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.

过去十年，人工智能（AI）对信息技术和商业产生了深远的影响，甚至影响了社会转型。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技术领域挑战性问题的研究。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何以及如何表现得如此出色，这使得它们的可预测性不太确定。该项目的目的是解决这些缺点。因为它们与人工智能有关该项目还将涉及华盛顿大学组织的外展活动，例如年轻人的培训和保留。研究人员包括明确计划让 STEM 领域中代表性不足的群体参与进来。机器学习 (ML) 的最新进展导致了解决逆问题的新技术的发展，但我们对这些方法的理论理解有限，其中大多数都是无法确定性该项目的目的是通过开发贝叶斯逆问题的 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 BIP 的测量理论解释。为了解决适定性、稳定性和一致性问题，将使用马尔可夫链蒙特卡罗算法、数据驱动的先验信息构建以及基于生成建模和最新的变分推理技术来开发新的计算技术。该奖项反映了 NSF 的法定使命，并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，被认为值得支持。