Feature-Based Data Assimilation and Uncertainty Quantification for Complex Systems in Science and Engineering

科学与工程中复杂系统基于特征的数据同化和不确定性量化

• 批准号: 1619630
• 负责人: Matthias Morzfeld
• 金额: $ 25万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-08-01 至 2019-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1619630&HistoricalAwards=false
• 关键词: Feature; Based; Data; Assimilation; Uncertainty

The basic idea of data assimilation is to update a computational model with information from sparse and noisy data so that the updated model can be used for predictions. Data assimilation is at the core of computational geophysics, most notably in numerical weather prediction, oceanography, and geomagnetism, and is used widely in engineering applications, ranging from robotics to reservoir modeling. In the usual approach one attempts to refine a computational model such that its outputs match data. However, matching model outputs directly to data is often unnecessary or even undesirable. In this project, data assimilation is extended so that computational models can be updated based on features in the data, rather than the raw data themselves. The feature approach reduces an intrinsic dimension and is applicable to large scale problems in geosciences and engineering, with specific applications in geomagnetic dipole reversals, cloud modeling, and uncertainty quantification for solar cells.The primary technical aim of this project is to extend data assimilation such that computational models can be calibrated against features observed in the data, rather than the raw data. This can be achieved within a Bayesian framework by replacing the data with a suitable low-dimensional feature, computed from the data. The resulting feature-based likelihood can be used to assimilate selected aspects of fine-scale data into coarse, low-dimensional models. More generally, the use of features reduces the dimension of the likelihood, which in turn reduces the computational requirements of feature-based data assimilation by Monte Carlo methods. The mathematical foundations of the feature-based approach will be explored by rigorous analysis. New computational methods for feature-based data assimilation will be created, which combine machine learning techniques with Monte Carlo sampling. The efficiency of these methods will be assessed by interdisciplinary collaboration with scientists in geosciences and engineering in three specific applications. Specifically, feature-based data assimilation algorithms will be developed for the study of superchrons of Earth's magnetic dipole field, to determine the geophysical relevance of low-dimensional cloud models, and for uncertainty quantification of thin-film polymeric reflectors for solar power generation. These applications will collaboratively connect scientists (faculty, postdocs and students) across several disciplines (geosciences, engineering, mathematics). Undergraduate and graduate students at the University of Arizona will be trained as part of the project and will aid in producing and disseminating key results. The research activities will be accompanied by an outreach plan, implemented as part of the G-Teams program within the Department of Mathematics at the University of Arizona. A central outreach theme is to demonstrate, for K-12 teachers and their students, mathematics "in action" by applying mathematical concepts to problems relevant to our society.

数据同化的基本思想是用来自稀疏和噪声数据的信息更新计算模型，以便更新后的模型可用于预测。数据同化是计算物理学的核心，最显著的是在数值天气预报，海洋学和地磁学中，并广泛用于工程应用，从机器人到油藏建模。在通常的方法中，人们试图改进计算模型，使其输出与数据匹配。然而，将模型输出直接匹配到数据通常是不必要的，甚至是不可取的。在这个项目中，数据同化得到了扩展，使得计算模型可以根据数据中的特征而不是原始数据本身进行更新。特征方法降低了固有维数，适用于地球科学和工程中的大规模问题，在地磁偶极反转，云建模和太阳能电池的不确定性量化中具有特定的应用。该项目的主要技术目标是扩展数据同化，使计算模型可以根据数据中观察到的特征进行校准，而不是原始数据。这可以在贝叶斯框架内通过用从数据计算的合适的低维特征替换数据来实现。由此产生的基于特征的可能性可以用来同化到粗，低维模型的细尺度数据的选定方面。更一般地说，功能的使用降低了可能性的维度，这反过来又降低了基于特征的数据同化蒙特卡罗方法的计算要求。基于特征的方法的数学基础将通过严格的分析进行探讨。将为基于特征的数据同化创造新的计算方法，这种方法将联合收割机机器学习技术与蒙特卡罗抽样相结合。这些方法的效率将通过与地球科学和工程科学家在三个具体应用中的跨学科合作进行评估。具体而言，将开发基于特征的数据同化算法，用于研究地球磁偶极子场的超年代，以确定低维云模型的地球物理相关性，并用于太阳能发电薄膜聚合物反射器的不确定性量化。这些应用程序将跨多个学科（地球科学，工程，数学）协作连接科学家（教师，博士后和学生）。亚利桑那大学的本科生和研究生将作为该项目的一部分接受培训，并将协助产生和传播关键成果。研究活动将伴随着一个推广计划，作为亚利桑那大学数学系G-Teams计划的一部分实施。一个中心的推广主题是展示，为K-12教师和他们的学生，数学“在行动中”，通过应用数学概念的问题，有关我们的社会。