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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 discretization at a Reynolds number Re = 500. The undisturbed two-dimensional flow remains periodic at this Reynolds number, unless a suitable forcing is applied on the naturally produced system. Three-dimensional simulations establish that three-dimensionality sets in at Re almost-equal-to 200. Successive supercritical states are established through a series of period-doublings, before a chaotic state is reached at a Re almost-equal-to 500. For the two-dimensional forced flow, all transport measures oscillate aperiodically in time and undergo a "crisis," i.e., a sudden and dramatic increase in their amplitude. The corresponding three-dimensional, naturally produced chaotic state corresponds to a less drastic change of the transport quantities with both rms and mean values lower than their two-dimensional counterparts.

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SEQUENTIAL CLASSIFICATION OF MODIS TIME SERIES

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SEQUENTIAL CLASSIFICATION OF MODIS TIME SERIES

IEEE International Geoscience and Remote Sensing Symposium

作者： T. L. Grobler E. R. Ackermann A. J. van Zyl W. Kleynhans B. P. Salmon J. C. Olivier University of Pretoria Department of Electrical Electronic and Computer Engineering Rice University Computational and Applied Mathematics Department University of Pretoria Department of Mathematics and Applied Mathematics University of Tasmania School of Engineering

ISBN: (纸本)9781467311601

In this paper a sequential time-varying maximum likelihood classifier is applied on coarse resolution MODIS surface reflectance data. It is shown that good class separability can be obtained after considering only one year of data. Finally it is shown that after NDVI, band 2 has the highest separability of all the MODIS land bands, and band 6 has the lowest separability for the presented case study.

关键词： Land cover classification Time-varying maximum likelihood classifier Time series MODIS Sequential

On the convergence of projected alternating maximization for equitable and optimal transport

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The Journal of Machine Learning Research

The Journal of Machine Learning Research 2024年第1期25卷 16456-16488页

作者： Minhui Huang Shiqian Ma Lifeng Lai Department of Electrical and Computer Engineering University of California Davis CA Department of Computational Applied Mathematics and Operations Research Rice University Houston TX

This paper studies the equitable and optimal transport (EOT) problem, which has many applications such as fair division problems and optimal transport with multiple agents etc. In the discrete distributions case, the EOT problem can be formulated as a linear program (LP). Since this LP is prohibitively large for general LP solvers, (Scetbon et al., 2021) suggests to perturb the problem by adding an entropy regularization. They proposed a projected alternating maximization algorithm (PAM) to solve the dual of the entropy regularized EOT. In this paper, we provide the first convergence analysis of PAM. A novel rounding procedure is proposed to help construct the primal solution for the original EOT problem. We also propose a variant of PAM by incorporating the extrapolation technique that can numerically improve the performance of PAM. Results in this paper may shed lights on block coordinate (gradient) descent methods for general optimization problems.

关键词： equitable and optimal transport fairness saddle point problem projected alternating maximization block coordinate descent acceleration rounding

A Chebyshev-accelerated primal-dual method for distributed optimization

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arXiv 2018年

作者： Seidman, Jacob H. Fazlyab, Mahyar Pappas, George J. Preciado, Victor M. Department of Applied Mathematics and Computational Science University of Pennsylvania Department of Electrical and Systems Engineering University of Pennsylvania

We consider a distributed optimization problem over a network of agents aiming to minimize a global objective function that is the sum of local convex and composite cost functions. To this end, we propose a distributed Chebyshev-accelerated primal-dual algorithm to achieve faster ergodic convergence rates. In standard distributed primal-dual algorithms, the speed of convergence towards a global optimum (i.e., a saddle point in the corresponding Lagrangian function) is directly influenced by the eigenvalues of the Laplacian matrix representing the communication graph. In this paper, we use Chebyshev matrix polynomials to generate gossip matrices whose spectral properties result in faster convergence speeds, while allowing for a fully distributed implementation. As a result, the proposed algorithm requires fewer gradient updates at the cost of additional rounds of communications between agents. We illustrate the performance of the proposed algorithm in a distributed signal recovery problem. Our simulations show how the use of Chebyshev matrix polynomials can be used to improve the convergence speed of a primal-dual algorithm over communication networks, especially in networks with poor spectral properties, by trading local computation by communication rounds. Copyright © 2018, The Authors. All rights reserved.

关键词： Matrix algebra

A free-energy principle for representation learning

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arXiv 2020年

作者： Gao, Yansong Chaudhari, Pratik Applied Mathematics and Computational Science University of Pennsylvania Department of Electrical and Systems Engineering University of Pennsylvania

This paper employs a formal connection of machine learning with thermodynamics to characterize the quality of learnt representations for transfer learning. We discuss how informationtheoretic functionals such as rate, distortion and classification loss of a model lie on a convex, so-called equilibrium surface. We prescribe dynamical processes to traverse this surface under constraints, e.g., an iso-classification process that trades off rate and distortion to keep the classification loss unchanged. We demonstrate how this process can be used for transferring representations from a source dataset to a target dataset while keeping the classification loss constant. Experimental validation of the theoretical results is provided on standard image-classification datasets. Copyright © 2020, The Authors. All rights reserved.

