Ant Colony Optimization for Density Functionals in Strongly Correlated Systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916005643550720 |
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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 |
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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 |