Collaborative Research: SI2-SSI: Integrating Data with Complex Predictive Models under Uncertainty: An Extensible Software Framework for Large-Scale Bayesian Inversion

合作研究：SI2-SSI：不确定性下的数据与复杂预测模型的集成：大规模贝叶斯反演的可扩展软件框架

• 批准号: 1550547
• 负责人: Noemi Petra
• 金额: $ 47.5万
• 依托单位: University of California - Merced
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-09-01 至 2021-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1550547&HistoricalAwards=false
• 关键词: Collaborative; Research; SI2; SSI; Integrating

Scientists often use mathematical models to predict the behavior of natural and engineered systems. These models are therefore fundamental to scientific and engineering progress and hence relevant to NSF's science mission. Most models of realistic physical systems use complex formulae (such as, partial differential equations) involving many variables. When using such a model for predicting the future behavior of a system, a scientist has to provide initial values for all the variables. This can be difficult because input values may not be directly measureable. Thus, scientists often must use "inverse" computations to calculate the initial input values of the variables of a system model based on external observations of the real world. In other words, scientists seek to infer inputs to a computer model of a physical process from real observational data of the outputs. There are many examples of inverse computations, ranging from computing the important dimensions of an organ from its CAT scan, reconstructing the source of a sound by measuring its volume and frequency at various places, calculating the density of the Earth from measurements of its gravity field, or calculating the initial condition of the atmosphere (temperature, pressure, etc.) from satellite and weather station observations over a time interval. Inverse problems are ubiquitous across all of science and engineering (and beyond). Many solutions exist for inverse problems, i.e. solutions that fit the data to the observations. However, there are variations in the solutions identified. That is, the solutions of an inverse problem are subject to uncertainty. Bayesian inferencing provides a systematic mathematical framework for characterizing this uncertainty. However, the Bayesian solution of inverse problems for large-scale complex models require enormous computational power. Only recently have algorithms begun to emerge that are computationally tractable. However, these algorithms have remained out of the reach of the mainstream of scientists who solve inverse problems, due to their complexity and the need for deeper information from the forward model. This project aims to develop, distribute, and support open-source software that encodes state-of-the-art algorithms for the solution of large-scale complex Bayesian inverse problems and is robust, scalable, flexible, modular, widely accessible, and easy to use.The project builds heavily on two complementary open-source software libraries the team has been developing: MUQ at MIT, and hIPPYlib at UT-Austin/UC-Merced. MUQ provides a spectrum of powerful Bayesian inversion models and algorithms, but expects forward models to come equipped with gradients/Hessians to permit large-scale solution. hIPPYlib implements powerful large-scale gradient/Hessian-based inverse solvers in an environment that can automatically generate needed derivatives, but it lacks full Bayesian capabilities. By integrating these two complementary libraries, the project will result in a robust, scalable, and efficient software framework that realizes the benefits of each to tackle complex large-scale Bayesian inverse problems across a broad spectrum of scientific and engineering disciplines. The resulting software, that will be distributed under an open-source license, will provide an environment for rapid development of inverse models equipped with gradient/Hessian information; benchmark problems for evaluation and comparison of algorithms; and tutorial problems for training and testing purposes.

