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algorithm refinement for the stochastic Burgers' equation

JOURNAL OF COMPUTATIONAL PHYSICS 2007年第1期223卷 451-468页

作者： Bell, John B. Foo, Jasmine Garcia, Alejandro L. Lawrence Berkeley Lab Ctr Computat Sci & Engn Berkeley CA 94720 USA

In this paper, we develop an algorithm refinement (AR) scheme for an excluded random walk model whose mean field behavior is given by the viscous Burgers' equation. AR hybrids use the adaptive mesh refinement framework to model a system using a molecular algorithm where desired while allowing a computationally faster continuum representation to be used in the remainder of the domain. The focus in this paper is the role of fluctuations on the dynamics. In particular, we demonstrate that it is necessary to include a stochastic forcing term in Burgers' equation to accurately capture the correct behavior of the system. The conclusion we draw from this study is that the fidelity of multiscale methods that couple disparate algorithms depends on the consistent modeling of fluctuations in each algorithm and on a coupling, such as algorithm refinement, that preserves this consistency. (c) 2006 Elsevier Inc. All rights reserved.

关键词： Burgers' equation stochastic partial differential equations adaptive mesh refinement algorithm refinement hybrid methods asymmetric excluded random walk

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Noise in algorithm refinement methods

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COMPUTING IN SCIENCE & ENGINEERING 2005年第3期7卷 32-38页

作者： Alexander, FJ Tartakovsky, DM Garcia, AL Los Alamos Natl Lab Los Alamos NM 87545 USA San Jose State Univ San Jose CA 95192 USA

Hybrid or algorithm refinement (AR) schemes have focused mainly on the mean behavior of system states. However, variances in these behaviors, such as spontaneous fluctuations, are important for modeling certain phenomena. This article discusses the effects of statistical fluctuations on hybrid computational methods that combine a particle algorithm with a partial differential equation solver.

关键词： fluctuations noise partial differential equations physics computing algorithm refinement hybrid computational methods hybrid refinement noise partial differentialequation solver particle algorithm phenomena modeling statistical fluctuations system state

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ERC - An object-oriented refinement calculus for Eiffel

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FORMAL ASPECTS OF COMPUTING 2004年第1期16卷 51-79页

作者： Paige, RF Ostroff, JS York Univ Dept Comp Sci N York ON M3J 1P3 Canada

We present a refinement calculus for transforming object-oriented (OO) specifications (or 'contracts') of classes into executable Eiffel programs. The calculus includes the usual collection of algorithmic refinement rules for assignments, if-statements, and loops. However, the calculus also deals with some of the specific challenges of OO, namely rules for introducing feature calls and reference types (involving aliasing). The refinement process is compositional in the sense that a class specification is refined to code based only on the specifications (not the implementations) of the classes that the specification depends upon. We discuss how automated support for such a process can be developed based on existing tools. This work is done in the context of a larger project involving methods for the seamless design of OO software in the graphical design notation BON (akin to UML). The goal is to maintain model and source code integrity, i.e., the software developer can work on either the model or the code, where (ideally) changes in one view are reflected instantaneously and automatically in all views.

关键词： refinement calculi algorithm refinement object orientation Eiffel modular reasoning

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Fluctuations and continuity in particle-continuum hybrid simulations of unsteady flows based on flux-exchange

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EUROPHYSICS LETTERS 2005年第6期69卷 959-965页

作者： Delgado-Buscalioni, R Flekkoy, EG Coveney, PV UCL Dept Chem Ctr Computat Sci London WC1H 0AJ England Univ Nacl Educ Distancia Dept Ciencias & Tecnicas Fisicoquim Fac Ciencias Madrid 28040 Spain Univ Oslo Dept Phys N-0316 Oslo Norway

This letter describes the treatment of unsteady liquid flow by a hybrid particle-continuum scheme. The scheme couples a particle region described by molecular dynamics with a coarse-grained domain solved by continuum fluid dynamics. The particle and continuum domains overlap in the coupling region, where two-way transfer of momentum flux is established. We demonstrate that this flux-coupling scheme is able to describe high-frequency oscillatory flows and to ensure the continuity of velocity across the particle-continuum interface. The effect of fluctuations within the particle system is also analysed and establishes the range in frequency and flow wave number for which hydrodynamic fluctuations need to be taken into account within the continuum description.

