CAREER: Symmetries and Classical Physics in Machine Learning for Science and Engineering

职业：科学与工程机器学习中的对称性和经典物理学

• 批准号: 2339682
• 负责人: Soledad Villar
• 金额: $ 59.36万
• 依托单位: Johns Hopkins University
• 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: 2024-07-01 至 2029-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2339682&HistoricalAwards=false
• 关键词: CAREER; Symmetries; Classical; Physics; Machine

The description of physical theories in terms of their symmetries –and the transformation rules of coordinate freedom– played a fundamental role in important developments in physics, including the discovery of general relativity. In modern machine learning, symmetries are key to the design of deep learning architectures: From the translation symmetry of convolutional neural networks; to the permutation symmetry of graph neural networks; to transformers, which are, in principle, permutation equivariant. This project, inspired by physics principles, develops new mathematical and computational techniques to further exploit symmetries and differential geometry in the design of machine learning models. In particular, it will focus on representation learning and physics emulation on point clouds and vector fields. The developed techniques will be applied to problems in cosmology and climate science in collaboration with physicists at New York University. The project involves PhD students from Johns Hopkins and high school student interns from Baltimore City public schools. It also includes activities to promote research in Latin America, and community-building activities for women in math and engineering.The project's first aim is to improve representation learning techniques that embed data such as text or images in a latent space in a self-supervised fashion. Based on recent work that introduced an algebraic structure in the embedding space through approximate group equivariance, the developed methods will enable users to translate interpretable modifications to the input data into linear transformations in the embedding space. This will refine the usability of the learned embeddings by providing a causal structure to the learned representations. We achieve this implicitly, using invariant theory, and explicitly, by learning a special (disentangled) coordinate system with differential geometry techniques. The project's second aim is to develop coordinate-free emulation methods for cosmology and climate science. One approach is to implement algorithms for point clouds that are invariant with respect to permutations and orthogonal (or Lorentz) transformations, on which n-body simulations can be built. In another approach, machine learning methods are built for vector and tensor fields, based on geometric principles from modern classical physics, discretized onto image grids. Success in these projects will lead to more accurate emulation with fewer expensive full-resolution simulations for the training sets.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.

物理理论的对称性以及协调自由的转型规则的描述在物理学的重要发展中起着基本作用，包括发现一般相对论。在现代机器学习中，对称性是深度学习体系结构设计的关键：从卷积神经网络的翻译对称性中；对于原则上是置换等效的变压器。受物理原理的启发，项目开发了新的数学和计算技术，以进一步利用机器学习模型设计中的对称性和差异几何形状。特别是，它将集中于对点云和向量字段上的表示学习和物理仿真。开发的技术将与纽约大学物理学家合作，将其应用于宇宙学和气候科学问题。该项目涉及来自约翰·霍普金斯（Johns Hopkins）的博士生和巴尔的摩市公立学校的高中生实习生。它还包括促进拉丁美洲研究的活动，以及针对数学和工程领域女性的社区建设活动。该项目的第一个目的是提高表示数据，以自我监督的方式将数据（例如文本或图像）嵌入潜在空间。基于最近的工作，该工作通过近似群体均衡性在嵌入空间中引入了代数结构，开发的方法将使用户能够将可解释的修改转化为输入数据为嵌入空间中的线性变换。这将通过为学到的表示形式提供因果结构来完善学习嵌入的可用性。我们通过学习具有差异几何技术的特殊（分离）坐标系，使用不变理论，并明确地实现这一目标。该项目的第二个目的是开发宇宙学和气候科学的无坐标仿真方法。一种方法是实现有关置换和正交（或洛伦兹）变换的点云的算法，可以在其中构建n体模拟。在另一种方法中，基于现代古典物理学的几何原理，为向量和张量场构建了机器学习方法，将其离散到图像网格上。这些项目的成功将导致更准确的仿真，并为培训集的昂贵的全分辨率模拟较少。该奖项反映了NSF的法定任务，并通过使用基金会的知识分子优点和更广泛的影响审查标准来评估诚实的支持。