Verification, Validation, and Uncertainty Quantification for Predictive Modeling in Computational Mechanics

计算力学预测建模的验证、确认和不确定性量化

• 批准号: 436199-2013
• 负责人: Prudhomme, Serge
• 金额: $ 1.09万
• 依托单位: École Polytechnique de Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=596884
• 关键词: Verification; Validation; Uncertainty; Quantification; Predictive

Computational predictions are increasingly used in science and engineering as a basis for critical decision making. It is thus becoming important to quantify, and possibly reduce, uncertainties in output quantities of computer simulations, as uncertainties usually arise from the use of imperfect physical models and from limited availability of data. The proposed research program aims at developing new theories, methodologies, and algorithms for predictive modeling, a term that has recently emerged in the literature to describe the systematic use of all relevant information to enhance the predictive power of theoretical and computational models. Applications will be in computational mechanics with a special focus on multi-scale and multi-physics modeling. Predictive modeling encompasses topics such as model validation, verification, and uncertainty quantification (UQ). Code and Solution Verification is the process of determining whether a computational model produces predictions with sufficient accuracy for meaningful comparisons with experimental data. Validation is the process of determining the accuracy by which a mathematical model can predict physical events with respect to a decision that has to be made. Finally, UQ is the process by which one characterizes all uncertainties in a system and its outputs. Validation and UQ are intimately related since the treatment of uncertainty involves three distinct processes: 1) the statistical estimation of random model parameters; 2) the validation process, which aims at determining, if only subjectively, whether or not the hypotheses of the model would hold for predictions of interest; 3) the propagation of input uncertainties through the stochastic system to quantify the uncertainties in quantities of interest. Outcomes of the proposed research program will be a collection of computational tools for a posteriori error estimation of discretization and modeling errors, adaptive schemes for multi-scale and multi-physics simulations, guidelines for model validation, including among others, planning, analysis of acceptance metrics, experimental design to select optimal data sets for calibration and validation, data quality assessment.

计算预测越来越多地用于科学和工程，作为关键决策的基础。因此，量化并尽可能减少计算机模拟输出量的不确定性变得越来越重要，因为不确定性通常来自使用不完善的物理模型和有限的数据。拟议的研究计划旨在开发新的理论，方法和算法的预测建模，一个术语，最近出现在文献中，描述系统地使用所有相关信息，以提高理论和计算模型的预测能力。应用程序将在计算力学与多尺度和多物理建模特别关注。预测建模包括模型验证、验证和不确定性量化（UQ）等主题。代码和解决方案验证是确定计算模型是否产生足够准确的预测，以便与实验数据进行有意义的比较的过程。验证是确定数学模型可以预测物理事件的准确性的过程。最后，UQ是描述系统及其输出中所有不确定性的过程。验证和UQ是密切相关的，因为不确定性的处理涉及三个不同的过程：1）随机模型参数的统计估计; 2）验证过程，其目的是确定，如果只是主观的，模型的假设是否将保持感兴趣的预测; 3）输入不确定性通过随机系统的传播以量化感兴趣的量中的不确定性。拟议的研究计划的成果将是一系列计算工具，用于离散化和建模误差的后验误差估计，多尺度和多物理场模拟的自适应方案，模型验证指南，包括规划，验收指标分析，实验设计，以选择最佳数据集进行校准和验证，数据质量评估。