Sampling algorithms for validation of supervised learning models for Ising-like systems

TL;DR

This paper introduces novel sampling algorithms, ID-MH and block-ID, for validating supervised learning models on Ising model data, effectively capturing phase transitions and improving model assessment.

Contribution

The paper proposes the ID-MH and block-ID sampling methods tailored for Ising systems, enhancing validation of machine learning models by preserving phase transition features.

Findings

ID-MH retains phase transitions in datasets

PCA-based Decision Tree best predicts magnetizations

Energy prediction accuracy remains limited

Abstract

In this paper, we build and explore supervised learning models of ferromagnetic system behavior, using Monte-Carlo sampling of the spin configuration space generated by the 2D Ising model. Given the enormous size of the space of all possible Ising model realizations, the question arises as to how to choose a reasonable number of samples that will form physically meaningful and non-intersecting training and testing datasets. Here, we propose a sampling technique called ID-MH that uses the Metropolis-Hastings algorithm creating Markov process across energy levels within the predefined configuration subspace. We show that application of this method retains phase transitions in both training and testing datasets and serves the purpose of validation of a machine learning algorithm. For larger lattice dimensions, ID-MH is not feasible as it requires knowledge of the complete configuration space. As such, we develop a new "block-ID" sampling strategy: it decomposes the given structure into square blocks with lattice dimension no greater than 5 and uses ID-MH sampling of candidate blocks. Further comparison of the performance of commonly used machine learning methods such as random forests, decision trees, k nearest neighbors and artificial neural networks shows that the PCA-based Decision Tree regressor is the most accurate predictor of magnetizations of the Ising model. For energies, however, the accuracy of prediction is not satisfactory, highlighting the need to consider more algorithmically complex methods (e.g., deep learning).