Machine Learning-driven improvement of the ground state configuration

This repository implements physical lattice models as gym environments to find their ground states with reinforcement learning.

It was created during bachelor thesis project supervised by prof. dr hab. Maciej M. Maśka.

Specifically the following models are implemented:

• Ising model,
• Falicov-Kimball model,
• XY model,
• model with Dzyaloshinskii-Moriya interaction,

and can be found in gym-latticemodels/gym_latticemodels/envs/ directory.

scripts contains scripts used to learn specific environment, and also to test them. Use paralleize.sh with specific script to train multiple agents in parallel.

src directory contains additional utils such as cosine annealing, custom CNN, and wrapper that returns reward at every step.

Installation

The easiest way of running this environment is with conda (https://conda.io/projects/conda/en/latest/user-guide/install/index.html or https://docs.anaconda.com/anaconda/install/index.html).

Firstly create the environment from the environment.yml file:

conda env create -f environment.yml

Then activate the new environment

conda activate latticerl

Install gym-latticemodels

pip install -e gym-latticemodels/

Install src helpers

pip install -e .

Ready to go!

Abstract

The search for ground states in physical models is a fundamental problem in physics, as it allows for a deeper understanding of the properties and behavior of complex systems. This thesis presents a new method for searching ground states of physical models using deep reinforcement learning. The method utilizes the proximal policy optimization (PPO) algorithm, a widely used algorithm in deep reinforcement learning. It was applied to various classical spin models such as the Ising model, the XY model, and the model with Dzyaloshinskii-Moriya interaction, as well as a simple quantum fermionic spinless Falicov-Kimball model. The results of the experiments show that the method presents a promising approach for finding ground states in physical models, however, it may encounter challenges when dealing with larger lattice sizes. The research provides a new perspective on solving the challenging problem of finding ground states in classical and quantum systems and suggests areas for future research in this field.

Keywords

Ground state, Energy minimization, Reinforcement Learning, Deep Reinforcement Learning, Spin Models, Fermionic models, Neural Network, Machine Learning, Markov Decision Process, Proximal Policy Optimization

Data availability

Data from performed experiments is available here: https://tensorboard.dev/experiment/F9pMBpqeQvGwr7xayu9lOQ/