Collaborative Research: Stochastic Approximations for the Solution and Uncertainty Analysis of Data-Intensive Inverse Problems

合作研究：数据密集型反问题的求解和不确定性分析的随机近似

• 批准号: 1723005
• 负责人: Matthias Chung
• 金额: $ 21万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-09-01 至 2022-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1723005&HistoricalAwards=false
• 关键词: Collaborative; Research; Stochastic; Approximations; Solution

In scientific fields ranging from geophysics and atmospheric science to medical imaging and network communication, data are being generated at remarkable rates. Such data are typically indirectly related to quantities of interest and the data sets are in many cases dynamically growing. Extracting desired information from these data then requires the solution of very large data-intensive inverse problems, perhaps repeatedly and in real time. The computational challenges of obtaining such a solution are compounded by the demands of validation and uncertainty analysis, which can easily become computationally prohibitive. This project will develop mathematical/statistical methods and computational tools for the solution of data-intensive inverse problems. The core of this approach is a stochastic reformulation of such problems that aims to significantly reduce the computational costs while adapting to modern hardware architectures.A framework will be developed to address the challenges arising at the interface between big data, inverse problems, data analysis, and uncertainty quantification. First, randomized methods for the solution of linear and nonlinear inverse problems will be introduced, so that efficient stochastic optimization methods can be used to overcome the hardware limitations of current algorithms and to generate solutions and uncertainty assessments in near-real time. New theory and scalable methods will be developed within the stochastic framework, thereby ensuring solution accuracy, reliability, and robustness. Second, advanced tools will be developed for model validation, error analysis, and uncertainty quantification. By partnering with application scientists (e.g., in atmospheric remote sensing), methods developed in this project will be of immediate practical utility for scientists and engineers.

在从地球物理学和大气科学到医学成像和网络通信的科学领域中，正在以显着的速度生成数据。此类数据通常与关注量间接相关，并且数据集在许多情况下是动态增长的。然后，从这些数据中提取所需的信息，就需要解决非常大的数据密集型反问题的解决方案，也许是反复的，实时的。获得此类解决方案的计算挑战是由验证和不确定性分析的需求加剧了，这很容易在计算上变得过时。该项目将开发数学/统计方法和计算工具，以解决数据密集型逆问题。这种方法的核心是对此类问题的随机重新重新制定，旨在显着降低计算成本，同时适应现代硬件体系结构。将开发一个框架，以应对大数据，逆问题，数据分析和不确定性量化之间在接口上产生的挑战。 首先，将引入用于线性和非线性逆问题解决方案的随机方法，因此可以使用有效的随机优化方法来克服当前算法的硬件限制，并在近乎现实的时间内生成解决方案和不确定性评估。新理论和可扩展方法将在随机框架内开发，从而确保解决方案的准确性，可靠性和鲁棒性。其次，将开发高级工具用于模型验证，错误分析和不确定性量化。通过与应用程序科学家合作（例如，在大气遥感中），该项目中开发的方法将对科学家和工程师立即实用。

项目成果

slimTrain---A Stochastic Approximation Method for Training Separable Deep Neural Networks

slimTrain---一种训练可分离深度神经网络的随机逼近方法

• DOI: 10.1137/21m1452512
• 发表时间: 2022
• 期刊: SIAM Journal on Scientific Computing
• 影响因子: 3.1
• 作者: Newman, Elizabeth;Chung, Julianne;Chung, Matthias;Ruthotto, Lars
• 通讯作者: Ruthotto, Lars

Least-squares finite element method for ordinary differential equations

常微分方程的最小二乘有限元法

• DOI: 10.1016/j.cam.2022.114660
• 发表时间: 2023
• 期刊: Journal of Computational and Applied Mathematics
• 影响因子: 2.4
• 作者: Chung, Matthias;Krueger, Justin;Liu, Honghu
• 通讯作者: Liu, Honghu

Hybrid Projection Methods with Recycling for Inverse Problems

• DOI: 10.1137/20m1349515
• 发表时间: 2020-07
• 期刊: SIAM J. Sci. Comput.
• 作者: Julianne Chung;E. D. Sturler;Jiahua Jiang

Iterative Sampled Methods for Massive and Separable Nonlinear Inverse Problems

大规模可分离非线性反问题的迭代采样方法

• 发表时间: 2019
• 期刊: Scale Space and Variational Methods in Computer Vision. SSVM 2019. Lecture Notes in Computer Science
• 作者: Julianne Chung, Matthias Chung

Efficient Krylov subspace methods for uncertainty quantification in large Bayesian linear inverse problems

• DOI: 10.1002/nla.2325
• 发表时间: 2020-08
• 期刊: Numerical Linear Algebra with Applications
• 影响因子: 4.3
• 作者: A. Saibaba;Julianne Chung;Katrina Petroske