检索结果-内蒙古大学图书馆

From atomistic to systematic coarse-grained models for molecular systems 2

学校读者我要写书评

暂无评论

From atomistic to systematic coarse-grained models for molec...

2nd International Conference on Uncertainty Quantification in computational Sciences and Engineering, UNCECOMP 2017

作者： Harmandaris, Vagelis Kalligiannaki, Evangelia Katsoulakis, Markos Plecháč, Petr Department of Mathematics and Applied Mathematics University of Crete Heraklion CreteGR-70013 Greece Institute of Applied and Computational Mathematics Foundation for Research and Technology Hellas IACM/FORTH Heraklion CreteGR-70013 Greece Applied Mathematics and Computational Science CEMSE King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia Department of Mathematics and Statistics University of Massachusetts at Amherst AmherstMA01003 United States Department of Mathematical Sciences University of Delaware NewarkDE19716 United States

ISBN: (纸本)9786188284449

The development of systematic (rigorous) coarse-grained mesoscopic models for complex molecular systems is an intense research area. Here we first give an overview of methods for obtaining optimal parametrized coarse-grained models, starting from detailed atomistic representation for high dimensional molecular systems. Different methods are described based on (a) structural properties (inverse Boltzmann approaches), (b) forces (force matching), and (c) path-space information (relative entropy). Next, we present a detailed investigation concerning the application of these methods in systems under equilibrium and non-equilibrium conditions. Finally, we present results from the application of these methods to model molecular systems. © 2017 The Authors.

关键词： Coarse-grained modeling

Conformal prediction after efficiency-oriented model selection

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Liang, Ruiting Zhu, Wanrong Barber, Rina Foygel Committee on Computational and Applied Mathematics University of Chicago United States Department of Statistics University of California Irvine United States Department of Statistics University of Chicago United States

Given a family of pretrained models and a hold-out set, how can we construct a valid conformal prediction set while selecting a model that minimizes the width of the set? If we use the same hold-out data set both to select a model (the model that yields the smallest conformal prediction sets) and then to construct a conformal prediction set based on that selected model, we suffer a loss of coverage due to selection bias. Alternatively, we could further splitting the data to perform selection and calibration separately, but this comes at a steep cost if the size of the dataset is limited. In this paper, we address the challenge of constructing a valid prediction set after efficiency-oriented model selection. Our novel methods can be implemented efficiently and admit finite-sample validity guarantees without invoking additional sample-splitting. We show that our methods yield prediction sets with asymptotically optimal size under certain notion of continuity for the model class. The improved efficiency of the prediction sets constructed by our methods are further demonstrated through applications to synthetic datasets in various settings and a real data example. Copyright © 2024, The Authors. All rights reserved.

关键词： Prediction models

Sampling real algebraic varieties for topological data analysis 18

学校读者我要写书评

暂无评论

Sampling real algebraic varieties for topological data analy...

18th IEEE International Conference on Machine Learning and Applications, ICMLA 2019

作者： Dufresne, Emilie Edwards, Parker Harrington, Heather Hauenstein, Jonathan Department of Mathematics University of York York United Kingdom Department of Mathematics University of Florida GainesvilleFL United States Mathematical Institute University of Oxford Oxford United Kingdom Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN United States

ISBN: (纸本)9781728145495

Topological data analysis (TDA) provides tools for computing geometric and topological information about spaces from a finite sample of points. We present an adaptive algorithm for finding provably dense samples of points on real algebraic varieties given a set of defining polynomials for use as input to TDA. The algorithm utilizes methods from numerical algebraic geometry to give formal guarantees about the density of the sampling, and also employs geometric heuristics to reduce the size of the sample. As TDA methods consume significant computational resources that scale poorly in the number of sample points, our sampling minimization makes applying TDA methods more feasible. We provide a software package that implements the algorithm, and showcase it through several examples. © 2019 IEEE.

