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arXiv 2021年

作者： Woodward, Michael Tian, Yifeng Hyett, Criston Fryer, Chris Stepanov, Mikhail Livescu, Daniel Chertkov, Michael Graduate Interdisciplinary Program in Applied Mathematics UArizona TucsonAZ85721 United States Department of Mathematics UArizona TucsonAZ85721 United States Computer Computational and Statistical Sciences Division LANL Los AlamosNM87544 United States

Building efficient, accurate and generalizable reduced order models of developed turbulence remains a major challenge. This manuscript approaches this problem by developing a hierarchy of parameterized reduced Lagrangian models for turbulent flows, and investigates the effects of enforcing physical structure through Smoothed Particle Hydrodynamics (SPH) versus relying on neural networks (NN)s as universal function approximators. Starting from Neural Network (NN) parameterizations of a Lagrangian acceleration operator, this hierarchy of models gradually incorporates a weakly compressible and parameterized SPH framework, which enforces physical symmetries, such as Galilean, rotational and translational invariances. Within this hierarchy, two new parameterized smoothing kernels are developed in order to increase the flexibility of the learn-able SPH simulators. For each model we experiment with different loss functions which are minimized using gradient based optimization, where efficient computations of gradients are obtained by using Automatic Differentiation (AD) and Sensitivity Analysis (SA). Each model within the hierarchy is trained on two data sets associated with weekly compressible Homogeneous Isotropic Turbulence (HIT): (1) a validation set using weakly compressible SPH;and (2) a high fidelity set from Direct Numerical Simulations (DNS). Numerical evidence shows that encoding more SPH structure improves generalizability to different turbulent Mach numbers and time shifts, and that including the novel parameterized smoothing kernels improves the accuracy of SPH at the resolved scales. Copyright © 2021, The Authors. All rights reserved.

关键词： Parameterization

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The influence of numerical error on an inverse problem methodology in PDE models

arXiv

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arXiv 2018年

作者： Nardini, John T. Bortz, D.M. Department of Applied Mathematics 526 UCB BoulderCO80309-0526 United States Interdisciplinary Quantitative Biology Graduate Program University of Colorado BoulderCO80309-0596 United States

The inverse problem methodology is a commonly-used framework in the sciences for parameter estimation and inference. It is typically performed by fitting a mathematical model to noisy experimental data. There are two significant sources of error in the process: 1. Noise from the measurement and collection of experimental data and 2. numerical error in approximating the true solution to the mathematical model. Little attention has been paid to how this second source of error alters the results of an inverse problem. As a first step towards a better understanding of this problem, we present a modeling and simulation study using a simple advection-driven PDE model. We present both analytical and computational results concerning how the different sources of error impact the least squares cost function as well as parameter estimation and uncertainty quantification. We investigate residual patterns to derive an autocorrelative statistical model that can improve parameter estimation and confidence interval computation for first order methods. Building on the results of our investigation, we provide guidelines for practitioners to determine when numerical or experimental error is the main source of error in their inference, along with suggestions of how to efficiently improve their results. Copyright © 2018, The Authors. All rights reserved.

关键词： Parameter estimation

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NOMAD: nonlinear manifold decoders for operator learning 22

NOMAD: nonlinear manifold decoders for operator learning

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Proceedings of the 36th International Conference on Neural Information Processing Systems

作者： Jacob H. Seidman Georgios Kissas Paris Perdikaris George J. Pappas Graduate Program in Applied Mathematics and Computational Science University of Pennsylvania Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania Department of Electrical and Systems Engineering University of Pennsylvania

ISBN: (纸本)9781713871088

Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling. By directly learning maps (operators) between infinite dimensional function spaces, these models are able to learn discretization invariant representations of target functions. A common approach is to represent such target functions as linear combinations of basis elements learned from data. However, there are simple scenarios where, even though the target functions form a low dimensional submanifold, a very large number of basis elements is needed for an accurate linear representation. Here we present NOMAD, a novel operator learning framework with a nonlinear decoder map capable of learning finite dimensional representations of nonlinear submanifolds in function spaces. We show this method is able to accurately learn low dimensional representations of solution manifolds to partial differential equations while outperforming linear models of larger size. Additionally, we compare to state-of-the-art operator learning methods on a complex fluid dynamics benchmark and achieve competitive performance with a significantly smaller model size and training cost.

