检索结果-内蒙古大学图书馆

Multilevel Particle Filters for a Class of Partially Observed Piecewise Deterministic Markov Processes

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Jasra, Ajay Kamatani, Kengo Maama, Mohamed Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Institute of Statistical Mathematics Tokyo190-0014 Japan

In this paper we consider the filtering of a class of partially observed piecewise deterministic Markov processes (PDMPs). In particular, we assume that an ordinary differential equation (ODE) drives the deterministic element and can only be solved numerically via a time discretization. We develop, based upon the approach in [20], a new particle and multilevel particle filter (MLPF) in order to approximate the filter associated to the discretized ODE. We provide a bound on the mean square error associated to the MLPF which provides guidance on setting the simulation parameter of that algorithm and implies that significant computational gains can be obtained versus using a particle filter. Our theoretical claims are confirmed in several numerical examples. Copyright © 2023, The Authors. All rights reserved.

关键词： Ordinary differential equations

Multilevel Particle Filters for Partially Observed McKean-Vlasov Stochastic Differential Equations

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Awadelkarim, Elsiddig Jasra, Ajay Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia School of Data Science The Chinese University of Hong Kong Shenzhen China

In this paper we consider the filtering problem associated to partially observed McKean-Vlasov stochastic differential equations (SDEs). The model consists of data that are observed at regular and discrete times and the objective is to compute the conditional expectation of (functionals) of the solutions of the SDE at the current time. This problem, even the ordinary SDE case is challenging and requires numerical approximations. Based upon the ideas in [3, 12] we develop a new particle filter (PF) and multilevel particle filter (MLPF) to approximate the afore-mentioned expectations. We prove under assumptions that, for ϵ > 0, to obtain a mean square error of O(ϵ2) the PF has a cost per-observation time of O(ϵ−5) and the MLPF costs O(ϵ−4) (best case) or O(ϵ−4 log(ϵ)2) (worst case). Our theoretical results are supported by numerical experiments. © 2024, CC BY.

关键词： Mean square error

Antithetic Multilevel Particle Filters

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Jasra, Ajay Maama, Mohamed Ombao, Hernando Applied Mathematics and Computational Science Program United States Statistics Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. This is a challenging problem which requires the use of advanced numerical schemes based upon time-discretization of the diffusion process and then the application of particle filters. Perhaps the state-of-the-art method for moderate dimensional problems is the multilevel particle filter of [12]. This is a method that combines multilevel Monte Carlo and particle filters. The approach in that article is based intrinsically upon an Euler discretization method. We develop a new particle filter based upon the antithetic truncated Milstein scheme of [10]. We show that for a class of diffusion problems, for ϵ > 0 given, that the cost to produce a mean square error (MSE) in estimation of the filter, of O(ϵ2) is O(ϵ−2 log(ϵ)2). In the case of multidimensional diffusions with non-constant diffusion coefficient, the method of [12] has a cost of O(ϵ−2.5) to achieve the same MSE. We support our theory with numerical results in several examples. Copyright © 2023, The Authors. All rights reserved.

关键词： Mean square error

Designing a Framework for Solving Multiobjective Simulation Optimization Problems

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Chang, Tyler H. Wild, Stefan M. Mathematics and Computer Science Division Argonne National Laboratory 9700 S Cass Ave Bldg 240 LemontIL60439 United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory 1 Cyclotron Rd BerkeleyCA94720 United States

Multiobjective simulation optimization (MOSO) problems are optimization problems with multiple conflicting objectives, where evaluation of at least one of the objectives depends on a black-box numerical code or real-world experiment, which we refer to as a simulation. While an extensive body of research is dedicated to developing new algorithms and methods for solving these and related problems, it is challenging and time consuming to integrate these techniques into real world production-ready solvers. This is partly due to the diversity and complexity of modern state-of-the-art MOSO algorithms and methods and partly due to the complexity and specificity of many real-world problems and their corresponding computing environments. The complexity of this problem is only compounded when introducing potentially complex and/or domain-specific surrogate modeling techniques, problem formulations, design spaces, and data acquisition functions. This paper carefully surveys the current state-of-the-art in MOSO algorithms, techniques, and solvers;as well as problem types and computational environments where MOSO is commonly applied. We then present several key challenges in the design of a Parallel Multiobjective Simulation Optimization framework (ParMOO) and how they have been addressed. Finally, we provide two case studies demonstrating how customized ParMOO solvers can be quickly built and deployed to solve real-world MOSO problems. Copyright © 2023, The Authors. All rights reserved.

