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Machine Learning and Scientific Computing


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


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Machine learning, scientific computing, optimization, partial differential equations, inverse problems, transport maps.
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied And Computational Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Stuart, Andrew M.
Thesis Committee:
  • Owhadi, Houman (chair)
  • Stuart, Andrew M.
  • Bhattacharya, Kaushik
  • Anandkumar, Anima
Defense Date:3 May 2022
Record Number:CaltechTHESIS:05252022-180406320
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for Chapter 2. adapted for Chapter 3. adapted for Chapter 4. adapted for Chapter 5. adapted for Chapter 6. adapted for Chapter 7.
Kovachki, Nikola Borislavov0000-0002-3650-2972
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14621
Deposited By: Nikola Kovachki
Deposited On:26 May 2022 21:07
Last Modified:02 Jun 2022 23:27

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