Machine Learning, Reservoir Computing, and Nonlinear Dynamics

该项目的目标是获得机器学习预测非线性动力系统演化的机制的基本理解，并探索如何使用这些知识来改进现有的机器学习预测并设计新的功能。 实现这一目标将促进我们对许多潜在的重要应用的理解，这些应用可以通过动力系统进行数学描述，从基因治疗到天气预测。 研究生从事该项目的研究。研究人员使用非线性动力学和混沌理论的概念来了解机器学习技术何时，如何以及为什么在预测动力系统状态的演变方面是有效的，包括考虑大型和复杂的动力系统（例如，基于空间的系统）。 此外，他还考虑了“气候保护”的问题，这意味着机器学习工具能够通过测量其状态演化的时间序列来复制动力系统的长期遍历特性，而对此知之甚少。 研究者使用这种能力来制定机器学习工具，以确定遍历特性（例如，李雅普诺夫指数谱）的未知系统的动态。 该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The goal of this project is to obtain basic understanding of the mechanisms by which machine learning can predict the evolution of nonlinear dynamical systems, and to explore how to use this knowledge to improve existing machine learning prediction and devise new capabilities. Achieving this goal would advance our understanding of a host of potential important applications that can be described mathematically by dynamical systems, ranging from gene therapies to weather prediction. Graduate students are engaged in the research of the project.The investigator uses concepts from nonlinear dynamics and chaos theory to obtain understanding of when, how, and why machine learning techniques are effective in predicting the evolution of the state of a dynamical system, including consideration of dynamical systems that are large and complex (e.g., spatially based systems). In addition, he considers the issue of "climate preservation," by which is meant the ability of machine learning tools to replicate the long-term ergodic properties of a dynamical system about which little is known, from measurements of time series of its state evolution. The investigator uses this ability to formulate machine learning tools for determining ergodic properties (e.g., Lyapunov exponent spectra) of the dynamics of the unknown system. Graduate students are engaged in the research of the project.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.