关键词： Software design

Unbiased Parameter Estimation for Bayesian Inverse Problems

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Chada, Neil K. Jasra, Ajay Maama, Mohamed Tempone, Raul Department of Mathematics City University of Hong Kong China School of Data Science The Chinese University of Hong Kong Shenzhen CN Shenzhen China Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a solution of a differential equation and, even if exact solutions are available, an analytical intractability of the marginal likelihood and its associated gradient, which is used for parameter estimation. The focus of this article is to deliver unbiased estimates of the unknown parameters, that is, stochastic estimators that, in expectation, are equal to the maximizer of the marginal likelihood, and possess no numerical approximation error. Based upon the ideas of [4] we develop a new approach for unbiased parameter estimation for Bayesian inverse problems. We prove unbiasedness and establish numerically that the associated estimation procedure is faster than the current state-of-the-art methodology for this problem. We demonstrate the performance of our methodology on a range of problems which include a PDE and ODE. Copyright © 2025, The Authors. All rights reserved.

关键词： Markov processes

A SPECTRAL LEVENBERG-MARQUARDT-DEFLATION METHOD FOR MULTIPLE SOLUTIONS OF SEMILINEAR ELLIPTIC SYSTEMS

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Li, Lin Zhou, Yuheng Xie, Pengcheng Li, Huiyuan School of Mathematics and Physics University of South China Hengyang China Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory 1 Cyclotron Road BerkeleyCA94720 United States State Key Laboratory of Computer Science Laboratory of Parallel Computing Institute of Software Chinese Academy of Sciences Beijing100190 China

Many nonlinear differential equations arising from practical problems may permit nontrivial multiple solutions relevant to applications, and these multiple solutions are helpful to deeply understand these practical problems and to improve some applications. Developing an efficient numerical method for finding multiple solutions is very necessary due to the nonlinearity and multiple solutions of these equations. Moreover, providing an efficient iteration plays an important role in successfully obtaining multiple solutions with fast and stable convergence. In the current paper, an efficient algorithm for finding multiple solutions of semilinear elliptic systems is proposed, where the trust region Levenberg-Marquardt method is firstly used to iterate the resulted nonlinear algebraic system. When the nonlinear term in these equations has only the first derivative, our algorithm can efficiently find multiple solutions as well. Several numerical experiments are tested to show the efficiency of our algorithm, and some solutions which have not been shown in the literature are also found and *** Codes 65N35, 65N22, 65F05, 65L10 Copyright © 2025, The Authors. All rights reserved.

关键词： Nonlinear equations

Multiphysics simulations of microstructure influence on hysteresis and eddy current losses of electrical steel

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Kühn, Patrick Yang, Yangyiwei Chen, Guanyu Foster, Shanelle N. Egger, Herbert Xu, Bai-Xiang Mechanics of Functional Materials Division Institute of Materials Science Technische Universität Darmstadt Darmstadt64287 Germany Department of Electrical and Computer Engineering Michigan State University MI48824 United States Johann Radon Institute for Computational and Applied Mathematics Linz Austria Institute for Numerical Mathematics Johannes Kepler University Linz Austria

