Optimal Transport Applications to Probability, Machine Learning, and Kinetic Theory
最优运输在概率、机器学习和动力学理论中的应用
基本信息
- 批准号:2205937
- 负责人:
- 金额:$ 22.9万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2022
- 资助国家:美国
- 起止时间:2022-08-01 至 2025-07-31
- 项目状态:未结题
- 来源:
- 关键词:
项目摘要
The project aims to transfer recently developed insights in mathematical analysis to other areas of interest including stochastic modelling, artificial intelligence, and kinetic theory. Stochastic models have recently become ubiquitous in physical science and social sciences to describe phenomena ranging from the evolution of political opinions to policy-driven segregation in urban environments. Artificial intelligence is a fast-growing field, relying on algorithms that have not yet been thoroughly studied mathematically. Kinetic theory has been studied in the context of many important applications such as space shuttle design, and it has become more relevant due to efforts to develop clean energy fusion reactors. The project will focus on developing mathematical frameworks and advancing the state of the art in those important fields. The project will also provide research training opportunities for graduate students. The project aims to develop mathematical frameworks for particle interactions, machine learning algorithms, and kinetic theory. The investigator will exploit theories developed in optimal mass transportation and gradient flows in metric spaces for complex dynamics by studying the associated free energy. For stochastic models, in particular weakly interacting diffusions, the project aims to develop a variational structure capturing the effect of phase transitions. For artificial intelligence, the project will focus on obtaining mean-field limits of parameter training and providing the functional structure of successful algorithms, such as Wasserstein generative adversarial network (GAN) and AlphaGo Zero. For kinetic theory, the project will exploit newly developed gradient flow formulations for the Landau and Boltzmann equations to obtain new insight into the behavior of these models.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.
该项目的目的是将最近在数学分析中开发的见解转移到其他感兴趣的领域,包括随机建模,人工智能和动力学理论。随机模型最近在物理科学和社会科学中变得无处不在,以描述从政治观点的演变到城市环境中政策驱动的隔离等现象。人工智能是一个快速增长的领域,依靠尚未在数学上进行彻底研究的算法。在许多重要应用(例如航天飞机设计)的背景下,研究了动力学理论,并且由于开发清洁能量融合反应堆的努力而变得更加相关。该项目将着重于开发数学框架,并在这些重要领域的艺术状态前进。该项目还将为研究生提供研究培训机会。 该项目旨在开发用于粒子相互作用,机器学习算法和动力学理论的数学框架。研究者将利用在最佳的质量运输和度量空间中开发的理论,通过研究相关的自由能来进行复杂的动力学。对于随机模型,尤其是弱相互作用的扩散,该项目旨在开发一种变异结构,以捕获相变的效果。对于人工智能,该项目将专注于获得参数训练的平均场限制,并提供成功算法的功能结构,例如Wasserstein生成性对抗网络(GAN)和Alphago Zero。对于动力学理论,该项目将为Landau和Boltzmann方程式开发新开发的梯度流程配方,以获得对这些模型行为的新见解。该奖项反映了NSF的法定任务,并被认为是值得通过基金会的知识分子优点和更广泛影响的审查标准来通过评估来获得支持的。
项目成果
期刊论文数量(2)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Phase Transitions, Logarithmic Sobolev Inequalities, and Uniform-in-Time Propagation of Chaos for Weakly Interacting Diffusions
- DOI:10.1007/s00220-023-04659-z
- 发表时间:2021-12
- 期刊:
- 影响因子:2.4
- 作者:M. Delgadino;Rishabh S. Gvalani;G. Pavliotis;Scott A. Smith
- 通讯作者:M. Delgadino;Rishabh S. Gvalani;G. Pavliotis;Scott A. Smith
Convergence of a particle method for a regularized spatially homogeneous Landau equation
正则化空间齐次朗道方程粒子法的收敛性
- DOI:10.1142/s0218202523500215
- 发表时间:2023
- 期刊:
- 影响因子:3.5
- 作者:Carrillo, José A.;Delgadino, Matias G.;Wu, Jeremy S.
- 通讯作者:Wu, Jeremy S.
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Matias Delgadino其他文献
Matias Delgadino的其他文献
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