关键词： algorithm refinement MOLECULAR-DYNAMICS TETHERED POLYMER EQUATIONS

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Towards Explainable AutoML Using Error Decomposition 35th

Towards Explainable AutoML Using Error Decomposition

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35th Australasian Joint Conference on Artificial Intelligence (AI)

作者： Owen, Caitlin A. Dick, Grant Whigham, Peter A. Univ Otago Dept Informat Sci Dunedin New Zealand

ISBN: (纸本)9783031226946;9783031226953

The important process of choosing between algorithms and their many module choices is difficult, even for experts. Automated machine learning allows users at all skill levels to perform this process. It is currently performed using aggregated total error, which does not indicate whether a stochastic algorithm or module is stable enough to consistently perform better than other candidates. It also does not provide an understanding of how the modules contribute to total error. This paper explores the decomposition of error for the refinement of genetic programming. Automated algorithm refinement is examined through choosing a pool of candidate modules and swapping pairs of modules to reduce the largest component of decomposed error. It is shown that a pool of candidates that are not examined for diversity in targeting different components of error can provide inconsistent module preferences. Manual algorithm refinement is also examined by choosing refinements based on their well-understood behaviour in reducing a particular error component. The results show that an effective process should exploit both the advantages of targeted improvements identified using a manual process and the simplicity of an automated process by choosing a hierarchy of the most important modules for reducing error components.

关键词： Genetic programming Automated machine learning algorithm refinement Symbolic regression

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Noise propagation in hybrid models of nonlinear systems: The Ginzburg-Landau equation

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JOURNAL OF COMPUTATIONAL PHYSICS 2014年第0期262卷 313-324页

作者： Taverniers, Soren Alexander, Francis J. Tartakovsky, Daniel M. Univ Calif San Diego Dept Mech & Aerosp Engn La Jolla CA 92093 USA Los Alamos Natl Lab Los Alamos NM 87545 USA

Every physical phenomenon can be described by multiple models with varying degrees of fidelity. The computational cost of higher fidelity models (e.g., molecular dynamics simulations) is invariably higher than that of their lower fidelity counterparts (e.g., a continuum model based on differential equations). While the former might not be suitable for large-scale simulations, the latter are not universally valid. Hybrid algorithms provide a compromise between the computational efficiency of a coarse-scale model and the representational accuracy of a fine-scale description. This is achieved by conducting a fine-scale computation in subdomains where it is absolutely required (e.g., due to a local breakdown of a continuum model) and coupling it with a coarse-scale computation in the rest of a computational domain. We analyze the effects of random fluctuations generated by the fine-scale component of a nonlinear hybrid on the hybrid's overall accuracy and stability. Two variants of the time-dependent Ginzburg-Landau equation (GLE) and their discrete representations provided by a nearest-neighbor Ising model serve as a computational testbed. Our analysis shows that coupling these descriptions in a one-dimensional simulation leads to erroneous results. Adding a random source term to the GLE provides accurate prediction of the mean behavior of the quantity of interest (magnetization). It also allows the two GLE variants to correctly capture the strength of the microscale fluctuations. Our work demonstrates the importance of fine-scale noise in hybrid simulations, and suggests the need for replacing an otherwise deterministic coarsescale component of the hybrid with its stochastic counterpart. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Stochastic partial differential equation Ising model Hybrid methods algorithm refinement Closure methods

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A Large-Scale Diverse GNSS/SINS Dataset: Construction, Publication, and Application

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2024年 73卷

作者： Zhu, Feng Chen, Xi Cai, Qinqing Zhang, Xiaohong Wuhan Univ Sch Geodesy & Geomat Minist Educ Wuhan 430079 Peoples R China Wuhan Univ Key Lab Geospace Environm & Geodesy Minist Educ Wuhan 430079 Hubei Peoples R China Wuhan Univ Sch Geodesy & Geomat Wuhan 430079 Hubei Peoples R China Wuhan Univ Sch Geodesy & Geomat Hubei Luojia Lab Wuhan 430079 Hubei Peoples R China Wuhan Univ Chinese Antarctic Ctr Surveying & Mapping Wuhan 430079 Hubei Peoples R China