Improving efficiency of electrical machines requires fundamental knowledge on the mechanisms behind magnetic and eddy current losses of the magnetic core materials, with Fe-Si alloy as a prototype. These losses are intrinsically influenced by the microstructure of the materials. This necessitates physics-based, microstructure-informed multiscale simulations. In the present paper, we utilised micromagnetic simulations and computational homogenization methods to calculate the effective hysteresis and effective conductivities of Fe-Si electrical steels. To demonstrate the methodology, binder-jet printed electrical steel material samples with different microstructure were investigated. The microstructure samples were digitized based on both the descriptor-based synthetic reconstruction and SEM-image-based digitization. More samples were generated with varying microstructure features such as grain size and grain boundary phases. The micromagnetic simulations were then performed to investigate the magnetic hysteresis and hysteresis loss. The eddy current loss was also evaluated by using the effective conductivity through computational homogenization. By performing parameter research on a series of synthetic microstructures, effects of average grain size and grain boundary (GB) phase thickness on the hysteresis loss and eddy current loss were unveiled. An average grain size around 120 µm has the lowest hysteresis loss, although the eddy current loss increases with the grain size. Increasing GB-phase thickness helps reduce both losses. Results indicate the potential to decrease loss of magnetic core materials by microstructure optimization. © 2025, CC BY.

关键词： Silicon alloys

Butterfly-Accelerated Solution of Coupled Volume Integral and Hydrodynamic Equations

学校读者我要写书评

暂无评论

Butterfly-Accelerated Solution of Coupled Volume Integral an...

USNC-URSI Radio Science Meeting (Joint with AP-S Symposium)

作者： Doolos Aibek Uulu Yang Liu Abdulkadir C. Yucel Hakan Bagci Department of Mathematics and Natural Sciences University of Central Asia (UCA) Naryn Kyrgyzstan Applied Mathematics & Computational Research Division Lawrence Berkeley National Laboratory Berkeley USA School of Electrical and Electronic Engineering Nanyang Technological University (NTU) Singapore Computer Electrical and Mathematical Science and Engineering Division King Abdullah University of Science and Technology (KAUST) Thuwal Saudi Arabia

ISBN: (数字)9789463968119

ISBN: (纸本)9798350359497

In recent years, advancements in plasmonic devices have enabled the localization of electromagnetic fields at subwavelength scales, contributing to breakthroughs in various scientific and engineering fields (J. C. Ndukaife, et al., ACS Nano, 2014,8,9,9035-9043). These structures are often made of metals and their electric properties are typically represented by the classical Drude model (S. A. Maier, 2007, Springer, New York). As the size of the plasmonic structures approaches the nanoscale, the classical Drude model falls short in explaining the collective movement of free electrons in metals. The interaction between moving charges and the electromagnetic fields can be described by a coupled system of the Maxwell and hydrodynamic equations (X. Zheng, et al., IEEE Trans. Antennas Propag., 2018,66,9, 4759-4771).

关键词： Location awareness Conferences Integral equations Metals Plasmons Hydrodynamics Mathematical models

Discovery and Recognition of Formula Concepts using Machine Learning

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Scharpf, Philipp Schubotz, Moritz Cohl, Howard S. Breitinger, Corinna Gipp, Bela University of Konstanz Germany University of Wuppertal and FIZ Karlsruhe Germany Applied and Computational Mathematics Division National Institute of Standards and Technology GaithersburgMD United States Institute of Computer Science University of Göttingen Germany

Citation-based Information Retrieval (IR) methods for scientific documents have proven effective for IR applications, such as Plagiarism Detection or Literature Recommender Systems in academic disciplines that use many references. In science, technology, engineering, and mathematics, researchers often employ mathematical concepts through formula notation to refer to prior knowledge. Our long-term goal is to generalize citation-based IR methods and apply this generalized method to both classical references and mathematical concepts. In this paper, we suggest how mathematical formulas could be cited and define a Formula Concept Retrieval task with two subtasks: Formula Concept Discovery (FCD) and Formula Concept Recognition (FCR). While FCD aims at the definition and exploration of a 'Formula Concept' that names bundled equivalent representations of a formula, FCR is designed to match a given formula to a prior assigned unique mathematical concept identifier. We present machine learning-based approaches to address the FCD and FCR tasks. We then evaluate these approaches on a standardized test collection (NTCIR arXiv dataset). Our FCD approach yields a precision of 68% for retrieving equivalent representations of frequent formulas and a recall of 72% for extracting the formula name from the surrounding text. FCD and FCR enable the citation of formulas within mathematical documents and facilitate semantic search and question answering as well as document similarity assessments for plagiarism detection or recommender *** Codes 68P20 (Primary), 68T50 (Secondary) © 2023, CC BY.

关键词： Machine learning