Ant Colony Optimization for Density Functionals in Strongly Correlated Systems

Fuente: arXiv
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Main Authors: Tonin, G. M., Pauletti, T., Santos, R. M. Dos, França, V. V.
Format: Preprint
Published: 2025
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author Tonin, G. M.
Pauletti, T.
Santos, R. M. Dos
França, V. V.
author_facet Tonin, G. M.
Pauletti, T.
Santos, R. M. Dos
França, V. V.
contents The Ant Colony Optimization (ACO) algorithm is a nature-inspired metaheuristic method used for optimization problems. Although not a machine learning method per se, ACO is often employed alongside machine learning models to enhance performance through optimization. We adapt an ACO algorithm to optimize the so-called FVC density functional for the ground-state energy of strongly correlated systems. We find the parameter configurations that maximize optimization efficiency, while reducing the mean relative error ($MRE$) of the ACO functional. We then analyze the algorithm's performance across different dimensionalities ($1D-5D$), which are related to the number of parameters to be optimized within the FVC functional. Our results indicate that $15$ ants with a pheromone evaporation rate superior to $0.2$ are sufficient to minimize the $MRE$ for a vast regime of parameters of the strongly-correlated system -- interaction, particle density and spin magnetization. While the optimizations $1D$, $2D$, and $4D$ yield $1.5\%< MRE< 2.7\%$, the $3D$ and $5D$ optimizations lower the $MRE$ to $\sim0.8\%$, reflecting a $67\%$ error reduction compared to the original FVC functional ($MRE = 2.4\%$). As simulation time grows almost linearly with dimension, our results highlight the potential of ant colony algorithms for density-functional problems, combining effectiveness with low computational cost.
format Preprint
id arxiv_https___arxiv_org_abs_2504_20317
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Ant Colony Optimization for Density Functionals in Strongly Correlated Systems
Tonin, G. M.
Pauletti, T.
Santos, R. M. Dos
França, V. V.
Strongly Correlated Electrons
Computational Physics
Data Analysis, Statistics and Probability
The Ant Colony Optimization (ACO) algorithm is a nature-inspired metaheuristic method used for optimization problems. Although not a machine learning method per se, ACO is often employed alongside machine learning models to enhance performance through optimization. We adapt an ACO algorithm to optimize the so-called FVC density functional for the ground-state energy of strongly correlated systems. We find the parameter configurations that maximize optimization efficiency, while reducing the mean relative error ($MRE$) of the ACO functional. We then analyze the algorithm's performance across different dimensionalities ($1D-5D$), which are related to the number of parameters to be optimized within the FVC functional. Our results indicate that $15$ ants with a pheromone evaporation rate superior to $0.2$ are sufficient to minimize the $MRE$ for a vast regime of parameters of the strongly-correlated system -- interaction, particle density and spin magnetization. While the optimizations $1D$, $2D$, and $4D$ yield $1.5\%< MRE< 2.7\%$, the $3D$ and $5D$ optimizations lower the $MRE$ to $\sim0.8\%$, reflecting a $67\%$ error reduction compared to the original FVC functional ($MRE = 2.4\%$). As simulation time grows almost linearly with dimension, our results highlight the potential of ant colony algorithms for density-functional problems, combining effectiveness with low computational cost.
title Ant Colony Optimization for Density Functionals in Strongly Correlated Systems
topic Strongly Correlated Electrons
Computational Physics
Data Analysis, Statistics and Probability
url https://arxiv.org/abs/2504.20317