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arXiv 2017年

作者： Abbe, Emmanuel Kulkarni, Sanjeev Lee, Eun Jee Program in Applied and Computational Mathematics Department of Electrical Engineering Princeton University Princeton United States Department of Electrical Engineering Princeton University Princeton United States Program in Applied and Computational Mathematics Princeton University Princeton United States

This paper develops upper and lower bounds on the influence measure in a network, more precisely, the expected number of nodes that a seed set can influence in the independent cascade model. In particular, our bounds exploit nonbacktracking walks, Fortuin–Kasteleyn–Ginibre (FKG) type inequalities, and are computed by message passing implementation. Nonbacktracking walks have recently allowed for headways in community detection, and this paper shows that their use can also impact the influence computation. Further, we provide a knob to control the trade-off between the efficiency and the accuracy of the bounds. Finally, the tightness of the bounds is illustrated with simulations on various network models. Copyright © 2017, The Authors. All rights reserved.

关键词： Economic and social effects

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Convolutional neural networks with low-rank regularization 4

Convolutional neural networks with low-rank regularization

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4th International Conference on Learning Representations, ICLR 2016

作者： Tai, Cheng Xiao, Tong Zhang, Yi Wang, Xiaogang Weinan, E. Program in Applied and Computational Mathematics Princeton University United States Department of Electronic Engineering Chinese University of Hong Kong Hong Kong Department of Electrical Engineering and Computer Science University of Michigan Ann Arbor United States

Large CNNs have delivered impressive performance in various computer vision applications. But the storage and computation requirements make it problematic for deploying these models on mobile devices. Recently, tensor decompositions have been used for speeding up CNNs. In this paper, we further develop the tensor decomposition technique. We propose a new algorithm for computing the low-rank tensor decomposition for removing the redundancy in the convolution kernels. The algorithm finds the exact global optimizer of the decomposition and is more effective than iterative methods. Based on the decomposition, we further propose a new method for training low-rank constrained CNNs from scratch. Interestingly, while achieving a significant speedup, sometimes the low-rank constrained CNNs delivers significantly better performance than their non-constrained counterparts. On the CIFAR-10 dataset, the proposed low-rank NIN model achieves 91.31% accuracy (without data augmentation), which also improves upon state-of-the-art result. We evaluated the proposed method on CIFAR-10 and ILSVRC12 datasets for a variety of modern CNNs, including AlexNet, NIN, VGG and GoogleNet with success. For example, the forward time of VGG-16 is reduced by half while the performance is still comparable. Empirical success suggests that low-rank tensor decompositions can be a very useful tool for speeding up large CNNs. © ICLR 2016: San Juan, Puerto Rico. All Rights Reserved.

关键词： Iterative methods

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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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Efficient Monolithic Solvers for Fluid-Structure Interaction applied to Flapping Membranes 26th

Efficient Monolithic Solvers for Fluid-Structure Interaction...

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26th International Conference on Domain Decomposition Methods, 2020

作者： Jodlbauer, D. Langer, U. Wick, T. Doctoral Program "Computational Mathematics" Johannes Kepler University Linz Altenberger Str. 69 LinzA-4040 Austria Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences Altenberger Str. 69 LinzA-4040 Austria Institut für Angewandte Mathematik Leibniz Universität Hannover Welfengarten 1 Hannover30167 Germany

ISBN: (纸本)9783030950248

This work is devoted to the efficient solution of variational-monolithic fluid-structure interaction (FSI) initial-boundary value problems. Solvers for such monolithic systems were developed, e.g., in [2, 3, 5, 7, 9, 11–13, 15]. Due to the interface coupling conditions, the development of robust scalable parallel solvers remains a challenging task, and to the best of our knowledge only semi-cost optimal parallel approaches could be derived [4, 9]. The main purpose of this work consists in further numerical studies of the solver, developed in [9], for a benchmark problem that is motivated by hemodynamic applications. Specifically, we consider channel flow with elastic membranes and elastic solid walls. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Fluid structure interaction

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DeePKS-kit: A package for developing machine learning-based chemically accurate energy and density functional models

arXiv

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arXiv 2020年

作者： Chen, Yixiao Zhang, Linfeng Wang, Han Weinan, E. Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Huayuan Road 6 Beijing100088 China Department of Mathematics Princeton University PrincetonNJ United States

We introduce DeePKS-kit, an open-source software package for developing machine learning based energy and density functional models. DeePKS-kit is interfaced with PyTorch, an open-source machine learning library, and PySCF, an ab initio computational chemistry program that provides simple and customized tools for developing quantum chemistry codes. It supports the DeePHF and DeePKS methods. In addition to explaining the details in the methodology and the software, we also provide an example of developing a chemically accurate model for water clusters. Copyright © 2020, The Authors. All rights reserved.

关键词： Electronic structure

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Using a level set to model multiple myeloma induced bone loss

Using a level set to model multiple myeloma induced bone los...

