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 fram...
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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.
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 phenom...
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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.
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 refi...
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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.
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 ...
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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.
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 p...
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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.
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...
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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.
作者：
Zhu, FengChen, XiCai, QinqingZhang, XiaohongWuhan 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 strapd...
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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.
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 equ...
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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.
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 suc...
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