THEORY AND APPLICATIONS OF DATA SCIENCE

This work is a collection of original research, contributing to various hot topics in contemporary data science, covering both theory and applications. The topics include discovering physical laws from data, data-driven epidemiological models, Gaussian random field surrogate models, and image texture classification. In Chapter 2, we introduce a novel method for discovering physical laws from data with uncertainty quantification. In Chapter 3, this method is enhanced to tackle high noise and outliers. In Chapter 4, the method is applied to discover the law of turbine component damage in industry. In Chapter 5, we propose a new framework for building trustworthy data-driven epidemiological models and apply it to the COVID-19 outbreak in New York City. In Chapter 6, we construct augmented Gaussian random field, a universal framework incorporating the data of observable and derivatives of any order. The theoretical framework as well as computational framework are established. In Chapter 7, we introduce the use of 2-dimensional signature, an object inspired by rough paths theory, as feature for image texture classification.