Machine Learning for Physics: from Symbolic Regression to Quantum Simulation

Abstract

In this thesis, we explore the application of machine learning (ML) methods to problems in physics.

Because ML has revolutionized a wide range of fields, it is natural to ask whether it may be a valuable tool for physics. Physics applications present a challenge as many physics problems have a precise mathematical definition and a classical (non-ML-based) solution, making ML models less likely to outperform existing techniques.

In this paper, we focus on two general problems for which ML techniques provide an improvement as compared to existing techniques in physics: 1) fast simulation, and 2) discovering new physics. To illustrate the potential of ML to advance physics by solving these problems, we develop a physics-optimized ML model for each of the problems identified above, respectively: 1) Q-Flow, a technique for faster bosonic quantum simulation using normalizing flows to simulate a compressed representation of a quantum state, and 2) OccamNet, a framework for scientific discovery through novel algorithms for efficient and parallelizable symbolic regression. Our methods demonstrate the potential for ML as a valuable tool for physics research.