A New Framework for Nonlinear Dynamical Model Reduction

非线性动力学模型简化的新框架

• 批准号: 1100031
• 负责人: David Chelidze
• 金额: $ 25万
• 依托单位: University of Rhode Island
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1100031&HistoricalAwards=false
• 关键词: New; Framework; Nonlinear; Dynamical; Model

The research objective of this project is to apply multivariate and nonlinear time series analyses in formulating comprehensive and systematic dynamical model and data reduction framework. In this framework, smooth orthogonal decomposition will be applied to the dimension reduction of deterministic nonlinear dynamical systems and will be contrasted with other alternatives - e.g., proper orthogonal decomposition. The research approach is to test the framework on several large-scale structural and molecular dynamics models' short time trajectories, and evaluate the resultant subspaces suitability for model reduction. Reduced-order models based on these subspaces will be simulated and compared with the full-scale models, using frequency response functions, bifurcation diagrams, phase portraits, and other dynamical characteristics such as fractal dimensions and Liapunov exponents.This framework will provide a systematic way of evaluating a particular model reduction procedure's effectiveness and its robustness with respect to the bounded variations in the system/forcing parameters, and initial conditions. This project is expected to provide new tools to study slow-time dynamics of complex engineered and biological systems (e.g., physics of protein conformational changes or folding, protein-protein association, large multi-physics dynamics, etc.). For a protein system, e.g., this methodology can be exploited in the rational design of next generation compound-antagonists. The plan also supports the curricular expansion of two interdisciplinary graduate courses, the organization of department-wide workshops on graduate research for junior and senior students, the regular organization of conferences and minisymposia, the dissemination of results through the web, personal communication, and traditional publications in top journals.

本计画的研究目标是应用多元非线性时间序列分析，建立全面系统的动力学模型与资料整理架构。在这个框架中，平滑正交分解将被应用于确定性非线性动力系统的降维，并将与其他替代方案进行对比-例如，本征正交分解研究方法是在几个大规模结构和分子动力学模型的短时间轨迹上测试框架，并评估由此产生的子空间对模型降阶的适用性。基于这些子空间的降阶模型将使用频率响应函数、分叉图、相图和其他动力学特征如分形维数和李雅普诺夫指数进行模拟，并与全尺度模型进行比较。这一框架将提供一种系统的方法，评估特定模型降阶程序的有效性及其对系统/强迫参数有界变化的鲁棒性，初始条件。该项目预计将提供新的工具来研究复杂工程和生物系统的慢时间动力学（例如，蛋白质构象变化或折叠的物理学、蛋白质-蛋白质缔合、大的多物理学动力学等）。 对于蛋白质系统，例如，该方法可用于下一代化合物拮抗剂的合理设计。该计划还支持两个跨学科研究生课程的课程扩展，为大三和大四学生组织全系范围的研究生研究讲习班，定期组织会议和minisymopsia，通过网络传播结果，个人交流和在顶级期刊上发表传统文章。