Andrea Tirelli

Giacomo Tenti, Kousuke Nakano, Andrea Tirelli et al.

We present a study of the principal deuterium Hugoniot for pressures up to $150$ GPa, using Machine Learning potentials (MLPs) trained with Quantum Monte Carlo (QMC) energies, forces and pressures. In particular, we adopted a recently proposed workflow based on the combination of Gaussian kernel regression and $Δ$-learning. By fully taking advantage of this method, we explicitly considered finite-temperature electrons in the dynamics, whose effects are highly relevant for temperatures above $10$ kK. The Hugoniot curve obtained by our MLPs shows a good agreement with the most recent experiments, particularly in the region below 60 GPa. At larger pressures, our Hugoniot curve is slightly more compressible than the one yielded by experiments, whose uncertainties generally increase, however, with pressure. Our work demonstrates that QMC can be successfully combined with $Δ$-learning to deploy reliable MLPs for complex extended systems across different thermodynamic conditions, by keeping the QMC precision at the computational cost of a mean-field calculation.

Andrea Tirelli, Giacomo Tenti, Kousuke Nakano et al.

We have developed a technique combining the accuracy of quantum Monte Carlo in describing the electron correlation with the efficiency of a Machine Learning Potential (MLP). We use kernel regression in combination with SOAP (Smooth Overlap of Atomic Position) features, implemented here in a very efficient way. The key ingredients are: i) a sparsification technique, based on farthest point sampling, ensuring generality and transferability of our MLPs and ii) the so called $Δ$-learning, allowing a small training data set, a fundamental property for highly accurate but computationally demanding calculations, such as the ones based on quantum Monte Carlo. As the first application we present a benchmark study of the liquid-liquid transition of high-pressure hydrogen and show the quality of our MLP, by emphasizing the importance of high accuracy for this very debated subject, where experiments are difficult in the lab, and theory is still far from being conclusive.

Andrea Tirelli, Danyella O. Carvalho, Lucas A. Oliveira et al.

In this paper with study phase transitions of the $q$-state Potts model, through a number of unsupervised machine learning techniques, namely Principal Component Analysis (PCA), $k$-means clustering, Uniform Manifold Approximation and Projection (UMAP), and Topological Data Analysis (TDA). Even though in all cases we are able to retrieve the correct critical temperatures $T_c(q)$, for $q = 3, 4$ and $5$, results show that non-linear methods as UMAP and TDA are less dependent on finite size effects, while still being able to distinguish between first and second order phase transitions. This study may be considered as a benchmark for the use of different unsupervised machine learning algorithms in the investigation of phase transitions.

Genki I. Prayogo, Andrea Tirelli, Keishu Utimula et al.

A common approach for studying a solid solution or disordered system within a periodic ab-initio framework is to create a supercell in which a certain amount of target elements is substituted with other ones. The key to generating supercells is determining how to eliminate symmetry-equivalent structures from the large number of substitution patterns. Although the total number of substitutions is on the order of trillions, only symmetry-inequivalent atomic substitution patterns need to be identified, and their number is far smaller than the total. A straightforward solution would be to classify them after determining all possible patterns, but it is redundant and practically unfeasible. Therefore, to alleviate this drawback, we developed a new formalism based on the {\it canonical augmentation}, and successfully applied it to the atomic substitution problem. Our developed \verb|python| software package, which is called \textsc{SHRY} (\underline{S}uite for \underline{H}igh-th\underline{r}oughput generation of models with atomic substitutions implemented by p\underline{y}thon), enables us to pick up only symmetry-inequivalent structures from the vast number of candidates very efficiently. We demonstrate that the computational time required by our algorithm to find $N$ symmetry-inequivalent structures scales {\it linearly} with $N$ up to $\sim 10^9$. This is the best scaling for such problems.

Andrea Tirelli, Natanael C. Costa

We implement a computational pipeline based on a recent machine learning technique, namely the Topological Data Analysis (TDA), that has the capability of extracting powerful information-carrying topological features. We apply such a method to the study quantum phase transitions and, to showcase its validity and potential, we exploit such a method for the investigation of two paramount important quantum systems: the 2D periodic Anderson model and the Hubbard model on the honeycomb lattice, both cases on the half-filling. To this end, we have performed unbiased auxiliary field quantum Monte Carlo simulations, feeding the TDA with snapshots of the Hubbard-Stratonovich fields through the course of the simulations The quantum critical points obtained from TDA agree quantitatively well with the existing literature, therefore suggesting that this technique could be used to investigate quantum systems where the analysis of the phase transitions is still a challenge.