High-precision continuous position and attitude determination are the critical modules of mobile mapping and autonomous driving (AD). Research in the integration of Global Navigation Satellite System (GNSS) and strapdown inertial navigation system (SINS) has greatly enhanced the accuracy and robustness of position and attitude in different scenes. However, the complexity and variability of the real scenes are still challenging for the existing models, parameters, strategies, and algorithms (MPSA). It is worth noting that high-quality datasets are key to accelerating the research and development of MPSA, which has been proved in the computer vision (CV) fields represented by the ImageNet dataset. Unfortunately, current public datasets either do not provide the raw observations of GNSS and inertial measurement unit (IMUs) or are not collected in abundant scenes and moving platforms. Therefore, a large-scale diverse GNSS/SINS dataset, named SmartPNT-POS, is presented. This dataset covers rich real-world environments, such as open-sky and complex urban, and multiple moving platforms, such as aircraft, land vehicles, and ships. In addition, different types of IMUs, including those manufactured in Hexagon, iMAR Navigation GmbH, and Honeywell, are contained in SmartPNT-POS as well. Moreover, it provides ground truths in each group of data for users to analyze and evaluate their MPSA. Now, the dataset is publicly available through Kaggle, a data science community, and the website to obtain the dataset is provided in the text. There have been 30 sets of data published on the website up to the present, and comprehensive analyses have been made in this contribution for the position and attitude determination results obtained by different processing modes. More data will be collected for different environments and applications and published on the same website in the future.

关键词： Global navigation satellite system Accuracy Roads Position measurement Heuristic algorithms Geodesy Geomagnetism Earth Artificial intelligence Robustness algorithm refinement autonomous driving (AD) dataset mobile mapping position and attitude determination

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Numerical methods for the stochastic Landau-Lifshitz Navier-Stokes equations

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Physical Review E 2007年第1期76卷 016708-016708页

作者： John B. Bell Alejandro L. Garcia Sarah A. Williams Center for Computational Sciences and Engineering Lawrence Berkeley National Laboratory Berkeley California 94720 USA Department of Physics San Jose State University San Jose California 95192 USA Department of Mathematics University of California Davis Davis California 95616 USA

The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several computational fluid dynamics approaches are considered (including MacCormack’s two-step Lax-Wendroff scheme and the piecewise parabolic method) and are found to give good results for the variance of momentum fluctuations. However, neither of these schemes accurately reproduces the fluctuations in energy or density. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce fluctuations in density, energy, and momentum. A variety of numerical tests, including the random walk of a standing shock wave, are considered and results from the stochastic LLNS solver are compared with theory, when available, and with molecular simulations using a direct simulation Monte Carlo algorithm.

关键词： SIMULATION MONTE-CARLO FLUCTUATING HYDRODYNAMIC EQUATIONS PARTIAL-DIFFERENTIAL-EQUATIONS SIMPLE-EXCLUSION PROCESS algorithm refinement SHOCK FLUCTUATIONS BOLTZMANN-EQUATION BROWNIAN RATCHETS DYNAMICS FLUID

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THE PROMOTION AND ACCUMULATION STRATEGIES IN TRANSFORMATIONAL PROGRAMMING

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ACM TRANSACTIONS ON PROGRAMMING LANGUAGES AND SYSTEMS 1984年第3期6卷 487-504页

作者： BIRD, RS Oxford University

The promotion strategy in transformational programming is a general method for achieving efficiency by exploiting the recursive structure in the dominant term of an algorithmic expression. For it to be carried out successfully, the original problem often has to be generalized by the inclusion of an extra parameter, a technique known as accumulation. These strategies are illustrated by deriving algorithms for two nontrivial problems: (1) determining whether a given digraph is acyclic, and (2) constructing the longest subsequence of a given sequence of vertices that forms a connected path in a given digraph. The derivations also serve to emphasize the usefulness of certain notational devices in applicative expressions, especially infix operators. Not only do such operators enhance the succinctness and readability of expressions, they also allow many transformations to be formulated as algebraic laws about their distributive and other properties. © 1984, ACM. All rights reserved.

关键词： algorithm refinement operators Transformational programming

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