Workshop on Large-Scale Inverse Problems and Quantification of Uncertainty

奥马尔·加塔斯德克萨斯大学奥斯汀分校研讨会：大规模逆问题和不确定性量化为期三天的研讨会将于2007年9月10日至12日在主教？在新墨西哥州圣达菲附近的洛奇旅馆，我们之前的两个车间的地点。参加人数将限制在50人以内，所有人都被邀请，以创造一个最佳的讨论和演讲环境。此外，还将从博士后和学生申请者中抽取另外10名参与者。知识的优点。在基于仿真的科学和工程中，许多问题的特点是观察、数据同化、预测和决策的循环。该过程的关键步骤包括：(1)将观测数据同化到大规模模拟中以估计输入参数的不确定性，(2)通过模拟传播这些不确定性以预测感兴趣的输出数量，以及(3)考虑不确定性输出的最优控制或决策策略的确定。对于许多问题，输入参数不能直接测量；相反，它们必须从对模拟输出的观察中推断出来。从观测和从连接输入和输出的计算模型中对输入参数和相关不确定性的估计构成了一个统计逆问题。输入参数的不确定性来自于观测误差、不完善的计算模型和输入的不确定先验模型，而贝叶斯推理通常起着核心作用。表征高维参数空间输入中的不确定性和昂贵的正演模拟仍然是当今许多问题的巨大挑战。然而，尽管存在这些困难，但对于解决大规模统计逆问题的可扩展数值算法的开发仍有一个关键的未满足的需求：模型输入中的不确定性估计是支持预测和决策的不确定性量化的重要先驱。虽然在过去，对大规模系统的反问题和数据同化的不确定性进行全面而严格的量化一直是棘手的，但最近的一些发展使这项事业变得可行：(1)正演模拟的算法和软件的成熟状态，以及它们以社区代码形式的可用性，适用于科学和工程中的许多类别的问题；(2)千万亿次计算时代的到来；(3)观测数据的爆炸式增长，其中大部分已存档并可通过数据网格访问。更广泛的影响。因此，P.I.建议组织一个研讨会，专门讨论将利用这三个网络基础设施发展的大型模型的不确定性估计。讲习班将评估目前的最新技术，并确定未来研究的需要和机会。我们将邀请大规模统计反演和数据同化领域的领军人物，以及有前途的初级研究者、博士后和学生。研讨会将汇集大规模优化、统计学、逆问题、应用和计算数学、高性能计算和前沿应用领域研究人员的观点，并使其相互促进。重点将放在通过解决统计逆问题来表征输入（通常是系数、初始条件或系统状态、边界条件、源或PDE模型的其他参数）中的不确定性的方法上。本次研讨会将不同于以往的研讨会，其重点是算法和方法，为非常大规模的模型和模拟提供可扩展性。研讨会将鼓励思想交流，讨论尚未解决的障碍，提出一般解决方案策略，建立未来的合作，并启动新的算法方向。目标将是确定解决与高维统计逆问题相关的困难的前进道路，以及在航空航天、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。

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.