Modeling, Analysis, Optimization, Computation, and Applications of Stochastic Systems

随机系统的建模、分析、优化、计算和应用

基本信息

批准号：
2204240
负责人：
Gang George Yin
金额：
$ 61.5万
依托单位：
University of Connecticut
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-06-01 至 2027-05-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2204240&HistoricalAwards=false
关键词：
Modeling Analysis Optimization Computation Applications

项目摘要

This project aims to study stochastic systems in which random disturbances play a significant role. This research will encompass the study of the dynamic behavior of mathematical models and applications in areas of ecological and biological systems, wireless communication, financial engineering, networked systems, and systems in control engineering. The research will focus on model systems under the random influence, switching among different configurations, and complex structures. The results will provide an understanding of the fundamental properties and the basic features of such modeling systems. This project will provide training opportunities for graduate and undergraduate students. The research will promote diversity and inclusion, increase public scientific literacy, and enhance interdisciplinary collaborations and the STEM workforce.This project will encompass analysis and computation of several important topics from emerging and existing applications in networked systems, control engineering, optimization of systems, wireless communications, biology, ecology, economics, and social networks. (1) It aims to develop a new methodology for analyzing switching jump-diffusion type Kolmogorov systems. Novel features to be studied include non-local behavior due to the jumps, and uncertain environment modeling using random switching. Long-standing fundamental issues such as minimal conditions needed for persistence and extinction in population dynamics will be addressed. (2) Treating discontinuity in the iterates and non-smooth dynamics in the limits for stochastic approximation algorithms is vitally important. This project will focus on this issue from a new angle. Stochastic differential inclusion limits will be obtained and used to ascertain rates of convergence and to improve asymptotic efficiency for the first time. (3) Although nonlinear filtering is an area deemed to be well developed, computation remains to be the main challenge because of the infinite dimensionality. This project aims to develop a methodology based on machine learning and neural networks with a new approach using adaptive learning rate recursion, leading to potentially more efficient computational methods. (4) A key in numerically solving nonlinear stochastic differential equations is to treat high nonlinearity and numerical finite time explosion. This project will develop a class of algorithms to handle the problem. A novel idea will be the use of randomly generated growing truncation bounds. Convergence and rates of convergence will be developed. (5) In response to the urgent need to handle coupled equations in networks, this project will focus on the study of coupled switching jump diffusions. By using ideas from dynamic systems and coupling methods in probability, this project aims to obtain stability and stabilization with impact on networked systems. Extensive numerical experiments and simulations will be performed to complement the mathematical analysis and algorithm design. It will open a new domain for further research in mathematics with a broader range of applications.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.

该项目旨在研究随机干扰起着重要作用的随机系统。这项研究将涵盖对生态和生物系统，无线通信，金融工程，网络系统和控制工程中数学模型和应用的动态行为的研究。该研究将集中于随机影响下的模型系统，在不同的配置之间切换和复杂的结构。结果将提供对此类建模系统的基本属性和基本特征的理解。该项目将为研究生和本科生提供培训机会。这项研究将促进多样性和包容性，提高公共科学素养，并增强跨学科合作和STEM劳动力。该项目将涵盖分析和计算网络系统中新兴和现有应用，控制工程，系统，无线通信，生物学，生物学，经济学，经济学和社交网络中的几个重要主题。（1）它旨在开发一种新方法来分析开关跳转类型Kolmogorov系统。要研究的新型特征包括由于跳跃而引起的非本地行为，以及使用随机切换的不确定环境建模。将解决长期存在的基本问题，例如持久性和人口动态灭绝所需的最小条件。（2）在随机近似算法的限制中处理迭代和非平滑动力学的不连续性至关重要。该项目将从新角度重点关注这个问题。将获得随机差分包含极限，并用于确定收敛速率并首次提高渐近效率。（3）尽管非线性过滤是被认为是发达的领域，但由于无限维度，计算仍然是主要挑战。该项目旨在使用自适应学习率递归的新方法开发基于机器学习和神经网络的方法，从而导致潜在的计算方法。（4）数值求解非线性随机微分方程的关键是处理高非线性和数值有限的时间爆炸。该项目将开发一类算法来解决问题。一个新颖的想法将是使用随机生成的生长截断界限。会收敛和收敛速率。（5）响应迫切需要处理网络中的耦合方程，该项目将重点放在耦合开关跳转扩散的研究上。通过在概率上使用动态系统和耦合方法的想法，该项目旨在获得稳定和稳定，并影响网络系统。将进行广泛的数值实验和模拟，以补充数学分析和算法设计。它将为具有更广泛应用的数学进一步研究开放一个新的领域。该奖项反映了NSF的法定任务，并使用基金会的知识分子优点和更广泛的影响审查标准，被认为值得通过评估来获得支持。