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A Study Of Machine Learning Techniques For Dynamical System Prediction, Rishi Pawar
A Study Of Machine Learning Techniques For Dynamical System Prediction, Rishi Pawar
Theses and Dissertations
Dynamical Systems are ubiquitous in mathematics and science and have been used to model many important application problems such as population dynamics, fluid flow, and control systems. However, some of them are challenging to construct from the traditional mathematical techniques. To combat such problems, various machine learning techniques exist that attempt to use collected data to form predictions that can approximate the dynamical system of interest. This thesis will study some basic machine learning techniques for predicting system dynamics from the data generated by test systems. In particular, the methods of Dynamic Mode Decomposition (DMD), Sparse Identification of Nonlinear Dynamics …
Random Iteration Of Rational Maps, Jesse Dean Feller
Random Iteration Of Rational Maps, Jesse Dean Feller
Theses and Dissertations
Random and non-autonomous iteration has been a subject of interest in Mathematics that has received some attention in the last few decades. The earliest paper on random iteration in the complex setting was written by Fornaess and Sibony. They have shown that given a family of functions $\{f_c\}_{c \in \W}$ where $\W$ is a small open set, for almost every z the random iteration is stable on a subset of $\W^\N$ of full probability measure. Later, Hiroki Sumi further extended these results to a more general situation using rational semigroups. We will show that the results of Fornaess and Sibony …