Both the three-body system and the inverse square potential carry a special significance in the study of renormalization group limit cycles. In this work, we pursue an exploratory approach and address the question which two-body interactions lead to limit cycles in the three-body system at low energies, without imposing any restrictions upon the scattering length. For this, we train a boosted ensemble of variational autoencoders, that not only provide a severe dimensionality reduction, but also allow to generate further synthetic potentials, which is an important prerequisite in order to efficiently search for limit cycles in low-dimensional latent space. We do so by applying an elitist genetic algorithm to a population of synthetic potentials that minimizes a specially defined limit-cycle-loss. The resulting fittest individuals suggest that the inverse square potential is the only two-body potential that minimizes this limit cycle loss independent of the hyperangle.

翻译：三体系统和反正方形潜力都具有研究再整顿组限制周期的特殊意义。 在这项工作中,我们采取探索性方法,解决两体相互作用导致三体系统在低能量下限制循环周期的问题,而不对散射长度施加任何限制。为此,我们训练了一组增强的变异自动变相组合体,不仅能提供严重的维度减低,而且还能产生进一步的合成潜力,这是有效寻找低维潜层空间限制周期的重要先决条件。我们这样做的办法是对合成潜力人群采用精英遗传算法,以尽量减少特定限周期损失。 由此产生的适者表明,反方形潜力是将这一限值周期损失降到最低的仅有的两体潜力,而不受超矩的影响。