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

这个I-Corps项目更广泛的影响/商业潜力是发展微分几何和最优运输的应用，以解决复杂的优化问题。该项目的重点是了解哪些生物力学参数捕捉在运动训练和招募领域的复杂的人类运动活动的关键特征。 所提出的技术可以在职业运动以及有抱负的业余运动员中具有许多应用。此外，它可能有利于降低运动员受伤的风险，减少运动员从伤病中恢复的时间。所提出的技术也可用于运动员技能发展，这在各级体育运动中起着核心作用。人才评估和球员招募也可能受到影响，这两个领域在专业和大学层面都获得了大量资源。 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项目是基于数学工具和算法的开发，其灵感来自完全非线性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点。 微分几何与来自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，以深入分析并发展对某些复杂的人类运动活动的新的生物力学理解，这些活动涉及同时使用多个肢体。 拟议的技术侧重于需要高度技能和协调的活动，这些活动对培训和学习具有挑战性。了解一个特定的方程是否可以用于优化复杂的人类活动的数学见解，可以提供这个方程的另一个现实世界的应用以及用于研究它的深层理论。微分几何中的迭代过程，如Ricci迭代和流，为无限大的训练模型提供了灵感。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准。

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.