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Analysis of Lead (Pb) and Zinc (Zn) Content in Sediments and Faunus ater at Bale Lhoknga Aceh Besar District 1

Analysis of Lead (Pb) and Zinc (Zn) Content in Sediments and...

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1st International Conference on Education, Science and Technology, ICON-EST 2018

作者： Agustina, Rahmi Sarong, M. Ali Yulianda, Fredinan Suhendrayatna Rahmadi Lelifajri Graduate School of Mathematics and Applied Sciences Syiah Kuala University Banda Aceh23111 Indonesia Departement of Biology Faculty of Teacher Training and Education Jabal Ghafur University Sigli24171 Indonesia Departement of Biology Faculty of Teacher Training and Education Syiah Kuala University Banda Aceh23111 Indonesia Departement of Water Resources Management Faculty of Fisheries and Marine Sciences Bogor Agricultural University Bogor16680 Indonesia Department of Chemical Engineering Faculty of Engineering Syiah Kuala University Banda Aceh23111 Indonesia Department of Chemistry Faculty of Mathematics and Science Post Graduate Program Syiah Kuala University Banda Aceh23111 Indonesia Department of Chemistry Faculty of Mathematics and Sci. Post Graduate Program Syiah Kuala Univ. Banda Aceh23111 Indonesia

Faunus ater is a favoritemollusca that is often found on the Bale River. Local people use these snails as food for consumption along with their main food. Bale River itself is located adjacent to the cement factory, used water washing machines distributed to the river is feared to support the presence of lead (Pb) and zinc (Zn) metals in the river. This study aims to analyze the relationship of Pb and Zn content in sediments to the content of Pb and Zn in Faunus ater. Data collection was carried out in Februari until April 2018. The relationship between Pb and Zn content in sediments with Pb and Zn content in the body of Faunus ater was analyzed by correlation analysis. The results of the data analysis showed that the metal content of Pb and Zn in sediment and Faunus aterwere found to vary. The highest Pb content in sediment was found at station 2 in March, amounting to 32.87 mg / kg. while the highest Zn content was found at station 1 in March amounting to 84 mg / kg. The relationship of heavy metals Pb and Zn in sediments to the content of Pb and Zn in the body of Faunus ater showed a negative correlation. The conclusion of this study is that there is no correlation between the content of Pb and Zn heavy metals in sediments on the content of lead Pb and Zn in the body of Faunus ater at the Bale Lhoknga River in Aceh Besar District. © Published under licence by IOP Publishing Ltd.

关键词： Rivers

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Exploring 3D Reconstruction with Drone Images: Advances and Challenges in Urban Environments 50

Exploring 3D Reconstruction with Drone Images: Advances and ...

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50th Annual Conference of the IEEE Industrial Electronics Society, IECON 2024

作者： Miranda Baldivieso, Thiago João da Silva Batista, Taise Grazielle Chagas, Fabio Suim Rodrigues Velho, Luiz Carlos Pacheco Ferreira Rosa, Paulo Fernando Defense Engineering Graduate Program Military Institute of Engineering Rio de Janeiro Brazil State Institute of the Environment Inea RJ Rio de Janeiro Brazil Department of Science and Industry systems University of South-Eastern Norway Kongsberg Norway Department of Computer Graphics Institute for Pure and Applied Mathematics Rio de Janeiro Brazil Electrical Engineering Graduate Program Military Institute of Engineering Rio de Janeiro Brazil

ISBN: (纸本)9781665464543

This working-in-progress paper aims to present a three-dimensional reconstruction using aerial images in different environments. The experiments were conducted with aircraft in both external and internal settings, starting with image acquisition, followed by the application of specific photogrammetry software-both commercial and open-source-and concluding with a qualitative evaluation of the results. © 2024 IEEE.