关键词： Adaptive algorithms

Fast-Slow Neural Networks for Learning Singularly Perturbed Dynamical Systemse

学校读者我要写书评

暂无评论

Journal of computational Physics 2025年

作者： Daniel A. Serino Allen Alvarez Loya J.W. Burby Ioannis G. Kevrekidis Qi Tang Los Alamos National Laboratory Los Alamos NM Los Alamos Nationall Laboratory Los Alamos NM Department of Physics University of Texas at Austin Austin TX Department of Chemical and Biomolecular Engineering and Department of Applied Mathematics and Statistics Johns Hopkins University Baltimore MD Los Alamos National Laboratoryy Los Alamos NM School of Computational Science and Engineering Georgia Institute of Technology Atlanta GA

Singularly perturbed dynamical systems play a crucial role in climate dynamics and plasma physics. A powerful and well-known tool to address these systems is the Fenichel normal form, which significantly simplifies fast dynamics near slow manifolds through a transformation. However, this normal form is difficult to realize in conventional numerical algorithms. In this work, we explore an alternative way of realizing it through structure-preserving machine learning. Specifically, a fast-slow neural network (FSNN) is proposed for learning data-driven models of singularly perturbed dynamical systems with dissipative fast timescale dynamics. Our method enforces the existence of a trainable, attracting invariant slow manifold as a hard constraint. Closed-form representation of the slow manifold enables efficient integration on the slow time scale and significantly improves prediction accuracy beyond the training data. We demonstrate the FSNN on examples including the Grad moment system, two-scale Lorenz96 equations, and Abraham-Lorentz dynamics modeling radiation reaction of electrons.

关键词：

Nonparametric Density Estimation via Variance-Reduced Sketching

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Peng, Yifan Khoo, Yuehaw Wang, Daren Committee on Computational and Applied Mathematics University of Chicago United States Department of Statistics University of Chicago United States Department of Statistics University of Notre Dame United States

Nonparametric density models are of great interest in various scientific and engineering disciplines. Classical density kernel methods, while numerically robust and statistically sound in low-dimensional settings, become inadequate even in moderate higher-dimensional settings due to the curse of dimensionality. In this paper, we introduce a new framework called Variance-Reduced Sketching (VRS), specifically designed to estimate multivariable density functions with a reduced curse of dimensionality. Our framework conceptualizes multivariable functions as infinite-size matrices, and facilitates a new sketching technique motivated by numerical linear algebra literature to reduce the variance in density estimation problems. We demonstrate the robust numerical performance of VRS through a series of simulated experiments and real-world data applications. Notably, VRS shows remarkable improvement over existing neural network estimators and classical kernel methods in numerous density models. Additionally, we offer theoretical justifications for VRS to support its ability to deliver nonparametric density estimation with a reduced curse of dimensionality. Copyright © 2024, The Authors. All rights reserved.

关键词： Matrix algebra

Deep learning with Gaussian differential privacy

学校读者我要写书评

暂无评论

arXiv 2019年

作者： Bu, Zhiqi Dong, Jinshuo Long, Qi Su, Weijie J. Graduate Group in Applied Mathematics and Computational Science Graduate Group in Applied Mathematics and Computational Science Department of Biostatistics Epidemiology and Informatics Department of Statistics

Deep learning models are often trained on datasets that contain sensitive information such as individuals' shopping transactions, personal contacts, and medical records. An increasingly important line of work therefore has sought to train neural networks subject to privacy constraints that are specified by differential privacy or its divergence-based relaxations. These privacy definitions, however, have weaknesses in handling certain important primitives (composition and subsampling), thereby giving loose or complicated privacy analyses of training neural networks. In this paper, we consider a recently proposed privacy definition termed f-differential privacy [17] for a refined privacy analysis of training neural networks. Leveraging the appealing properties of f-differential privacy in handling composition and subsampling, this paper derives analytically tractable expressions for the privacy guarantees of both stochastic gradient descent and Adam used in training deep neural networks, without the need of developing sophisticated techniques as [3] did. Our results demonstrate that the f-differential privacy framework allows for a new privacy analysis that improves on the prior analysis [3], which in turn suggests tuning certain parameters of neural networks for a better prediction accuracy without violating the privacy budget. These theoretically derived improvements are confirmed by our experiments in a range of tasks in image classification, text classification, and recommender systems. Copyright © 2019, The Authors. All rights reserved.