关键词： Signal distortion

A control-theoretic approach to analysis and parameter selection of douglas-rachford splitting

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arXiv 2019年

作者： Seidman, Jacob H. Fazlyab, Mahyar Preciado, Victor M. Pappas, George J. Department of Applied Mathematics and Computational Science University of Pennsylvania Department of Electrical and Systems Engineering University of Pennsylvania

Douglas-Rachford splitting and its equivalent dual formulation ADMM are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on the choice of step size parameters, for which the optimal values are known in some specific cases, and otherwise are set heuristically. We provide a new unified method of convergence analysis and parameter selection by interpreting the algorithm as a linear dynamical system with nonlinear feedback. This approach allows us to derive a dimensionally independent matrix inequality whose feasibility is sufficient for the algorithm to converge at a specified rate. By analyzing this inequality, we are able to give performance guarantees and parameter settings of the algorithm under a variety of assumptions regarding the convexity and smoothness of the objective function. In particular, our framework enables us to obtain a new and simple proof of the O(1/k) convergence rate of the algorithm when the objective function is not strongly convex. Copyright © 2019, The Authors. All rights reserved.

关键词： Lyapunov methods

Stable super-resolution of images: A theoretical study

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arXiv 2018年

作者： Eftekhari, Armin Bendory, Tamir Tang, Gongguo Institute of Electrical Engineering École Polytechnique Fédérale de Lausanne Program in Applied and Computational Mathematics Princeton University Department of Electrical Engineering Colorado School of Mines

We study the ubiquitous super-resolution problem, in which one aims at localizing positive point sources in an image, blurred by the point spread function of the imaging device. To recover the point sources, we propose to solve a convex feasibility program, which simply finds a nonnegative Borel measure that agrees with the observations collected by the imaging device. In the absence of imaging noise, we show that solving this convex program uniquely retrieves the point sources, provided that the imaging device collects enough observations. This result holds true if the point spread function of the imaging device can be decomposed into horizontal and vertical components, and if the translations of these components form a Chebyshev system, namely, a system of continuous functions that loosely behave like algebraic polynomials. Building upon recent results for one-dimensional signals [1], we prove that this super-resolution algorithm is stable (in the generalized Wasserstein metric) to model mismatch (namely, when the image is not sparse) and to additive imaging noise. In particular, the recovery error depends on the noise level and how well the image can be approximated with well-separated point sources. As an example, we verify these claims for the important case of a Gaussian point spread function. The proofs rely on the construction of novel interpolating polynomials, which are the main technical contribution of this paper, and partially resolve the question raised in [2] about the extension of the standard machinery to higher dimensions. Copyright © 2018, The Authors. All rights reserved.

关键词： Optical transfer function

A deep neural network based surrogate model for damage identification in full-scale structures with incomplete noisy measurements

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Frontiers of Structural and Civil engineering 2024年第3期18卷 393-410页

作者： Tram BUI-NGOC Duy-Khuong LY Tam T TRUONG Chanachai THONGCHOM T.NGUYEN-THOI Laboratory for Computational Mechanics Institute for Computational Science and Artificial IntelligenceVan Lang UniversityHo Chi Minh City 70000Vietnam Faculty of Mechanical-Electrical and Computer Engineering School of TechnologyVan Lang UniversityHo Chi Minh City 70000Vietnam Faculty of Civil Engineering School of TechnologyVan Lang UniversityHo Chi Minh City 70000Vietnam Department of Computer Science Aarhus UniversityAarhus 8000Denmark Thammasat University research unit in structural and foundation engineering Department of Civil EngineeringThammasat UniversityPathumthani 12120Thailand Laboratory for Applied and Industrial Mathematics Institute for Computational Science and Artificial IntelligenceVan Lang UniversityHo Chi Minh City 70000Vietnam Thammasat School of Engineering Thammasat UniversityPathumthani 12120Thailand

The paper introduces a novel approach for detecting structural damage in full-scale structures using surrogate models generated from incomplete modal data and deep neural networks(DNNs).A significant challenge in this field is the limited availability of measurement data for full-scale structures,which is addressed in this paper by generating data sets using a reduced finite element(FE)model constructed by SAP2000 software and the MATLAB programming *** surrogate models are trained using response data obtained from the monitored structure through a limited number of measurement *** proposed approach involves training a single surrogate model that can quickly predict the location and severity of damage for all potential *** achieve the most generalized surrogate model,the study explores different types of layers and hyperparameters of the training algorithm and employs state-of-the-art techniques to avoid overfitting and to accelerate the training *** approach’s effectiveness,efficiency,and applicability are demonstrated by two numerical *** study also verifies the robustness of the proposed approach on data sets with sparse and noisy measured ***,the proposed approach is a promising alternative to traditional approaches that rely on FE model updating and optimization algorithms,which can be computationally *** approach also shows potential for broader applications in structural damage detection.

关键词： vibration-based damage detection deep neural network full-scale structures finite element model updating noisy incomplete modal data

Heterogeneous inputs to central pattern generators can shape insect gaits.

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arXiv 2018年

作者： Aminzare, Zahra Holmes, Philip Program in Applied and Computational Mathematics Princeton University NJ United States Program in Applied and Computational Mathematics Department of Mechanical and Aerospace Engineering Princeton Neuroscience Institute Princeton University NJ United States

In our previous work [1], we studied an interconnected bursting neuron model for insect locomotion, and its corresponding phase oscillator model, which at high speed can generate stable tripod gaits with three legs off the ground simultaneously in swing, and at low speed can generate stable tetrapod gaits with two legs off the ground simultaneously in swing. However, at low speed several other stable locomotion patterns, that are not typically observed as insect gaits, may coexist. In the present paper, by adding heterogeneous external input to each oscillator, we modify the bursting neuron model so that its corresponding phase oscillator model produces only one stable gait at each speed, specifically: a unique stable tetrapod gait at low speed, a unique stable tripod gait at high speed, and a unique branch of stable transition gaits connecting them. This suggests that control signals originating in the brain and central nervous system can modify gait patterns.34C15, 34C60, 37G10, 92B20, 92C20 Copyright © 2018, The Authors. All rights reserved.

关键词： Neurons