Fixed Point Theory, Nonlinear Differential Equations and Computational Algorithms on Data Analytics

数据分析中的不动点理论、非线性微分方程和计算算法

• 批准号: RGPIN-2016-06098
• 负责人: Feng, Wenying
• 金额: $ 1.31万
• 依托单位: Trent University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=709145
• 关键词: Fixed; Point; Theory; Nonlinear; Differential

The proposed research overlaps with three closely related areas in applied mathematics and computing: fixed point theory, nonlinear differential equations and computational algorithms for data analytics. Each topic on its own is important and substantial. Connecting the three areas together (fixed-point theory, nonlinear differential equations, and neural networks) along a continuum from theory to real-world applications is innovative and the central focus of my research. As a very powerful and important tool in studying differential equations, fixed point theory has diverse applications in various fields such as Biology, Chemistry, Economics, Engineering, Game Theory, Physics, and Computer Sciences. The research lies in the development and application of new mathematical techniques in fixed point theory to study solutions for nonlinear differential equations arising from population dynamics, reaction-diffusion systems, image classifications, neural networks and social activities. In particular, systems of differential equations involving multiple parameters with non-local boundary or initial conditions will be considered. In applications, this class of differential systems represents gas diffusion, heat conduction, elastic beam and in general feedback controls by which the “sum” of the states of the process along its evolution equals the initial state in real processes from Physics, Chemistry or Biology. In addition to topological methods from functional analysis, nonlinear analysis and linear operator theory, constructional techniques such as iteration, monotone mappings, upper and lower solutions will also be applied. On the computational side, new algorithms will be developed, implemented and tested using real-world data sets. System performance will be evaluated and documented. Computational approaches including numerical methods and computer simulations will be applied. New tools and methods will also be developed. The results will contribute across several fields in nonlinear analysis, dynamical systems, mathematical modeling and computational algorithms for data analytics. The last field, in particular, has received considerable attention of late. Our work will continue to contribute to the well-being of our Canadian research community, both in fundamental and applied terms.

所提出的研究与应用数学和计算中三个密切相关的领域重叠：不动点理论、非线性微分方程和数据分析的计算算法。每个主题本身都是重要而充实的。将这三个领域（不动点理论、非线性微分方程和神经网络）沿着从理论到现实应用的连续体连接在一起是创新的，也是我研究的中心焦点。