I-Corps: Optimization Applications of Differential Geometry and Optimal Transport

I-Corps:微分几何和最优传输的优化应用

基本信息

  • 批准号:
    2129211
  • 负责人:
  • 金额:
    $ 5万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2021
  • 资助国家:
    美国
  • 起止时间:
    2021-04-01 至 2022-09-30
  • 项目状态:
    已结题

项目摘要

The broader impact/commercial potential of this I-Corps project is the development of applications of differential geometry and optimal transportation toward solving complex optimization problems. The focus of this project is understanding which bio-mechanical parameters capture the key features of complex human motor activities in the area of sports training and recruitment. The proposed technology may have numerous applications for professional sports as well as for aspiring and amateur athletes. Moreover, it may be beneficial for reducing injury risk for athletes and reducing recovery times for athletes returning from injury. The proposed technology also may be used for player skill development, which plays a central role in sports at all levels. Talent evaluation and player recruitment, which also receives significant resources both at the professional and collegiate levels may also be impacted. Other fields that may benefit include weather forecasting, optimal network design, economics, physics, and optics.This I-Corps project is based on the development of mathematical tools and algorithms inspired by the deep theory of the fully nonlinear Monge-Ampere equation that is a common denominator for the vast fields of Differential Geometry and Optimal Transportation. Differential Geometry is combined with data-analytic tools from Machine Learning and state-of-the-art bio-mechanical research in order to analyze in-depth and develop a new bio-mechanical understanding of certain complex human motor activities that involve the simultaneous use of multiple limbs. The proposed technology is focused on activities that require a high degree of skill and coordination and that are challenging to train and learn. Understanding whether a specific equation may be used to give mathematical insights on optimizing complex human activities could provide yet another real-world application of this equation and the deep theories used to study it. Iterative processes from Differential Geometry such as the Ricci iteration and flow provide inspiration for training models in infinite-dimensional configuration spaces that may model complex human activities and optimization algorithms.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.
这个i-Corps项目的更广泛的影响/商业潜力是开发微分几何和最优运输的应用程序,以解决复杂的优化问题。该项目的重点是了解哪些生物机械参数反映了运动训练和招募领域中复杂的人体运动活动的关键特征。这项拟议的技术可能会在职业体育以及有抱负的和业余运动员身上有很多应用。此外,这可能有利于降低运动员的受伤风险,缩短运动员伤愈恢复的时间。拟议的技术还可以用于运动员技能发展,这在所有级别的体育运动中都发挥着核心作用。人才评估和球员招聘也可能受到影响,这两个方面也在专业和大学两级都获得了大量资源。其他可能受益的领域包括天气预报、最优网络设计、经济学、物理学和光学。这个i-Corps项目基于数学工具和算法的开发,灵感来自于完全非线性Monge-Ampere方程的深层理论,该方程是微分几何和最优运输等广泛领域的共同分母。微分几何与机器学习和最先进的生物力学研究的数据分析工具相结合,以深入分析和发展对涉及同时使用多个肢体的某些复杂的人类运动活动的新的生物力学理解。拟议的技术侧重于需要高度技能和协调以及具有挑战性的培训和学习的活动。了解一个特定的方程是否可以用来为优化复杂的人类活动提供数学见解,可以为这个方程和用于研究它的深层理论提供另一个真实世界的应用。微分几何的迭代过程,如RICCI迭代和FLOW,为无限维配置空间中的培训模型提供了灵感,这些配置空间可能对复杂的人类活动和优化算法进行建模。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

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Yanir Rubinstein其他文献

Yanir Rubinstein的其他文献

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{{ truncateString('Yanir Rubinstein', 18)}}的其他基金

Microlocal Analysis and Monge-Ampère Type Equations in Geometry
几何中的微局域分析和 Monge-Ampère 型方程
  • 批准号:
    2204347
  • 财政年份:
    2022
  • 资助金额:
    $ 5万
  • 项目类别:
    Standard Grant
Microlocal Analysis and Monge-Ampere Type Equations in Geometry
几何中的微局域分析和Monge-Ampere型方程
  • 批准号:
    1906370
  • 财政年份:
    2019
  • 资助金额:
    $ 5万
  • 项目类别:
    Standard Grant
Microlocal Analysis and Monge-Ampere Type Equations in Geometry
几何中的微局域分析和Monge-Ampere型方程
  • 批准号:
    1515703
  • 财政年份:
    2015
  • 资助金额:
    $ 5万
  • 项目类别:
    Standard Grant
Monge-Ampere equations and microlocal analysis on Kahler manifolds
Monge-Ampere 方程和 Kahler 流形上的微局域分析
  • 批准号:
    1206284
  • 财政年份:
    2012
  • 资助金额:
    $ 5万
  • 项目类别:
    Standard Grant
PostDoctoral Research Fellowship
博士后研究奖学金
  • 批准号:
    0802923
  • 财政年份:
    2008
  • 资助金额:
    $ 5万
  • 项目类别:
    Fellowship Award

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  • 批准号:
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