CDS&E: Collaborative Research: Strategies for Managing Data in Uncertainty Quantification at Extreme Scales

测量和数据量的指数级增长为数据驱动的科学发现和决策带来了巨大的希望。在许多情况下，数据驱动的科学发现在数学上被表述为一个逆问题。对于作为复杂问题发现和决策基础的逆问题，必须对其解中的不确定性进行量化。尽管在过去的几十年里，反问题的理论和计算算法都取得了巨大的进步，但在考虑大数据问题的情况下，量化反问题解决方案中的不确定性（UQ）仍然具有挑战性。这在很大程度上是由于现有数学技术对计算的要求很高，无法扩展到生成的数据量。因此，许多可用数据仍然未被使用。该项目开发的UQ算法既可计算扩展，又可数据扩展，有助于在地球科学和医学成像领域取得科学进展。特别是，所提出的方法在两个具有挑战性的数据驱动应用的背景下进行了评估：(1)从大量的地震图（地面运动的记录）执行地球物理成像来推断地球的内部结构，以更好地了解地震；(2)从磁共振（MR）电影图像的病人估计心脏的功能（如运动，收缩），以检测心脏病（心肌病）的早期发作。该合作研究项目的目标是开发一个综合研究项目，解决观测和科学模拟中产生的数据管理和数据分析问题，并在极端规模下应用于不同领域。该项目开发了创新的统计、数学和并行计算方法，以管理大量的模拟数据，以及一般极端尺度UQ问题，特别是贝叶斯反问题所需的不断增加的观测数据。这些方法将对科学家和工程师在基于传感的学科、地球科学、气候学、医学成像等领域处理大数据和大规模UQ问题具有直接的实用价值。该项目的成功完成将为开发数学和计算方法提供第一步，用于广泛的数据驱动的大规模逆和UQ挑战，这些挑战可以导致原始的科学发现并促进科学进步。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The exponential increase in the quantity of measurements and data holds tremendous promise for data-driven scientific discovery and decision making. In many cases, data-driven scientific discovery is mathematically formulated as an inverse problem. For inverse problems that serve as a basis for discovery and decision-making for complex problems, the uncertainty in its solutions must be quantified. Though the past decades have seen tremendous advances in both theories and computational algorithms for inverse problems, quantifying the uncertainty (UQ) in their solutions taking big-data issues into account remains challenging. This is largely due to computationally demanding nature of existing mathematical techniques that are unable to scale up to the amount of data being generated. Consequently, much of the available data remains unused. This project develops UQ algorithms that are both computationally scalable as well as datascalable for making scientific progresses in geosciences and medical imaging. In particular, the proposed methods are evaluated in the context of two challenging data-driven applications: (1) from large amount of seismograms (records of the ground motion) perform geophysical imaging to infer earth's interior structure to better understand earthquakes, and (2) from magnetic resonance (MR) cine images of patients estimate the heart's function (e.g. motion, contraction) to detect early onset of heart disease (cardiomyopathy).The goal of this collaborative research project is to develop an integrated research program that addresses the data management and data analytics arising from both observations and scientific simulations, with applications from diverse domains at extreme scales. The project develops innovative statistical, mathematical, and parallel computational methods to manage the large amounts of simulation data as well as the ever increasing amounts of observation data required for extreme-scale UQ problems in general and Bayesian inverse problems in particular. These methods will be of immediate practical utility to scientists and engineers dealing with big data and large-scale UQ problems in sensing-based disciplines, geosciences, climatology, medical imaging, etc. The successful completion of the project would provide a first step towards the development of mathematical and computational methods for a wide range of data-driven large-scale inverse and UQ challenges that can lead to original scientific discoveries and promote the progress of science.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.