Workshop on Large-Scale Inverse Problems and Quantification of Uncertainty

大规模反问题和不确定性量化研讨会

• 批准号: 0754077
• 负责人: Omar Ghattas
• 金额: $ 1万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-09-15 至 2008-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0754077&HistoricalAwards=false
• 关键词: Workshop; Large; Scale; Inverse; Problems

OCI 0738145Omar GhattasUniversity of Texas at AustinWorkshop: Large-scale Inverse Problems and Quantification of UncertaintyThe three-day workshop will be held on September 10-12, 2007, at the Bishop?s Lodge near Santa Fe, NM, site of our two previous workshops. The number of participants will be limited to 50, all invited, to create an optimal environment for discussion and discourse. In addition, another 10 participants will be drawn from an applicant pool of postdocs and students.Intellectual Merits.Many classes of problems in simulation-based science and engineering are characterized by a cycle of observation, data assimilation, prediction, and decision-making. The critical steps in this process involve: (1) assimilating observational data into large-scale simulations to estimate uncertainties in input parameters, (2) propagation of those uncertainties through the simulation to predict output quantities of interest, and (3) determination of an optimal control or decision-making strategy taking into account the uncertain outputs.For many problems, the input parameters cannot be measured directly; instead they must be inferred from observations of simulation outputs. The estimation of input parameters and associated uncertainties from observations and from a computational model linking inputs to outputs constitutes a statistical inverse problem. The uncertainties in the input parameters result from observational errors, inadequate computational models, and uncertain prior models of the inputs, and Bayesian inference often plays a central role. Characterization of the uncertainties in the inputs for high-dimensional parameter spaces and expensive forward simulations remains a tremendous challenge for many problems today. Yet despite their difficulties, there is a crucial unmet need for the development of scalable numerical algorithms for the solution of large scale statistical inverse problems: uncertainty estimation in model inputs is an important precursor of the quantification of uncertainties underpinning prediction and decision-making. While in the past, full and rigorous quantification of uncertainty in inverse problems and data assimilation for large scale systems has been intractable, several recent developments are making this enterprise viable: (1) the maturing state of algorithms and software for forward simulation, and their availability in the form of community codes, for many classes of problems in science and engineering; (2) the arrival of the petascale computing age; and (3) the explosion of observational data, much of it archived and accessible over data grids.Broader impacts.Accordingly, the P.I. proposes to organize a workshop dedicated to uncertainty estimation for large-scalemodels that will capitalize on these three Cyberinfrastructure developments. The workshop will assess the current state-of-the-art and identify needs and opportunities for future research. Leading figures in larges scale statistical inversion and data assimilation will be invited, along with promising junior investigators, postdocs, and students. The workshop will bring together and cross-fertilize the perspectives of researchers in the areas of large scale optimization, statistics, inverse problems, applied and computational math, high performance computing, and forefront applications. The focus will be on methods to characterize uncertainty in inputs (typically coefficients, initial conditions or system state, boundary conditions, sources, or other parameters of PDE models) via solution of statistical inverse problems. The workshop will differ from previous workshops in its focus on algorithms and methods that offer scalability to very large-scale models and simulations. The workshop will encourage the exchange of ideas, discuss outstanding unresolved barriers, present general solution strategies, establish future collaborations, and initiate new algorithmic directions. The goal will be to identify the path forward for resolving the difficulties associated with high-dimensional statistical inverse problems, and opportunities in such areas as aerospace, astrophysics, biomedical, chemical, geological, industrial, mechanical, and petroleum engineering and sciences.

OCI 0738145在Austinworkshop上的德克萨斯州的Ghattasuniversity：大规模的逆问题和不确定性的量化为期三天的研讨会将于2007年9月10日至12日在NM附近的NM附近的Bishop's Lodge举行。 参与者的数量将被限制为50，所有参与者都被邀请创造一个最佳的讨论和话语环境。此外，将从申请人和学生的申请人群中吸取另外10名参与者。智能优点。基于模拟的科学和工程中的许多问题的类别的特征是观察，数据同化，预测和决策。此过程中的关键步骤涉及：（1）将观察数据吸收到大规模模拟中，以估计输入参数中的不确定性，（（2）通过模拟来传播这些不确定性以预测感兴趣的输出数量，并且（3）确定最佳的控制策略或确定最佳的决策策略。取而代之的是，必须从模拟输出的观察结果中推断出它们。从观察值和将输入与输出联系起来的计算模型中对输入参数和相关不确定性的估计构成统计反问题。输入参数的不确定性是由观察误差，计算模型不足以及输入的先前模型不确定的，而贝叶斯推论通常起着核心作用。对于当今许多问题，对高维参数空间和昂贵的远期模拟的输入中不确定性的表征仍然是一个巨大的挑战。尽管遇到了困难，但对于开发用于解决大规模统计反问题的可扩展数值算法的至关重要的需求：模型输入中的不确定性估计是基于预测和决策制定的不确定性量化的重要先驱。在过去，大规模系统的反问题和数据同化的不确定性的全面量化非常棘手，但最近的一些发展使该企业可行：（1）算法和远程模拟的成熟状态，以进行远程模拟，以及它们以社区代码的形式，在科学和工程中的许多类别的社区代码形式； （2）Petascale计算年龄的到来； （3）观察数据的爆炸爆炸，其中大部分是在数据网格上访问和访问的。建议组织一个专门针对大规模模型的不确定性估计的研讨会，该研讨会将利用这三个网络基础设施发展。研讨会将评估当前的最新最新，并确定未来研究的需求和机会。 LARGES中的主要数字规模统计反演和数据同化，以及有前途的初级研究人员，博士后和学生。该研讨会将在大规模优化，统计，反问题，应用和计算数学，高性能计算以及最前沿应用程序的领域中汇集在一起​​并跨批准研究人员的观点。重点将放在通过统计逆问题的解决方案解决输入（通常是系数，初始条件或系统状态，边界条件，源或其他参数）中的不确定性的方法。该研讨会将与以前的研讨会不同，重点是算法和方法，这些算法和方法为非常大规模的模型和模拟提供了可扩展性。研讨会将鼓励思想的交流，讨论未解决的未解决的障碍，提出一般解决方案策略，建立未来的合作并启动新的算法指示。目的是确定解决与高维统计反问题相关的困难以及航空航天，天体物理学，生物医学，化学，地质，工业，机械和石油工程和科学等领域的机会。