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544 USA
Compositional lipid domains (“lipid rafts”) in plasma membranes are believed to be important components of many cellular processes. The mechanisms by which cells regulate the sizes and lifetimes of these spatially e... 详细信息
来源: 评论