检索结果-内蒙古大学图书馆

PHYSICS INFORMED MACHINE LEARNING WITH SMOOTHED PARTICLE HYDRODYNAMICS: HIERARCHY OF REDUCED LAGRANGIAN MODELS OF TURBULENCE

学校读者我要写书评

暂无评论

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

Representation formulas and pointwise properties for Barron functions

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Weinan, E. Wojtowytsch, Stephan Department of Mathematics Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Princeton University Program in Applied and Computational Mathematics 205 Fine Hall - Washington Road PrincetonNJ08544 United States

We study the natural function space for infinitely wide two-layer neural networks with ReLU activation (Barron space) and establish different representation formulae. In two cases, we describe the space explicitly up to isomorphism. Using a convenient representation, we study the pointwise properties of two-layer networks and show that functions whose singular set is fractal or curved (for example distance functions from smooth submanifolds) cannot be represented by infinitely wide two-layer networks with finite path-norm. We use this structure theorem to show that the only C1-diffeomorphisms which Barron space are affine. Furthermore, we show that every Barron function can be decomposed as the sum of a bounded and a positively one-homogeneous function and that there exist Barron functions which decay rapidly at infinity and are globally Lebesgue-integrable. This result suggests that two-layer neural networks may be able to approximate a greater variety of functions than commonly *** Codes 68T07, 46E15, 26B35, 26B40 Copyright © 2020, The Authors. All rights reserved.

关键词： Network layers

Identification of fishing ground hotspot of traditional purse seine fisher at northern waters of Aceh - A community-based data collection approach 1

学校读者我要写书评

暂无评论

Identification of fishing ground hotspot of traditional purs...

1st International and National Symposium on Aquatic Environment and Fisheries, INSAEF 2020

作者： Haridhi, H.A. Rizal, S. Nanda, M. Muhammad Wilson, C.R. Department of Marine Sciences Faculty of Marine and Fisheries Syiah Kuala University Banda Aceh Indonesia Marine and Fisheries Research Center Syiah Kuala University Banda Aceh Indonesia Doctoral Program of Mathematics and Applied Science Graduate School Syiah Kuala University Banda Aceh Indonesia Asian Development Bank Mandaluyong Philippines

Fishing grounds are among the most important key of information kept by the fishermen. Understanding the fishing ground locations are considered important as an evaluation of the fishing effort being reached by the fishermen as well as understanding the pressure being received to the fish stock at the surrounding water. The recent study has shown that a community-based data collection approach was found successful in recording and analyzing the fishing ground locations and its properties. One of the few projects implementing this concept is the Community-Based Bathymetric Survey (CBBS), which was realized by the Body of Rehabilitation and Reconstruction (BRR) Nanggroe Aceh Darussalam (NAD) - Nias with funding from the Asian Development Bank (ADB). As many as 151 GPS-transducer recording devices were installed to the fishermen boats along the coast of Aceh, with 45 devices were installed to the traditional purse seine fisher at the northern water of Aceh. These devices were configured to automatically record locations each time the boat moved 30 m. Other important information, such as water depth, time, speed, and sea surface temperature (SST) were recorded as well. This study aims to examine the fishing ground and its fishing hotspot of the traditional purse seine fisher in the northern waters of Aceh. The data collection was performed between June 2007 and May 2009 and gathered as many as 922 data sets consist of 6,170,648 data points, from the 45 purse seine boats. Trough the data, we are able to identify the typical fishing activities of purse seiner and as many as 1,619 data points were being detected. The results indicate that there are five main regions of the fishing ground hotspot in the northern waters of Aceh, i.e. 1. Western offshore of Lhok Nga, 2. Northern offshore of Ulee Lheue, 3. Western offshore of Aceh Islands, 4. Eastern offshore of Aceh Island, and 5. Northern offshore of Krueng Raya. Among the fishing ground hotspot analyzed, the Western offshor

关键词： Location

On the existence of the maximum likelihood estimate and convergence rate under gradient descent for multi-class logistic regression

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Nwaigwe, Dwight Rychlik, Marek Program in Applied Mathematics The University of Arizona Tucson United States Department of Mathematics The University of Arizona Tucson United States

