Fast Algorithms for Solving Big Data PDE Parameter Estimation Problems on Cloud Computing Platforms

云计算平台上解决大数据偏微分方程参数估计问题的快速算法

• 批准号: 1522599
• 负责人: Lars Ruthotto
• 金额: $ 18万
• 依托单位: Emory University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-09-15 至 2019-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1522599&HistoricalAwards=false
• 关键词: Fast; Algorithms; Solving; Big; Data

Parameter estimation problems arise in many scientific and economic disciplines, for example, in medical imaging, geophysical explorations, nondestructive testing, and economic structural estimation. Despite enormous effort put into designing efficient methods, solving parameter estimation problems is still very challenging, since the parametrized equations have to be solved repeatedly until the parameters are estimated with satisfactory accuracy. This research project aims to develop and implement efficient numerical methods for solving parameter estimation problems that involve a large number of measurements and partial differential equations. Reusable, open source software will be developed and made available to the scientific community. The techniques under development in the project will be applicable in geophysics to reduce the computational costs of large surveys that are of high economic impact, for example, in oil and gas exploration and groundwater surveys. The results from this project will also be applicable in medical imaging to reduce health care screening costs and improve diagnosis of certain diseases.Parameter estimation can be formulated as an optimization problem with constraints that are given by the parametrized partial differential equations (PDEs). The unknowns are parameters of the PDEs, which correspond to physical properties of the object to be measured. The objective is to minimize the misfit between PDE simulations and measured data plus some regularization term. Cloud computing platforms provide access to immense computational resources at moderate costs and are thus highly attractive for solving PDE parameter estimation problems. This holds particularly for big data problems since the computational costs of the estimation are dominated by the computational costs for PDE simulations. The latter, in many cases, grows linearly with the number of data. Straightforward extensions of the currently most reliable parameter estimation algorithms to massively parallel platforms, however, lead to huge communication overhead and memory requirement. This project seeks to design alternative tailored algorithms that make efficient use of cloud platforms and are able to solve parameter estimation problem with massive amounts of data in reasonable time. The approach undertaken in this project is based on three cornerstones. First, two reduced-order modeling techniques and their combination will be investigated. The PDEs will be discretized on rather coarse rectangular meshes that are aligned to the problem domain. On these meshes, reduced order models with adaptive multiscale bases will be used. Both techniques will dramatically reduce the computational cost associated with the PDE simulations. Second, stochastic optimization methods will be designed to exploit redundancy typically present in big data sets. The goal is to reduce the required number of PDE simulations, derive parameter selection rules, and quantify uncertainty of the solution. Third, the above steps will be combined and implemented on massively parallel cloud computing platforms.

参数估计问题出现在许多科学和经济学科中，例如，在医学成像、地球物理勘探、无损检测和经济结构估计中。尽管在设计有效的方法上投入了巨大的努力，解决参数估计问题仍然是非常具有挑战性的，因为参数化方程必须重复求解，直到参数以令人满意的精度估计。该研究项目旨在开发和实施有效的数值方法，用于解决涉及大量测量和偏微分方程的参数估计问题。 将开发可重复使用的开放源码软件并提供给科学界。该项目正在开发的技术将适用于地球物理学，以减少石油和天然气勘探及地下水调查等具有高经济影响的大型调查的计算成本。该项目的成果也将应用于医学成像，以降低医疗保健筛查成本和改善某些疾病的诊断。参数估计可以表示为一个具有参数化偏微分方程（PDE）给出的约束的优化问题。未知量是PDE的参数，其对应于待测量对象的物理性质。目标是最小化偏微分方程模拟和测量数据之间的失配加上一些正则化项。云计算平台以适中的成本提供对巨大计算资源的访问，因此对于解决PDE参数估计问题具有高度吸引力。这尤其适用于大数据问题，因为估计的计算成本主要由PDE模拟的计算成本决定。在许多情况下，后者随数据数量线性增长。然而，目前最可靠的参数估计算法的大规模并行平台的直接扩展，导致巨大的通信开销和内存需求。该项目旨在设计替代的定制算法，有效利用云平台，并能够在合理的时间内解决大量数据的参数估计问题。本项目采用的方法基于三个基石。首先，将研究两种降阶建模技术及其组合。偏微分方程将在与问题域对齐的相当粗糙的矩形网格上离散化。在这些网格上，将使用具有自适应多尺度基础的降阶模型。这两种技术将大大减少与PDE模拟相关的计算成本。其次，随机优化方法将被设计为利用通常存在于大数据集中的冗余。我们的目标是减少所需的PDE模拟，推导参数选择规则，并量化的解决方案的不确定性。第三，上述步骤将在大规模并行云计算平台上组合和实现。

项目成果

Layer-Parallel Training of Deep Residual Neural Networks

• DOI: 10.1137/19m1247620
• 发表时间: 2018-12
• 期刊: ArXiv
• 作者: Stefanie Günther;Lars Ruthotto;J. Schroder;E. Cyr;N. Gauger

An Uncertainty-Weighted Asynchronous ADMM Method for Parallel PDE Parameter Estimation

• DOI: 10.1137/18m119166x
• 发表时间: 2018-06
• 期刊: SIAM J. Sci. Comput.
• 作者: Samy Wu Fung;Lars Ruthotto

Improved Susceptibility Artifact Correction of Echo-Planar MRI using the Alternating Direction Method of Multipliers

• DOI: 10.1007/s10851-017-0757-x
• 发表时间: 2018-02-01
• 期刊: JOURNAL OF MATHEMATICAL IMAGING AND VISION
• 影响因子: 2
• 作者: Macdonald, Jan;Ruthotto, Lars
• 通讯作者: Ruthotto, Lars

LeanResNet: A Low-cost yet Effective Convolutional Residual Networks

• 发表时间: 2019-04
• 期刊: ArXiv
• 作者: Jonathan Ephrath;Lars Ruthotto;E. Haber;Eran Treister

Deep Neural Networks Motivated by Partial Differential Equations

由偏微分方程驱动的深度神经网络

• DOI: 10.1007/s10851-019-00903-1
• 发表时间: 2020
• 期刊: Journal of Mathematical Imaging and Vision
• 影响因子: 2
• 作者: Ruthotto, Lars;Haber, Eldad
• 通讯作者: Haber, Eldad