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.