We revisit the problem of the existence of the maximum likelihood estimate for multi-class logistic regression. We show that one method of ensuring its existence is by assigning positive probability to every class in the sample dataset. The notion of data separability is not needed, which is in contrast to the classical set up of multi-class logistic regression in which each data sample belongs to one class. We also provide a general and constructive estimate of the convergence rate to the maximum likelihood estimate when gradient descent is used as the optimizer. Our estimate involves bounding the condition number of the Hessian of the maximum likelihood function. The approaches used in this article rely on a simple operator-theoretic *** Codes 62J12, 65K10, 47N10 Copyright © 2020, The Authors. All rights reserved.

关键词： Gradient methods

Ordered and disordered stealthy hyperuniform point patterns across spatial dimensions

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Morse, Peter K. Steinhardt, Paul J. Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Institute of Materials Princeton University PrincetonNJ08544 United States Princeton Center for Theoretical Science Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

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 the structure factor is exactly zero in a spherical region around the origin in analogy with the pair-correlation function of real-space hard spheres. In this work, we exploit this correspondence to confirm that the densest Fourier-space hard-sphere system is that of a Bravais lattice. This is in contrast to real-space hard-spheres, whose densest configuration is conjectured to be disordered. We also extend the virial series previously suggested for disordered stealthy hyperuniform systems to higher dimensions in order to predict spatial decorrelation as function of dimension. This prediction is then borne out by numerical simulations of disordered stealthy hyperuniform ground states in dimensions d = 2-8. © 2024, CC BY.

关键词： Ground state

Fast principal component analysis for cryo-electron microscopy images

学校读者我要写书评

暂无评论

Biological imaging 2023年 3卷 e2-e2页

作者： Nicholas F Marshall Oscar Mickelin Yunpeng Shi Amit Singer Department of Mathematics Oregon State University Corvallis Oregon 97331 USA. Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA. Department of Mathematics Princeton University Princeton New Jersey 08544 USA.

Principal component analysis (PCA) plays an important role in the analysis of cryo-electron microscopy (cryo-EM) images for various tasks such as classification, denoising, compression, and ab initio modeling. We introduce a fast method for estimating a compressed representation of the 2-D covariance matrix of noisy cryo-EM projection images affected by radial point spread functions that enables fast PCA computation. Our method is based on a new algorithm for expanding images in the Fourier-Bessel basis (the harmonics on the disk), which provides a convenient way to handle the effect of the contrast transfer functions. For images of size × , our method has time complexity ( + ) and space complexity ( + ). In contrast to previous work, these complexities are independent of the number of different contrast transfer functions of the images. We demonstrate our approach on synthetic and experimental data and show acceleration by factors of up to two orders of magnitude.

关键词： Covariance estimation Fourier–Bessel cryo-EM denoising principal component analysis single particle reconstruction

Effects of wild mango (Spondias pinnata) on quality of salted duck eggs

学校读者我要写书评

暂无评论

AIP Conference Proceedings 2024年第1期3027卷

作者： Muliadi Ramli Rustam Effendi Lia Amalia Nasrullah Idris Saiful Muhammad Rizal Rara Mitaphonna Sarah Aprilia Ulfia Rahmatillah Minati Maisarah Department of Chemistry Universitas Syiah Kuala Faculty of Mathematics and Natural Sciences 23111 Banda AcehAceh Indonesia Department of Physics Universitas Syiah Kuala Faculty of Mathematics and Natural Sciences 23111 Banda Aceh Aceh Indonesia Doctoral Program of Mathematics and Applied Sciences Universitas Syiah Kuala 23111 Banda Aceh Aceh Indonesia

The salted egg has been popular as a rural economic product which are mostly prepared by housewives in Aceh Besar regency. In order to support the rural economic activity, this experiment was designed and focused on utilization of the local fruits, namely wild mango (Spondias pinnata), which is recognized locally as “Kedondong hutan” to preserve quality of the salted egg. This biomass was employed as a green material on salting process of duck eggs. Initially, the pH level of “kedondong hutan” in liquid phase was determined by chemical method and a pH value of around 4.2 was obtained. While a phytochemical analysis of wild mango fruits revealed that it contains terpenoids, phenolic acids, saponins, alkaloids, flavonoids, and phenolic compounds. The oil exudation (OE) content in the salted eggs products was examined using a gravimetric method, and it was found that OE level of the salted eggs produced in Aceh Besar was around 19.83 %. Finally, this research demonstrated that “Kedondong hutan” fruit have a positive impact on preventing microbial growth in the salted duck egg product, thus useful for preserving its quality.

