Strategic Package: Centre for Predictive Modelling in Science and Engineering

预测建模和不确定性量化不仅仅是与科学和工程相关的另一个研究方向。它们构成了一种不同的思维方式，几乎影响了科学和工程分析与设计的各个方面。对于复杂的问题，我们不是得到确定性的答案，而是得到分布（误差条），它解释了我们对感兴趣的问题的不完整和经常不准确的信息。在大尺度上不确定的物理和几何性质的建模，在小尺度上的内在随机性或随机闭包的结合需要在许多多尺度问题中使用随机模拟，这对计算资源造成了沉重的负担。新兴的百亿亿次计算机将允许对现实系统进行随机模拟，但用现有方法分析pb级数据库可能效率太低，而且全尺寸模型无法用于优化、设计或实时控制。为此，华威大学建议建立一个新的中心，专注于预测建模和不确定性量化，其使命是开发不确定性量化（UQ）和预测建模的计算，数学和统计方法，应用于广泛的应用。新中心将强调几个基础研究领域的动态整合，包括：1)随机多尺度/多物理系统的公式，分析和数值解决，探索数学，统计和机器学习方法之间的协同作用。2)数据驱动的认证随机降阶模型开发。3)发展不确定条件下系统综合、设计、优化和控制的概率方法。这项工作将为在不同尺度收集的实验数据驱动的多尺度模拟中量化不确定性开发方法。为了解释输入不确定性和由此产生的随机输出的高维性质，建议为输入不确定性和多尺度系统的输出开发降阶代理模型。主题(1)-(3)是许多学科共同的统一主题。汇集华威大学内部现有的力量来解决这些问题，将同时影响多个应用，并推动解决不确定性量化的瓶颈问题（例如高维、有限数据、长期时间集成、罕见事件）。

Predictive modelling and uncertainty quantification are more than just another research direction relevant to science and engineering. They constitute a different way of thinking that impacts practically all aspects of scientific and engineering analysis and design. Rather than deriving deterministic answers to complex problems, distributions (error-bars) are obtained that account for our incomplete and often inaccurate information about the problems of interest. Modelling of uncertain physical and geometric properties in the large scales, intrinsic randomness in the small scales or incorporation of stochastic closures necessitate the use of stochastic simulations in many multiscale problems, heavily taxing computational resources. The emerging exascale computers will allow stochastic simulations of realistic systems but analysing petabyte data bases with existing methods can be too inefficient, and full-scale models cannot be used in optimisation, design or real-time control. To this end, the University of Warwick proposes to establish a new centre focused on Predictive Modelling and uncertainty quantification with the mission to develop computational, mathematical and statistical methodologies for uncertainty quantification (UQ) and predictive modelling applied to a broad range of applications. The new centre will emphasises a dynamic integration of several fundamental research areas including the following:1) Formulation, analysis and numerical solution of stochastic multiscale/multiphysics systems exploring synergies between mathematical, statistical and machine learning approaches.2) Data-driven development of certified stochastic reduced-order models. 3) Development of a probabilistic approach to systems synthesis, design, optimisation and control under uncertainty. This proposed work will develop methods for quantifying uncertainty in multiscale simulations driven by experimental data collected at different scales. In order to account for the high-dimensional nature of the input uncertainties and resulting stochastic outputs, it is proposed to develop reduced-order surrogate models both for the input uncertainties and for the output of multiscale systems. Topics (1)-(3) are unifying themes that are common to many disciplines. Bringing together existent strengths within the University of Warwick to address these problems would allow simultaneously to impact multiple applications and move forward the problem of resolving bottlenecks in uncertainty quantification (e.g. high-dimensionality, limited data, long term time integration, rare events).