关键词： Aerial photography

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Author Correction: Environmentally dependent interactions shape patterns in gene content across natural microbiomes

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Nature microbiology 2025年第2期10卷 599页

作者： Kyle Crocker Kiseok Keith Lee Milena Chakraverti-Wuerthwein Zeqian Li Mikhail Tikhonov Madhav Mani Karna Gowda Seppe Kuehn Department of Ecology and Evolution The University of Chicago Chicago IL USA. Center for the Physics of Evolving Systems The University of Chicago Chicago IL USA. Center for Living Systems The University of Chicago Chicago IL USA. Biophysical Sciences Graduate Program The University of Chicago Chicago IL USA. Department of Physics The University of Illinois at Urbana-Champaign Urbana IL USA. Department of Physics Washington University in St. Louis St. Louis MO USA. Department of Engineering Sciences and Applied Mathematics Northwestern University Evanston IL USA. Department of Molecular Biosciences Northwestern University Evanston IL USA. NSF-Simons Center for Quantitative Biology Northwestern University Evanston IL USA. National Institute for Theory and Mathematics in Biology Northwestern University and The University of Chicago Chicago IL USA. Department of Microbiology The Ohio State University Columbus OH USA. karna.gowda@***. Biophysics Graduate Program The Ohio State University Columbus OH USA. karna.gowda@***. Department of Ecology and Evolution The University of Chicago Chicago IL USA. seppe.kuehn@***. Center for the Physics of Evolving Systems The University of Chicago Chicago IL USA. seppe.kuehn@***. Center for Living Systems The University of Chicago Chicago IL USA. seppe.kuehn@***. National Institute for Theory and Mathematics in Biology Northwestern University and The University of Chicago Chicago IL USA. seppe.kuehn@***.

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Angklung Smart Band: An IoT-Based System to Support Music Activities for Elderly in Thailand

Angklung Smart Band: An IoT-Based System to Support Music Ac...

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2022 IEEE European Technology and Engineering Management Summit, E-TEMS 2022

作者： Hiranpanthaporn, Saranya Phoasavadi, Pornprapit Cooharojananone, Nagul Technopreneurship and Innovation Management Program Graduate School Chulalongkorn University Bangkok Bangkok Thailand Emili Sagol Creative Arts Research and Innovation for Well-being Center Chulalongkorn University Faculty of Fine and Applied Arts Department of Thai Music Bangkok Bangkok Thailand Chulalongkorn University Faculty of Science Department of Mathematics and Computer Science Bangkok Bangkok Thailand

ISBN: (数字)9781665411004

ISBN: (纸本)9781665411004

Organizing music activities for the elderly is another way that supports their well-being. Angklung, an Indonesian musical instrument, has been used for music activities for the elderly in Thailand with the hand signs method. Unfortunately, music activity is not widely used because the experts with the hand sign skills are few and not enough for demanding in the aging healthcare. At the same time, technologies of remote systems using the Internet of Things (IoT) have been developed to assist the elderly in supporting and improving their quality of life. This paper will introduce 'Angklung Smart Band,' an IoT-based system to support Angklung music activities for the elderly in Thailand. This work aims at setting up Angklung music activities for the elderly by using technology instead of hand signs. The system is composed of a web application, IoT devices, and Angklung musical instruments connected together via a wireless network. We did a preliminary study with the experts to improve experiences and system performance. After that, we asked the music experts to use the smart band to conduct the music activities experiment with the elderly for three days and give us feedback. The results found that the smart band could assist the Angklung music experts and help with the shortage of music expertise in aged care facilities or nursing homes. © 2022 IEEE.

关键词： Music

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Forcing a (κ)-like principle to hold at a weakly compact cardinal

arXiv

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arXiv 2019年

作者： Cody, Brent Gitman, Victoria Lambie-Hanson, Chris Virginia Commonwealth University Department of Mathematics and Applied Mathematics 1015 Floyd Avenue RichmondVA23284 United States City University of New York CUNY Graduate Center Mathematics Program 365 Fifth Avenue New YorkNY10016 United States

