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

基本信息

  • 批准号:
    2339682
  • 负责人:
  • 金额:
    $ 59.36万
  • 依托单位:
  • 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

项目摘要

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.
对物理理论的对称性的描述--以及坐标自由度的变换规则--在物理学的重要发展中发挥了基础性的作用,包括广义相对论的发现。在现代机器学习中,对称性是深度学习结构设计的关键: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,再到原则上是排列等变的转换器。这个项目在物理学原理的启发下,开发了新的数学和计算技术,以进一步在机器学习模型的设计中利用对称性和微分几何。特别是,它将专注于点云和矢量场的表示学习和物理仿真。开发的技术将与纽约大学的物理学家合作,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。它还包括在拉丁美洲促进研究的活动,以及为女性在数学和工程领域建立社区的活动。该项目的第一个目标是改进表征学习技术,以自我监督的方式将文本或图像等数据嵌入潜在空间。基于最近通过近似群等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将对输入数据的可解释修改转换为嵌入空间中的线性变换。这将通过为所学习的表示提供因果结构来改进所学习的嵌入的可用性。我们使用不变量理论隐式地实现了这一点,并通过使用微分几何技术学习特殊的(解缠的)坐标系来显式地实现这一点。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。一种方法是实现相对于排列和正交(或洛伦兹)变换不变的点云算法,在此基础上可以建立n体模拟。在另一种方法中,基于现代经典物理的几何原理,建立了矢量场和张量场的机器学习方法,并将其离散到图像网格上。这些项目的成功将带来更准确的仿真,为培训集提供更少的昂贵的全分辨率模拟。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。

项目成果

期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ monograph.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ sciAawards.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ conferencePapers.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ patent.updateTime }}

Soledad Villar其他文献

Manifold optimization for k-means clustering
k 均值聚类的流形优化
A polynomial-time relaxation of the Gromov-Hausdorff distance
Gromov-Hausdorff 距离的多项式时间松弛
  • DOI:
  • 发表时间:
    2016
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Soledad Villar;A. Bandeira;A. Blumberg;Rachel A. Ward
  • 通讯作者:
    Rachel A. Ward
MarkerMap: nonlinear marker selection for single-cell studies
MarkerMap:单细胞研究的非线性标记选择
  • DOI:
    10.1038/s41540-024-00339-3
  • 发表时间:
    2022
  • 期刊:
  • 影响因子:
    4
  • 作者:
    Nabeel Sarwar;Wilson Gregory;George A. Kevrekidis;Soledad Villar;Bianca Dumitrascu
  • 通讯作者:
    Bianca Dumitrascu
Shuffled linear regression through graduated convex relaxation
通过分级凸松弛进行洗牌线性回归
  • DOI:
    10.48550/arxiv.2209.15608
  • 发表时间:
    2022
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Efe Onaran;Soledad Villar
  • 通讯作者:
    Soledad Villar
Three proofs of the Benedetto-Fickus theorem
Benedetto-Fickus 定理的三个证明
  • DOI:
  • 发表时间:
    2021
  • 期刊:
  • 影响因子:
    0
  • 作者:
    D. Mixon;Tom Needham;C. Shonkwiler;Soledad Villar
  • 通讯作者:
    Soledad Villar

Soledad Villar的其他文献

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

{{ truncateString('Soledad Villar', 18)}}的其他基金

Collaborative Research: CIF: Medium: Understanding Robustness via Parsimonious Structures.
合作研究:CIF:中:通过简约结构了解鲁棒性。
  • 批准号:
    2212457
  • 财政年份:
    2022
  • 资助金额:
    $ 59.36万
  • 项目类别:
    Standard Grant
Optimization Techniques for Geometrizing Real-World Data
现实世界数据几何化的优化技术
  • 批准号:
    2044349
  • 财政年份:
    2020
  • 资助金额:
    $ 59.36万
  • 项目类别:
    Standard Grant
Optimization Techniques for Geometrizing Real-World Data
现实世界数据几何化的优化技术
  • 批准号:
    1913134
  • 财政年份:
    2019
  • 资助金额:
    $ 59.36万
  • 项目类别:
    Standard Grant

相似海外基金

REU Site: Research in Symmetries at the University of Kentucky
REU 网站:肯塔基大学对称性研究
  • 批准号:
    2349261
  • 财政年份:
    2024
  • 资助金额:
    $ 59.36万
  • 项目类别:
    Continuing Grant
Geometric evolution of spaces with symmetries
具有对称性的空间的几何演化
  • 批准号:
    DP240101772
  • 财政年份:
    2024
  • 资助金额:
    $ 59.36万
  • 项目类别:
    Discovery Projects
Lagrangian Multiforms for Symmetries and Integrability: Classification, Geometry, and Applications
对称性和可积性的拉格朗日多重形式:分类、几何和应用
  • 批准号:
    EP/Y006712/1
  • 财政年份:
    2024
  • 资助金额:
    $ 59.36万
  • 项目类别:
    Fellowship
Canonical Singularities, Generalized Symmetries, and 5d Superconformal Field Theories
正则奇点、广义对称性和 5d 超共形场论
  • 批准号:
    EP/X01276X/1
  • 财政年份:
    2023
  • 资助金额:
    $ 59.36万
  • 项目类别:
    Fellowship
Characterization of Systematic Effects in Ultracold Neutron Tests of Fundamental Symmetries
基本对称性超冷中子测试中系统效应的表征
  • 批准号:
    2310015
  • 财政年份:
    2023
  • 资助金额:
    $ 59.36万
  • 项目类别:
    Standard Grant
Research in Novel Symmetries of Quantum Field Theory and String Theory
量子场论和弦理论的新对称性研究
  • 批准号:
    2310279
  • 财政年份:
    2023
  • 资助金额:
    $ 59.36万
  • 项目类别:
    Continuing Grant
Categorical Symmetries of Operator Algebras
算子代数的分类对称性
  • 批准号:
    2247202
  • 财政年份:
    2023
  • 资助金额:
    $ 59.36万
  • 项目类别:
    Standard Grant
CAREER: Low-energy Nuclear Physics and Fundamental Symmetries with Neutrons and Cryogenic Technologies
职业:低能核物理以及中子和低温技术的基本对称性
  • 批准号:
    2232117
  • 财政年份:
    2023
  • 资助金额:
    $ 59.36万
  • 项目类别:
    Continuing Grant
Random curves and surfaces with conformal symmetries
具有共形对称性的随机曲线和曲面
  • 批准号:
    2246820
  • 财政年份:
    2023
  • 资助金额:
    $ 59.36万
  • 项目类别:
    Continuing Grant
Polymorphism in the symmetries of gastric pouch arrangements in the sea anemone Diadumene lineata
海葵胃袋排列对称性的多态性
  • 批准号:
    22KJ3132
  • 财政年份:
    2023
  • 资助金额:
    $ 59.36万
  • 项目类别:
    Grant-in-Aid for JSPS Fellows
{{ showInfoDetail.title }}

作者:{{ showInfoDetail.author }}

知道了