关键词：

Local order metrics for many-particle systems across length scales

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Maher, Charles Emmett Torquato, Salvatore Department of Chemistry Princeton University New Jersey08544 United States Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Formulating order metrics that sensitively quantify the degree of order/disorder in many-particle systems in d-dimensional Euclidean space Rd across length scales is an outstanding challenge in physics, chemistry, and materials science. Since an infinite set of n-particle correlation functions is required to fully characterize a system, one must settle for a reduced set of structural information, in practice. We initiate a program to use the local number variance σN2 (R) associated with a spherical sampling window of radius R (which encodes pair correlations) and an integral measure derived from it ΣN(Ri, Rj) that depends on two specified radial distances Ri and Rj. Across the first three space dimensions (d = 1, 2, 3), we find these metrics can sensitively describe and categorize the degree of order/disorder of 41 different models of antihyperuniform, nonhyperuniform, disordered hyperuniform, and ordered hyperuniform many-particle systems at a specified length scale R. Using our local variance metrics, we demonstrate the importance of assessing order/disorder with respect to a specific value of R. These local order metrics could also aid in the inverse design of structures with prescribed length-scale-specific degrees of order/disorder that yield desired physical properties. In future work, it would be fruitful to explore the use of higher-order moments of the number of points within a spherical window of radius R [S. Torquato et al., Phys. Rev. X, 11, 021028 (2021)] to devise even more sensitive order metrics. © 2024, CC BY.

关键词： Inverse problems

Hyperuniformity of maximally random jammed packings of hyperspheres across spatial dimensions

学校读者我要写书评

暂无评论

Physical Review E 2023年第6期108卷 064602-064602页

作者： Charles Emmett Maher Yang Jiao Salvatore Torquato Department of Chemistry Princeton University Princeton New Jersey 08544 USA Materials Science and Engineering Arizona State University Tempe Arizona 85287 USA Department of Physics Arizona State University Tempe Arizona 85287 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Materials Institute Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

The maximally random jammed (MRJ) state is the most random (i.e., disordered) configuration of strictly jammed (mechanically rigid) nonoverlapping objects. MRJ packings are hyperuniform, meaning their long-wavelength density fluctuations are anomalously suppressed compared to typical disordered systems, i.e., their structure factors S(k) tend to zero as the wave number |k| tends to zero. Here we show that generating high-quality strictly jammed states for Euclidean space dimensions d=3,4, and 5 is of paramount importance in ensuring hyperuniformity and extracting precise values of the hyperuniformity exponent α>0 for MRJ states, defined by the power-law behavior of S(k)∼|k|α in the limit |k|→0. Moreover, we show that for fixed d it is more difficult to ensure jamming as the particle number N increases, which results in packings that are nonhyperuniform. Free-volume theory arguments suggest that the ideal MRJ state does not contain rattlers, which act as defects in numerically generated packings. As d increases, we find that the fraction of rattlers decreases substantially. Our analysis of the largest truly jammed packings suggests that the ideal MRJ packings for all dimensions d≥3 are hyperuniform with α=d−2, implying the packings become more hyperuniform as d increases. The differences in α between MRJ packings and the recently proposed Manna-class random close packed (RCP) states, which were reported to have α=0.25 in d=3 and be nonhyperuniform (α=0) for d=4 and d=5, demonstrate the vivid distinctions between the large-scale structure of RCP and MRJ states in these dimensions. Our paper clarifies the importance of the link between true jamming and hyperuniformity and motivates the development of an algorithm to produce rattler-free three-dimensional MRJ packings.

关键词： Granular solids