Hellsten [Hel03a] proved that when κ is Π1 n-indescribable, the n- club subsets of κ provide a filter base for the Π1 n-indescribability ideal, and hence can also be used to give a characterization of Π1 n-indescribable sets which resembles the definition of stationarity: a set S ⊂ k is Π1 n-indescribable if and only if S ∩ C 6= Ø for every n-club C ⊂ ≠. By replacing clubs with n-clubs in the definition of (κ), one obtains a (κ)-like principle n(κ), a version of which was first considered by Brickhill and Welch [BW]. The principle n(κ) is consistent with the Π1 n-indescribability of but inconsistent with the Π1 n+1-indescribability of κ. By generalizing the standard forcing to add a (κ)-sequence, we show that if κ is κ+-weakly compact and GCH holds then there is a cofinality-preserving forcing extension in which κ remains +- weakly compact and 1(κ) holds. If is Π1 2-indescribable and GCH holds then there is a cofinality-preserving forcing extension in which is κ+-weakly compact, 1(κ) holds and every weakly compact subset of κ has a weakly compact proper initial segment. As an application, we prove that, relative to a Π1 2-indescribable cardinal, it is consistent that is κ+-weakly compact, every weakly compact subset of has a weakly compact proper initial segment, and there exist two weakly compact subsets S0 and S1 of such that there is no β MSC Codes 03E55, 03E35 Copyright © 2019, The Authors. All rights reserved.

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Dynamic Mode Decomposition and Sparse Measurements for Characterization and Monitoring of Power System Disturbances

arXiv

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arXiv 2019年

作者： Ramos, J. Jorge Kutz, J. Nathan Graduate Program in Electrical Engineering Cinvestav Unidad Guadalajara Guadalajaram Jal Mexico Department of Applied Mathematics University of Washington SeattleWA98195 United States

We introduce the dynamics mode decomposition for monitoring wide-area power grid networks from sparse measurement data. The mathematical framework fuses data from multiple sensors based on multivariate statistics, providing accurate full state estimation from limited measurements and generating data-driven forecasts for the state of the system. Our proposed data-driven strategy, which is based on energy metrics, can be used for the analysis of major disturbances in the network. The approach is tested and validated using time domain simulations in the IEEE 118 bus system under various disturbance scenarios and under different sparse observations of the system. In addition to state reconstruction, the minimal number of sensors required for monitoring disturbances can be evaluated. Visualization techniques are developed in order to aid in the analysis and characterization of the system after disturbance. Copyright © 2019, The Authors. All rights reserved.

关键词： Time domain analysis

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DATA-DRIVEN MORI-ZWANZIG: REDUCED ORDER MODELING OF SPARSE SENSORS MEASUREMENTS FOR BOUNDARY LAYER TRANSITION

arXiv

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arXiv 2023年

作者： Woodward, Michael Tian, Yifeng Mohan, Arvind Lin, Yen Ting Hader, Christoph Fasel, Hermann Chertkov, Michael Livescu, Daniel Computer Computational and Statistical Sciences Division Los Alamos National Laboratory Los AlamosNM87544 United States Graduate Interdisciplinary Program in Applied Mathematics Department of Mathematics University of Arizona TucsonAZ85721 United States Department of Aerospace and Mechanical Engineering University of Arizona TucsonAZ85721 United States

Understanding, predicting and controlling laminar-turbulent boundary-layer transition is crucial for the next generation aircraft design. However, in real flight experiments, or wind tunnel tests, often only sparse sensor measurements can be collected at fixed locations. Thus, in developing reduced models for predicting and controlling the flow at the sensor locations, the main challenge is in accounting for how the surrounding field of unobserved (or unresolved) variables interacts with the observed (or resolved) variables at the fixed sensor locations. This makes the Mori-Zwanzig (MZ) formalism a natural choice, as it results in the Generalized Langevin Equations which provides a mathematically sound framework for constructing non-Markovian reduced-order models that include the effects the unresolved variables have on the resolved variables. These effects are captured in the so called memory kernel and orthogonal dynamics, which, when using Mori's linear projection, provides a higher order approximation to the traditional approximate Koopman learning methods. In this work, we explore recently developed data-driven methods for extracting the MZ operators to two boundary-layer flows obtained from high resolution data;a low speed incompressible flow over a flat plate exhibiting bypass transition;and a high speed compressible flow over a flared cone at Mach 6 and zero angle of attack where transition was initiated using a broadband forcing approach ("natural" transition). In each case, an array of "sensors" are placed near the surface of the solid boundary, and the MZ operators are learned and the predictions are compared to the Extended Dynamic Mode Decomposition (EDMD), both using delay embedded coordinates. Further comparisons are made with Long Short-Term Memory (LSTM) and a regression based projection framework using neural networks for the MZ operators. First, we compare the effects of including delay embedded coordinates with EDMD and Mori based MZ and provide

关键词： Dynamic mode decomposition

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