CAREER: Gaussian Processes for Scientific Machine Learning: Theoretical Analysis and Computational Algorithms

职业：科学机器学习的高斯过程：理论分析和计算算法

• 批准号: 2337678
• 负责人: Bamdad Hosseini
• 金额: $ 60万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-06-01 至 2029-05-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2337678&HistoricalAwards=false
• 关键词: CAREER; Gaussian; Processes; Scientific; Machine

Machine learning and artificial intelligence are increasingly changing our lives at every scale, from our personal day-to-day activities to large scale shifts in our society, economy, and geopolitics. These technologies have also profoundly transformed sciences with new ideas and algorithms being developed at an immense speed. However, our mathematical understanding of these algorithms is still far beyond their practical development and widespread adoption. Put simply, in many cases we do not know how or why machine learning algorithms work so well, which in turn limits our ability to safely deploy them in safety critical engineering and scientific scenarios. The goal of this project is to develop mathematical formalism and understanding of problems at the intersection of machine learning and science (i.e., scientific machine learning) using rigorous mathematics, leading to novel algorithms and computational methodologies that are interpretable, supported by rigorous theory, and aware of uncertainties.The project is focused on the development of novel Gaussian Process (GP) based computational frameworks for scientific machine learning that are provably well-posed, robust, and stable, thereby meeting the high standards of scientific computing. The developed methodologies will be capable of rigorous uncertainty quantification and inherit the desirable properties of machine learning algorithms such as flexibility, generalizability, and applicability in high-dimensions. The efforts of the project are directed in three primary directions: (1) GPs for solving nonlinear, high-dimensional and parametric PDEs; (2) GPs for operator learning, emulation, and physics discovery; and (3) GPs for high-dimensional sampling, inference, and generative modeling. Each research direction focuses on the development of algorithms, foundational theory, and concrete applications in engineering and science. The project also contains an extensive education plan focused on machine learning and data science education from high-school through graduate levels with extensive opportunities for training of graduate and undergraduate students as well as local and international outreach.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.

机器学习和人工智能正在各个层面日益改变我们的生活，从我们的个人日常活动到社会、经济和地缘政治的大规模转变。这些技术还深刻地改变了科学，新的想法和算法正在以惊人的速度发展。然而，我们对这些算法的数学理解仍然远远超出了它们的实际发展和广泛采用。简而言之，在许多情况下，我们不知道机器学习算法如何或为何如此有效，这反过来限制了我们在安全关键工程和科学场景中安全部署它们的能力。该项目的目标是使用严格的数学来发展数学形式主义和对机器学习与科学（即科学机器学习）交叉点问题的理解，从而产生可解释的、有严格理论支持的新颖算法和计算方法，以及该项目的重点是开发基于高斯过程（GP）的新型科学机器学习计算框架，该框架已被证明是适定的、稳健的和稳定的，从而满足科学计算的高标准。所开发的方法将能够进行严格的不确定性量化，并继承机器学习算法的理想特性，例如灵活性、泛化性和高维适用性。该项目的工作主要集中在三个方向：(1) 求解非线性、高维和参数偏微分方程的 GP； (2) 用于操作员学习、仿真和物理发现的 GP； (3) 用于高维采样、推理和生成建模的 GP。每个研究方向都侧重于算法的开发、基础理论以及工程和科学中的具体应用。该项目还包含一项广泛的教育计划，重点关注从高中到研究生阶段的机器学习和数据科学教育，为研究生和本科生提供广泛的培训机会以及本地和国际推广。该奖项反映了 NSF 的法定使命，并已通过使用基金会的智力优点和更广泛的影响审查标准进行评估，认为值得支持。