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，这些模型对于科学和工程进步至关重要，因此与 NSF 的科学使命相关。大多数现实物理系统模型都使用涉及许多变量的复杂公式（例如偏微分方程）。当使用这样的模型来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，科学家经常必须使用“逆”计算来基于对现实世界的外部观察来计算系统模型的变量的初始输入值。换句话说，科学家试图从输出的真实观测数据推断物理过程计算机模型的输入。逆计算的例子有很多，从通过 CAT 扫描计算器官的重要尺寸，通过测量不同位置的音量和频率来重建声源，通过测量地球的重力场来计算地球的密度，或根据卫星和气象站在一段时间内的观测结果计算大气的初始状况（温度、压力等）。逆问题在所有科学和工程（及其他领域）中普遍存在。反问题存在许多解决方案，即使数据与观察结果相匹配的解决方案。然而，所确定的解决方案存在差异。也就是说，逆问题的解具有不确定性。贝叶斯推理提供了一个系统的数学框架来表征这种不确定性。然而，大规模复杂模型反问题的贝叶斯求解需要巨大的计算能力。直到最近才开始出现计算上易于处理的算法。然而，由于这些算法的复杂性以及需要从正向模型中获得更深入的信息，这些算法仍然超出了解决逆问题的主流科学家的能力范围。该项目旨在开发、分发和支持开源软件，该软件编码用于解决大规模复杂贝叶斯逆问题的最先进算法，并且具有健壮、可扩展、灵活、模块化、可广泛访问且易于使用的特点。该项目很大程度上建立在团队一直在开发的两个互补的开源软件库的基础上：麻省理工学院的 MUQ 和 UT-Austin/UC-Merced 的 hIPPYlib。 MUQ 提供了一系列强大的贝叶斯反演模型和算法，但预计正演模型将配备梯度/Hessians 以允许大规模解决方案。 hIPPYlib 在可以自动生成所需导数的环境中实现了强大的大规模梯度/基于 Hessian 的逆求解器，但它缺乏完整的贝叶斯功能。通过集成这两个互补的库，该项目将形成一个强大、可扩展且高效的软件框架，该框架可以发挥每个框架的优势，以解决广泛的科学和工程学科中复杂的大规模贝叶斯逆问题。由此产生的软件将在开源许可下分发，将为快速开发配备梯度/Hessian 信息的逆模型提供环境；用于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: An Extensible Software Framework for Large-Scale Inverse Problems Governed by PDEs: Part I: Deterministic Inversion and Linearized Bayesian Inference

hIPPYlib：由偏微分方程控制的大规模反问题的可扩展软件框架：第一部分：确定性反演和线性贝叶斯推理

• DOI: 10.1145/3428447
• 发表时间: 2021
• 期刊: ACM Transactions on Mathematical Software
• 影响因子: 2.7
• 作者: Villa, Umberto;Petra, Noemi;Ghattas, Omar
• 通讯作者: Ghattas, Omar