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，数据的生成速度非常快。这些数据通常与感兴趣的数量间接相关，并且数据集在许多情况下动态增长。从这些数据中提取所需的信息，然后需要解决非常大的数据密集型的逆问题，也许重复和真实的时间。获得这样的解决方案的计算挑战是由验证和不确定性分析的需求，这很容易成为计算上的禁止。该项目将开发数学/统计方法和计算工具，用于解决数据密集型逆问题。该方法的核心是对此类问题进行随机重构，旨在显著降低计算成本的同时适应现代硬件架构。将开发一个框架来解决大数据、反问题、数据分析和不确定性量化之间的接口所带来的挑战。 首先，随机方法的线性和非线性逆问题的解决方案将被引入，以便有效的随机优化方法可以用来克服当前算法的硬件限制，并产生解决方案和不确定性评估在近实时。新的理论和可扩展的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，将开发先进的工具，用于模型验证、误差分析和不确定性量化。通过与应用科学家合作（例如，在大气遥感方面），该项目中开发的方法将对科学家和工程师立即产生实际效用。

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

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

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

Efficient learning methods for large-scale optimal inversion design

• DOI: 10.3934/naco.2022036
• 发表时间: 2021-10
• 期刊: ArXiv
• 作者: Julianne Chung;Matthias Chung;S. Gazzola;M. Pasha