Machine Learning for Bayesian Inverse Problems

在过去的十年里，人工智能(AI)对信息技术和商业产生了深远的影响，在一定程度上促进了社会转型。人工智能的显著成功引发了一股研究洪流，旨在利用人工智能解决科学和工程中具有挑战性的问题。尽管这些方法取得了经验上的成功，但我们对基本算法的数学理解是有限的，我们也不完全理解这些算法为什么以及如何表现得如此好，这使得它们的可预测性变得不那么确定。这个项目的目的是解决与人工智能算法有关的这些缺点，这些算法用于解决一大类被称为“逆问题”的工程问题，其中未知参数是通过间接测量(如MRI成像)预测的。该项目还将涉及通过华盛顿大学组织的外展活动，例如培训和留住年轻研究人员，包括明确计划让代表不足的群体参与到科学、经济和经济研究领域。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，而且大多数方法不能进行不确定性量化fi。本项目的目的是通过发展贝叶斯反问题最大似然方法的基础理论来解决这些缺点，并设计新的计算技术，使最大似然方法能够量化不确定性。在我们的理论分析中，我们将采用对BIP的度量理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科夫链蒙特卡罗算法、先验信息的数据驱动构建以及基于生成性建模和最优运输的最新变分推理技术来开发。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.