标题： 用于强关联体系的密度泛函的蚁群优化方法 显示英文标题

标题： Ant Colony Optimization for Density Functionals in Strongly Correlated Systems

摘要： 蚁群优化（ACO）算法是一种受自然启发的元启发式方法，用于解决优化问题。 虽然本身不是一种机器学习方法，但ACO通常与机器学习模型结合使用，通过优化来提高性能。 我们适应一种ACO算法来优化所谓的FVC密度泛函，以获得强关联系统的基态能量。 我们找到能够最大化优化效率的参数配置，同时减少ACO泛函的平均相对误差（$MRE$）。 然后我们分析算法在不同维度（$1D-5D$）下的性能，这些维度与FVC泛函中需要优化的参数数量有关。 我们的结果表明，具有优于$0.2$的信息素蒸发率的$15$只蚂蚁就足以在强关联系统的大范围参数——相互作用、粒子密度和自旋磁化——下最小化$MRE$。 虽然优化$1D$、$2D$和$4D$产生$1.5\%< MRE< 2.7\%$，但$3D$和$5D$优化将$MRE$降低到$\sim0.8\%$，与原始 FVC 泛函 ($MRE = 2.4\%$) 相比，反映了$67\%$的误差减少。 随着模拟时间几乎与维度线性增长，我们的结果突显了蚁群算法在密度泛函问题中的潜力，结合了有效性与低计算成本。 显示英文摘要

摘要： 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.