CAREER: Uncertainty Quantification and Big Data Analysis in Interconnected Systems: Algorithms, Computations, and Applications

近年来，不确定性量化和大数据分析受到越来越多的关注。人们对这些问题进行了广泛的研究，并开发了新的数值方法来有效地处理大规模数据集和具有不确定性的复杂问题。UQ和大数据分析都使我们能够更好地了解各种不确定输入(边界和初始数据、参数值、几何形状、网络等)的影响。到数字预测。因此，UQ和大数据分析对于气候建模、天气预报、海洋动力学和智能电网等许多重要的实际问题至关重要。随着参数空间的数据量和维度的增加，UQ计算和大数据分析中最大的挑战之一是分析数据和运行模拟的计算成本。对于大规模的复杂互联系统，确定性仿真可能非常耗时，而进行UQ仿真则进一步增加了仿真成本，并且可能昂贵得令人望而却步。该项目旨在应对这些关键挑战。将开发一套新的高效UQ和大数据分析算法，使大数据分析和UQ仿真适用于大规模复杂互联系统。新算法将显著提升UQ和大数据分析方法的当前水平。该项目还整合了教育机会，包括让一系列本科生接触UQ和大数据，向研究生提供应用它们所需的高级技能，以及指导博士生成为UQ和大数据教育和研究领域的领导者。本研究项目中正在开发的方法基于多变量贝叶斯-树状高斯过程和电网简化的可扩展算法；高维UQ算法；非高斯噪声数据的动态状态估计和模型校准；以及高级随机事故分析。新的算法将基于在网络模型和概率空间中建立多保真模型。这样的算法可以在线性时间内容纳大数据。此外，虽然目前的事故分析只允许评估静态电网状态，而不考虑不确定性，但新方法将允许动态和概率地分析连锁故障的事故。新算法将允许调查人员建立一个有效的框架，以严格量化不确定性，分析大数据，并为智能电网模拟赋予复合误差条。

Uncertainty quantification (UQ) and big data analysis have received increasing attention in recent years. Extensive research effort has been devoted to these topics, and novel numerical methods have been developed to efficiently deal with large-scale data sets and complex problems with uncertainty. Both UQ and big data analysis enable us to better understand the impacts of various uncertain inputs (boundary and initial data, parameter values, geometry, network etc.) to numerical predictions. UQ and big data analysis are thus critical to many important practical problems such as climate modeling, weather prediction, ocean dynamics, and smart grids. As the data size and dimensions of parameter space increase, one of the biggest challenges in UQ computations and big data analysis is the computational cost for analyzing the data and running the simulations. For large-scale complex interconnected systems, deterministic simulations can be very time-consuming, and conducting UQ simulations further increases the simulation cost and can be prohibitively expensive. This project aims to address these critical challenges. A novel set of highly efficient UQ and big data analysis algorithms will be developed to make big data analysis and UQ simulations amenable for large-scale complex interconnected systems. The new algorithms will significantly advance the current state of the art of UQ and big data analysis methods. The project also integrates educational opportunities, including exposing a range of undergraduate students to UQ and big data, giving graduate students the advanced skills needed to apply them, and mentoring Ph.D. students to be leaders in UQ and big data education and research. The approach under development in this research project is based on scalable algorithms for multivariate Bayesian-treed Gaussian process and power network reduction; high-dimensional UQ algorithms; dynamic state estimation and model calibration for non-Gaussian noisy data; and advanced stochastic contingency analysis. The new algorithms will be based on building multi-fidelity models in both network models and probability space. Such algorithms can accommodate big data in linear time. In addition, while current contingency analysis allows only assessment of a static power grid status without considering uncertainty, the new approaches will allow analysis of contingency dynamically and probabilistically for cascade failures. The new algorithms will allow investigators to establish an efficient framework to rigorously quantify the uncertainty, analyze big data, and endow smart grid simulations with a composite error bar.