CAREER: A Nonlinear Model Reduction Framework for Oscillatory Systems and Associated Data-Driven Inference Strategies

职业：振荡系统的非线性模型简化框架和相关的数据驱动推理策略

• 批准号: 2140527
• 负责人: Dan Wilson
• 金额: $ 59.9万
• 依托单位: University of Tennessee Knoxville
• 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: 2022-03-01 至 2027-02-28
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2140527&HistoricalAwards=false
• 关键词: CAREER; Nonlinear; Model; Reduction; Framework

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2).This Faculty Early Career Development Program (CAREER) grant will fund research that enables improved understanding and control of collective neurological rhythms, for example pathological synchronization of neurons contributing to the motor symptoms of Parkinson’s disease, thereby promoting the progress of science, and advancing the national health. Deep brain stimulation injects electrical pulses into the brains of patients suffering from Parkinson’s to alleviate muscle tremors and rigidity. Because of the large inputs required, standard theoretical tools for predicting and analyzing the neuronal response are inadequate, since they assume small deviations from the synchronized behavior. This project will overcome such limitations by developing a new theoretical approach, suitable for complex and high-dimensional systems with oscillatory dynamics even for large deviations dominated by system nonlinearities. By combining this approach with machine-learning techniques, it will be possible to derive relevant dynamical models entirely from measurements, with potential applications to treating recovery from jet lag or controlling the air flow around vehicles and aircraft. Through close integration of research and education, this project will contribute to an engineering and science curriculum of inquiry-based, hands-on learning experiences for high school students attending outreach activities or specially designed, multi-day immersive programs at Lone Oaks Farm, a STEM education center in west Tennessee that serves large populations of underrepresented students from under-resourced local communities. Completion of this project will also yield a series of tutorial sessions, a set of online learning modules, and a computational toolbox, each promoting the use of powerful mathematical techniques for dynamical systems analysis to members of the larger research community.This research aims to make fundamental contributions to a theory of model reduction techniques for oscillatory high-dimensional systems whose dynamics are dominated by system nonlinearities, with particular emphasis on accuracy, analytical tractability, and suitability for control design. It achieves this aim by augmenting traditional phase-based reduction methods with a description of transversal dynamics in terms of isostable coordinates, which characterize the slowest decaying modes of the system Koopman operator. Adaptive updates to model parameters are then introduced to bound the time evolution of the isostable coordinates and ensure convergence of asymptotic expansions used in the model reduction. Generalizations to non-periodic dynamics and, importantly, to data-driven model identification in the absence of known underlying dynamical equations will be explored in theoretical models and in applications to circadian cycles, neural brain rhythms, and fluid flow systems.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.

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2).This Faculty Early Career Development Program (CAREER) grant will fund research that enables improved understanding and control of collective neurologic rhythms, for example pathological synchronization of neurons contributing to the motor symptoms of Parkinson’s disease, thereby promoting the progress of science, and advancing the national health.深脑刺激将脉冲注射到患有帕金森氏症患者的大脑中，以减轻肌肉震颤和僵化。由于所需的大量输入，用于预测和分析神经元反应的标准理论工具是不足的，因为它们假设与同步行为相比很小。该项目将通过开发一种新的理论方法来克服此类局限性，该方法适用于具有振荡动力学的复杂和高维系统，即使对于由系统非线性主导的大型偏离也是如此。通过将这种方法与机器学习技术相结合，可以完全从测量中得出相关的动态模型，以及潜在的应用程序来处理从喷气滞后滞后或控制车辆和飞机周围的空气流量的恢复。通过紧密整合研究和教育，该项目将为参加外展活动或专门设计的，多天的沉浸式课程的高中生的基于询问的，动手学习经验的工程和科学课程做出贡献，该课程是西田纳西州的STEM教育中心，该中心是西田纳西州的STEM教育中心，该中心为来自不足不足的地方社区的大量学生提供了很多人群。该项目的完成还将产生一系列的教程，一组在线学习模块和一个计算工具箱，每个研究都促进了对较大研究社区成员的动态系统分析的强大数学技术的使用。本研究旨在通过对振动性的振动性进行启发性的模型降低理论的基本贡献，以启发性化的系统来构成敏捷性，以启发性能，以启发性地位，以启发性地位，以启发性地位，以启发性地位，以启发性地位，以启发性地位，以启发性地位，以启发性地位，以启发性地位，以启发性地位，以启发性地位，以启发性地位，以启发性地位，以启发性地位，以启发性地位，以启发性地统治该系统。障碍和控制设计的适用性。它通过通过同等坐标来描述横向动力学来增强传统基于阶段的还原方法来实现这一目标，该方法表征了系统Koopman操作员的慢速衰减模式。然后引入对模型参数的自适应更新，以限制等量坐标的时间演变，并确保模型还原中使用的不对称扩展的收敛性。在缺乏已知基本动态方程式的数据驱动的模型识别上，将在理论模型以及对昼夜节律周期，中性的大脑节律和流体流动系统的应用中探索对数据驱动的模型识别的概括，这些奖项反映了NSF的法定任务和范围的范围。

项目成果

A direct method approach for data-driven inference of high accuracy adaptive phase-isostable reduced order models

高精度自适应相位等稳降阶模型的数据驱动推理的直接方法

• DOI: 10.1016/j.physd.2023.133675
• 发表时间: 2023
• 期刊: Physica D: Nonlinear Phenomena
• 作者: Wilson, Dan

Control of coupled neural oscillations using near-periodic inputs

使用近周期输入控制耦合神经振荡

• DOI: 10.1063/5.0076508
• 发表时间: 2022
• 期刊: Chaos: An Interdisciplinary Journal of Nonlinear Science
• 作者: Toth, Kaitlyn;Wilson, Dan
• 通讯作者: Wilson, Dan

Koopman Operator Inspired Nonlinear System Identification

库普曼算子启发的非线性系统辨识

• DOI: 10.1137/22m1512272
• 发表时间: 2023
• 期刊: SIAM Journal on Applied Dynamical Systems
• 影响因子: 2.1
• 作者: Wilson, Dan

Data-driven model identification using forcing-induced limit cycles

使用强制引起的极限环进行数据驱动的模型识别

• DOI: 10.1016/j.physd.2023.134013
• 发表时间: 2024
• 期刊: Physica D: Nonlinear Phenomena
• 作者: Wilson, Dan

Phase-Amplitude Coordinate-Based Neural Networks for Inferring Oscillatory Dynamics

用于推断振荡动力学的基于相位振幅坐标的神经网络

• DOI: 10.1007/s00332-023-09994-y
• 发表时间: 2024
• 期刊: Journal of Nonlinear Science
• 影响因子: 3
• 作者: Ahmed, Talha;Wilson, Dan
• 通讯作者: Wilson, Dan