Machine Learning and Scientific Computing

Citation

Kovachki, Nikola Borislavov (2022) Machine Learning and Scientific Computing. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/8nc5-cc67. https://resolver.caltech.edu/CaltechTHESIS:05252022-180406320

Abstract

The remarkable success of machine learning methods for tacking problems in computer vision and natural language processing has made them auspicious tools for applications to scientific computing tasks. The present work advances both machine learning techniques by using ideas from numerical analysis, inverse problems, and data assimilation and introduces new machine learning based tools for accurate and computationally efficient scientific computing. Chapters 2 and 3 introduce new methods and analyze existing methods for the optimization of deep neural networks. Chapters 4 and 5 formulate approximation architectures acting between infinite dimensional functions spaces for applications to parametric PDE problems. Chapter 6 demonstrates how to re-formulate GAN(s) so they can condition on continuous data and exhibits applications to Bayesian inverse problems. In Chapter 7, we present a novel regression-clustering method and apply it to the problem of predicting molecular activation energies.

Thesis Files