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6th European Congress on computational Methods in applied Sciences and Engineering, ECCOMAS 2012

作者： Ayati, Bruce P. Graham, Jason M. Holstein, Sarah A. Department of Mathematics and Program in Applied Mathematical and Computational Sciences University of Iowa Iowa City IA 52242-1419 United States Department of Internal Medicine University of Iowa Iowa City IA 52242-1081 United States

ISBN: (纸本)9783950353709

Multiple myeloma is a hematological malignancy characterized by proliferation of malignant plasma cells and derangement of bone homeostasis. Myeloma bone disease results in significant morbidity as a result of bone pain, hypercalcemia, diffuse osteopenia, and pathologic fractures. We present a spatially explicit mathematical model of multiple myeloma and bone remodeling, synthesizing the existing model of local "microenvironment" interactions in Ayati et al. 2010 [1] with a level set approach for representing the sharp interface been bone and marrow introduced in [6]. computational results show the feasibility of using a level set to capture the spatial structure in the context of a geometrically straightforward interface, but one that nonetheless captures the essence of the rich geometries seen in bone marrow biopsy slides. In particular, we are able to model the formation of an osteolytic lesion in the case of multiple myeloma dysregulated bone remodeling, but not, using the same remodeling parameter set, in the case of normal bone remodeling.

关键词： Bone

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On the non stationary Navier-Stokes equations with an external force

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Advances in Differential Equations 1999年第5期4卷 697-730页

作者： Cannone, Marco Planchon, Fabrice UMR 7599 du CNRS UFR Mathématiques Université Denis Diderot Paris VII 75251 Paris Cedex 05 2 Place Jussieu France Program for Applied and Computational Mathematics Princeton University Princeton NJ 08544-1000 United States

We present two different existence and uniqueness algorithms for constructing global mild solutions in C([0, T);L3(ℝ3)) to the Cauchy problem for the Navier-Stokes equations with an external force.

We present two different existence and uniqueness algorithms for constructing global mild solutions in C([0, T);L³(ℝ³)) to the Cauchy problem for the Navier-Stokes equations with an external force.

关键词： 35Q30 76D03 76D05

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Isotope effects in x-ray absorption spectra of liquid water

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Physical Review B 2020年第11期102卷 115155-115155页

作者： Chunyi Zhang Linfeng Zhang Jianhang Xu Fujie Tang Biswajit Santra Xifan Wu Department of Physics Temple University Philadelphia Pennsylvania 19122 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

The isotope effects in x-ray absorption spectra of liquid water are studied by a many-body approach within electron-hole excitation theory. The molecular structures of both light and heavy water are modeled by path-integral molecular dynamics based on the advanced deep-learning technique. The neural network is trained on ab initio data obtained with SCAN density functional theory. The experimentally observed isotope effect in x-ray absorption spectra is reproduced semiquantitatively in theory. Compared to the spectrum in normal water, the blueshifted and less pronounced pre- and main-edge in heavy water reflect that the heavy water is more structured at short- and intermediate-range of the hydrogen-bond network. In contrast, the isotope effect on the spectrum is negligible at post-edge, which is consistent with the identical long-range ordering in both liquids as observed in the diffraction experiment.

关键词： Atomic & molecular structure Electronic excitation & ionization Water Density functional calculations Electronic structure First-principles calculations Machine learning Molecular dynamics X-ray absorption spectroscopy

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DeePKS: A comprehensive data-driven approach towards chemically accurate density functional theory

arXiv

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arXiv 2020年

We propose a general machine learning-based framework for building an accurate and widely-applicable energy functional within the framework of generalized Kohn-Sham density functional theory. To this end, we develop a way of training self-consistent models that are capable of taking large datasets from different systems and different kinds of labels. We demonstrate that the functional that results from this training procedure gives chemically accurate predictions on energy, force, dipole, and electron density for a large class of molecules. It can be continuously improved when more and more data are available. Copyright © 2020, The Authors. All rights reserved.

关键词： Large dataset

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Ground state energy functional with Hartree-Fock efficiency and chemical accuracy

arXiv

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arXiv 2020年

We introduce the Deep Post–Hartree–Fock (DeePHF) method, a machine learning-based scheme for constructing accurate and transferable models for the ground-state energy of electronic structure problems. DeePHF predicts the energy difference between results of highly accurate models such as the coupled cluster method and low accuracy models such as the the Hartree-Fock (HF) method, using the ground-state electronic orbitals as the input. It preserves all the symmetries of the original high accuracy model. The added computational cost is less than that of the reference HF or DFT and scales linearly with respect to system size. We examine the performance of DeePHF on organic molecular systems using publicly available datasets and obtain the state-of-art performance, particularly on large datasets. Copyright © 2020, The Authors. All rights reserved.

关键词： Molecular physics

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