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.

用对称性来描述物理理论——以及坐标自由的变换规则——在物理学的重要发展中发挥了基础作用，包括广义相对论的发现。在现代机器学习中，对称性是深度学习设计的关键。架构：从卷积神经网络的平移对称性；到图神经网络的排列对称性；原则上，变换器是排列等变的。该项目受物理原理的启发，开发了新的数学和计算技术。在机器学习模型的设计中进一步利用对称性和微分几何，它将重点关注点云和矢量场的表示学习和物理仿真，并将与物理学家合作应用于宇宙学和气候科学的问题。该项目涉及约翰·霍普金斯大学的博士生和巴尔的摩市公立学校的高中生实习生。该项目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。目的是改进以自我监督的方式将文本或图像等数据嵌入到潜在空间中的表示学习技术，基于最近通过近似群等方差在嵌入空间中引入代数结构的工作，所开发的方法将使用户能够翻译可解释的内容。将输入数据修改为嵌入空间中的线性变换，这将通过为学习的表示提供因果结构来完善学习的嵌入的可用性，并且我们使用不变理论隐式地实现了这一点。明确地说，通过使用微分几何技术学习特殊的（解缠结的）坐标系，该项目的第二个目标是开发宇宙学和气候科学的无坐标仿真方法，一种方法是实现排列不变的点云算法。在另一种方法中，基于现代经典物理学的几何原理，可以构建向量和张量场的机器学习方法，并将其离散化。这些项目的成功将带来更准确的仿真，并减少昂贵的全分辨率模拟训练集。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。 。