Deep learning methods for large-scale physics

The explosion of abundant high-quality data in the 21st century has generated the need for new methods and approaches to mathematical modeling. Machine learning leads the forefront of this change but still requires theoretical frameworks to manage large-scale data and increase the usefulness of models, especially when using deep learning. The field of physics is a poignant example of this, where modern models are increasingly combining data and first-principles. This thesis provides mathematical approaches for applying deep learning in large-scale physics problems. The challenges addressed include solving deep learning problems in physics (1) that require significant hyperparameter tuning and (2) for which traditional techniques are computationally prohibitive. To this end, this thesis addresses these problems by drawing on connections between different branches of mathematics, optimization, statistics, and machine learning. For example, modeling complex distributions is a core problem in physics and statistics and can be particularly difficult especially when modeling large-scale datasets using deep learning. This thesis provides a framework for solving such problems that minimizes the need for hyperparameter tuning by taking advantage of a mathematical connection between continuous normalizing flows and optimal transport. Another problem of recent interest in geology is modeling the mapping from shortwave infrared (SWIR) data to abundances of critical minerals provided by a scanning electron microscope. The work in this thesis proposes a method for determining critical mineral abundances by making connections with large-scale statistics by applying preprocessing methods that allow for more effective deep learning models, even for minerals not detectable using traditional techniques. Finally, an application in physics where traditional methods are particularly intractable is swarm optimal control (OC) which has myriad robotics applications such as self-driving cars and unmanned aerial vehicles (UAV). We use deep learning-based kernel basis expansions to parallelize the computation of the optimal control when many agents interact non-locally. Using this approach, we generate simulations for quadrotor swarms of up to 5000 agents.

Name thesis:degree_name

Doctor of Philosophy (Ph.D.)

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Applied Mathematics and Statistics

Grantor dc:publisher

Colorado School of Mines. Arthur Lakes Library

Year dc:date.issued

2024

Author dc:creator

• Vidal, Alexander Robert

Advisors dc:contributor.advisor

• Wu Fung, Samy
• Tenorio, Luis

Committee members dc:contributor.committeemember

• Fasshauer, Gregory
• Nychka, Douglas
• Nurbekyan, Levon
• Monecke, Thomas

• deep learning
• generative models
• optimal control
• optimal transport
• optimization

Statement dc:rights

• Copyright of the original work is retained by the author.

Language dc:language.iso

eng, English

Dc Identifier Other

T 9868

OAI identifier oai:identifier

oai:repository.mines.edu:11124/180299