Predicting parameters of a model cuprate superconductor using machine learning

TL;DR

This paper introduces a machine learning approach, specifically a U-Net model, to predict parameters of a cuprate superconductor's Hamiltonian from phase diagrams, improving parameter inference in complex physical models.

Contribution

The study adapts U-Net for regression in physics, demonstrating its effectiveness in predicting Hamiltonian parameters from phase diagrams with high accuracy.

Findings

U-Net outperformed VGG and ResNet in parameter prediction.

The model accurately predicts all Hamiltonian parameters.

Prediction accuracy drops in regions of parametric insensitivity.

Abstract

The computational complexity of calculating phase diagrams for multi-parameter models significantly limits the ability to select parameters that correspond to experimental data. This work presents a machine learning method for solving the inverse problem - forecasting the parameters of a model Hamiltonian for a cuprate superconductor based on its phase diagram. A comparative study of three deep learning architectures was conducted: VGG, ResNet, and U-Net. The latter was adapted for regression tasks and demonstrated the best performance. Training the U-Net model was performed on an extensive dataset of phase diagrams calculated within the mean-field approximation, followed by validation on data obtained using a semi-classical heat bath algorithm for Monte Carlo simulations. It is shown that the model accurately predicts all considered Hamiltonian parameters, and areas of low prediction accuracy correspond to regions of parametric insensitivity in the phase diagrams. This allows for the extraction of physically interpretable patterns and validation of the significance of parameters for the system. The results confirm the promising potential of applying machine learning to analyze complex physical models in condensed matter physics.