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Machine Learning for Bayesian Inverse Problems

贝叶斯逆问题的机器学习

基本信息

批准号：
2208535
负责人：
Bamdad Hosseini
金额：
$ 27.46万
依托单位：
University of Washington
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-09-01 至 2025-08-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2208535&HistoricalAwards=false
关键词：
Machine Learning Bayesian Inverse Problems

项目摘要

Artificial intelligence (AI) has had a profound impact in information technology and commerce to the degree of inﬂuencing societal transformation over the last decade. The remarkable success of AI has led to a torrent of research aiming to use AI to solve challenging problems in science and engineering. Despite the empirical success of these methods, our mathematical understanding of the underlying algorithms is limited and we do not fully understand why and how these algorithms perform so well, making their predictability less certain. The aim of this project is to address these shortcomings as they pertain to AI algorithms for a large family of engineering problems called "inverse problems", where an unknown parameter is predicted from indirect measurements, such as MRI imaging. The project will also involve outreach activities organized through the University of Washington such as the training and retention of young researchers including explicit plans to involve underrepresented groups in the STEM fields.Recent advances in Machine Learning (ML) have led to the development of novel techniques for the solution of inverse problems but our theoretical understanding of these methods is limited and the majority of them are incapable of uncertainty quantiﬁcation. The purpose of this project is to address these shortcomings by developing foundational theory for ML methods for Bayesian inverse problems and to design novel computational techniques that enable ML methods to quantify uncertainties. A measure theoretic interpretation of BIPs will be employed in our theoretical analysis to address the questions of well-posedness, stability, and consistency. New computational techniques will be developed using Markov chain Monte Carlo algorithms, data-driven construction of prior information, and recent variational inference techniques based on generative modeling and optimal transport.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

人工智能（AI）对信息技术和商业产生了深远的影响，在过去十年中，人工智能在一定程度上促进了社会转型。人工智能的巨大成功引发了一系列旨在利用人工智能解决科学和工程中具有挑战性的问题的研究。尽管这些方法在经验上取得了成功，但我们对底层算法的数学理解是有限的，我们并不完全理解这些算法为什么以及如何表现得如此出色，这使得它们的可预测性不那么确定。该项目的目的是解决这些缺点，因为它们涉及用于称为“逆问题”的一大类工程问题的AI算法，其中未知参数是从间接测量（如MRI成像）中预测的。该项目还将涉及通过华盛顿大学组织的外联活动，例如培训和留住年轻研究人员，包括明确计划让STEM领域代表性不足的群体参与进来。已经导致了新技术的发展，用于解决反问题，但我们对这些方法的理论理解是有限的，其中大多数是无法不确定性量化。该项目的目的是通过开发贝叶斯逆问题ML方法的基础理论来解决这些缺点，并设计新的计算技术，使ML方法能够量化不确定性。在我们的理论分析中，将采用BIPs的测度论解释来解决适定性、稳定性和一致性问题。新的计算技术将使用马尔可夫链蒙特卡罗算法，数据驱动的先验信息的建设，以及最近的变分推理技术的基础上生成建模和最佳transport.This奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。