科学家经常使用数学模型来预测自然和工程系统的行为。因此，这些模型是科学和工程进步的基础，因此与NSF的科学任务有关。大多数现实的物理系统模型都使用复杂的公式（例如部分微分方程），涉及许多变量。当使用这样的模型预测系统的未来行为时，科学家必须为所有变量提供初始值。 这可能很困难，因为输入值可能无法直接测量。因此，科学家通常必须使用“逆”计算来计算基于现实世界的外部观察结果的系统模型变量的初始输入值。换句话说，科学家试图从输出的真实观察数据中推断出物理过程的计算机模型。有许多反向计算的示例，范围从计算器官的猫扫描中的重要尺寸，通过测量各个地方的体积和频率来重建声音的来源，从重力场的测量中计算地球的密度，或者从大气场的初始条件（温度，压力等）中计算出对卫星的初始状态（智能，压力等），并观察到了时间间隔。在整个科学和工程（及以后）中，逆问题无处不在。存在许多解决方案的反问题，即将数据适合观测值的解决方案。但是，在确定的解决方案中存在差异。也就是说，反问题的解决方案可能会出现不确定性。贝叶斯推论提供了一个系统的数学框架，用于表征这种不确定性。但是，大规模复杂模型的贝叶斯逆问题解决方案需要巨大的计算能力。直到最近，才开始出现算法，这些算法在计算方面都可以进行。但是，这些算法仍然无法触及解决反问题的科学家的主流，因为它们的复杂性以及从远期模型中需要更深入的信息。该项目旨在开发，分发和支持开源软件，该软件编码最新的算法，以解决大规模复杂的贝叶斯逆问题的解决方案，并且是可靠的，可扩展的，灵活的，灵活的，可易于使用的，可访问的，易于使用的，易于使用。 UT-Austin/UC-Merced。 MUQ提供了一系列功能强大的贝叶斯反转模型和算法，但期望远期模型配备梯度/黑姐妹，可以允许大规模解决方案。 Hippylib在可以自动生成所需的衍生物的环境中实现强大的大规模梯度/基于Hessian的反向求解器，但缺乏完整的贝叶斯能力。通过整合这两个互补的库，该项目将导致一个强大，可扩展和高效的软件框架，该框架实现了每个项目的好处，以解决各种科学和工程学科的复杂大规模贝叶斯逆问题。最终的软件将根据开源许可分发，它将为配备梯度/Hessian信息的反向模型的快速开发提供一个环境；评估和比较算法的基准问题；以及用于培训和测试目的的教程问题。

项目成果

Statistical Treatment of Inverse Problems Constrained by Differential Equations-Based Models with Stochastic Terms

• DOI: 10.1137/18m122073x
• 发表时间: 2018-10
• 期刊: SIAM/ASA J. Uncertain. Quantification
• 作者: E. Constantinescu;N. Petra;J. Bessac;C. Petra

Estimation of the Robin coefficient field in a Poisson problem with uncertain conductivity field

• DOI: 10.1088/1361-6420/aad91e
• 发表时间: 2018-01
• 期刊: Inverse Problems
• 影响因子: 2.1
• 作者: R. Nicholson;N. Petra;J. Kaipio

Linearized Bayesian inference for Young’s modulus parameter field in an elastic model of slender structures

细长结构弹性模型中杨氏模量参数场的线性贝叶斯推理

• DOI: 10.1098/rspa.2019.0476
• 发表时间: 2020
• 期刊: Physical and Engineering Sciences
• 作者: Fatehiboroujeni, Soheil;Petra, Noemi;Goyal, Sachin
• 通讯作者: Goyal, Sachin

Scalable Algorithms for Bayesian Inference of Large-Scale Models from Large-Scale Data

用于从大规模数据进行大规模模型的贝叶斯推理的可扩展算法

• DOI: 10.1007/978-3-319-61982-8_1
• 发表时间: 2017
• 期刊: Springer
• 作者: Ghattas, Omar;Isaac, Toby;Petra, Noemi;Stadler, Georg
• 通讯作者: Stadler, Georg

hIPPYlib-MUQ: A Bayesian Inference Software Framework for Integration of Data with Complex Predictive Models under Uncertainty

hIPPYlib-MUQ：用于在不确定性下将数据与复杂预测模型集成的贝叶斯推理软件框架

• 发表时间: 2021
• 期刊: 33nd International Conference on Parallel Computational Fluid Dynamics
• 作者: Kim, KT;Villa, U;Parno, M;Petra, N;Marzouk, Y;Ghattas, O
• 通讯作者: Ghattas, O