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On numerical solver selection and related uncertainty terminology

机译：关于数值解算器选择及相关不确定性术语

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摘要

Mathematical models provide insight into numerous biological, physical and chemical systems. They can be used in process design, optimisation, control and decision support, as acknowledged in many different fields of scientific research. Mathematical models do not always yield reliable results and uncertainty should be taken into account. At present, it is possible to identify some factors contributing to uncertainty, and the awareness of the necessity of uncertainty assessment is rising. In the fields of Environmental Modelling and Computational Fluid Dynamics, for instance, terminology related to uncertainty exists and is generally accepted. However, the uncertainty due to the choice of the numerical solver and its settings used to compute the solution of the models did not receive much attention in the past. A motivating example on the existence and effect of numerical uncertainty is provided and clearly shows that we can no longer ignore it. This paper introduces a new terminology to support communication about uncertainty caused by numerical solvers, so that scientists become perceptive to it.
机译：数学模型可洞悉众多生物，物理和化学系统。正如许多不同科学研究领域所公认的那样，它们可用于过程设计，优化，控制和决策支持。数学模型并不总是能产生可靠的结果，应考虑不确定性。目前，可以确定一些导致不确定性的因素，并且人们对不确定性评估的必要性的认识正在提高。例如，在环境建模和计算流体动力学领域，存在与不确定性相关的术语，并且该术语被普遍接受。但是，由于选择了数值求解器及其用于计算模型解的设置而导致的不确定性在过去并没有引起太多关注。提供了一个关于数值不确定性存在和影响的激励性例子，清楚地表明我们不能再忽略它。本文介绍了一种新的术语，以支持有关数值解算器引起的不确定性的交流，从而使科学家对它有所了解。

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  • 来源
    《Journal of Hydroinformatics》 |2010年第3期|P.241-250|共10页
  • 作者

    Petra Claeys; Ann van Griensven; Lorenzo Benedetti; Bernard De Baets; Peter A. Vanrolleghem;

  • 作者单位

    BIOMATH and KERMIT, Department of Applied Mathematics, Biometrics and Process Control, Ghent University,Coupure links 653, B-9000 Ghent, Belgium;

    rnHIKM, Hydroinformatics and Knowledge Management, UNESCO-IHE Institute for water Education, Westvest 7, 2611 AX Delft, The Netherlands;

    rnBIOMATH and KERMIT, Department of Applied Mathematics, Biometrics and Process Control, Ghent University,Coupure links 653, B-9000 Ghent, Belgium;

    rnKERMIT, Department of Applied Mathematics, Biometrics and Process Control,Ghent University, Coupure links 653, B-9000 Ghent, Belgium;

    rnmodeIEAU, Departement de genie civil, Pavilion Pouliot, Universite Laval, Quebec QC,Canada G1K 7P4;

  • 收录信息 美国《科学引文索引》(SCI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    mathematical models; numerical solver; terminology; uncertainty; uncertainty matrix;

    机译：数学模型;数值求解器术语;不确定;不确定矩阵;

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