关键词： Text processing

Abel transforms with low regularity with applications to X-ray tomography on spherically symmetric manifolds

学校读者我要写书评

暂无评论

arXiv 2017年

作者： De Hoop, Maarten V. Ilmavirta, Joonas Department of Computational and Applied Mathematics Rice University Department of Mathematics and Statistics University of Jyväskylä

We study ray transforms on spherically symmetric manifolds with a piecewise C1;1 metric. Assuming the Herglotz condition, the X-ray transform is injective on the space of L2 functions on such manifolds. We also prove injectivity results for broken ray transforms (with and without periodicity) on such manifolds with a C1;1 metric. To make these problems tractable in low regularity, we introduce and study a class of generalized Abel transforms and study their properties. This low regularity setting is relevant for geophysical applications. Copyright © 2017, The Authors. All rights reserved.

关键词： Differential equations

Machine learning the real discriminant locus

学校读者我要写书评

暂无评论

Journal of Symbolic Computation 2023年 115卷 409-426页

作者： Bernal, Edgar A. Hauenstein, Jonathan D. Mehta, Dhagash Regan, Margaret H. Tang, Tingting FLX AI Rochester 14607 NY United States Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre Dame 46556 IN United States The Vanguard Group Malvern 19355 PA United States Department of Mathematics Duke University Durham 27708 NC United States Department of Mathematics and Statistics San Diego State University Imperial Valley 92231 CA United States

Parameterized systems of polynomial equations arise in many applications in science and engineering with the real solutions describing, for example, equilibria of a dynamical system, linkages satisfying design constraints, and scene reconstruction in computer vision. Since different parameter values can have a different number of real solutions, the parameter space is decomposed into regions whose boundary forms the real discriminant locus. This article views locating the real discriminant locus as a supervised classification problem in machine learning where the goal is to determine classification boundaries over the parameter space, with the classes being the number of real solutions. This article presents a novel sampling method which carefully samples a multidimensional parameter space. At each sample point, homotopy continuation is used to obtain the number of real solutions to the corresponding polynomial system. Machine learning techniques including nearest neighbors, support vector classifiers, and neural networks are used to efficiently approximate the real discriminant locus. One application of having learned the real discriminant locus is to develop a real homotopy method that only tracks real solution paths unlike traditional methods which track all complex solution paths. Examples show that the proposed approach can efficiently approximate complicated solution boundaries such as those arising from the equilibria of the N=4 Kuramoto model which was previously intractable using traditional methods. © 2022 Elsevier Ltd

关键词： Deep learning Discriminant locus Machine learning Numerical algebraic geometry

Benchmarking projection-based real coded genetic algorithm on BBOB-2013 noiseless function testbed

学校读者我要写书评

暂无评论

Benchmarking projection-based real coded genetic algorithm o...

15th Annual Conference on Genetic and Evolutionary Computation, GECCO 2013

作者： Sawyerr, Babatunde A. Adewumi, Aderemi O. Ali, Montaz M. Department of Computer Sciences University of Lagos Lagos Nigeria School of Mathematics Statistics and Computer Science University of KwaZulu-Natal Westville South Africa School of Computational and Applied Mathematics University of Witwatersrand Johannesburg South Africa

ISBN: (纸本)9781450319645

In this paper, a real-coded genetic algorithm (RCGA) which incorporates an exploratory search mechanism based on vector projection termed projection-based RCGA (PRCGA) is benchmarked on the noisefree BBOB 2013 testbed. It is an enhanced version of RCGA-P in [22, 23]. The projection operator incorporated in PRCGA shows promising exploratory search capability in some problem landscape. PRCGA is equipped with a multiple independent restart mechanism and a stagnation alleviation mechanism. The maximum number of function evaluations (#FEs) for each test run is set to 105 times the problem dimension. PRCGA shows encouraging results on several problems in the low and moderate search dimensions. It is able to solve each type of problem with the dimension up to 40 with lower precision but not all the functions to the desired level of accuracy of 10 -8 especially for high conditioning and multi-modal functions within the specified maximum #FEs.

关键词： Benchmarking