The DNA of Calabi–Yau Hypersurfaces

Abstract Genetic Algorithms are implemented for triangulations of four‐dimensional reflexive polytopes, which induce Calabi–Yau threefold hypersurfaces via Batyrev's construction. These algorithms are shown to efficiently optimize physical observables such as axion decay constants or axion–photon couplings in string theory compactifications. For our implementation, a parameterization of triangulations is choosen that yields homotopy inequivalent Calabi–Yau threefolds by extending fine, regular triangulations of two‐faces, thereby eliminating exponentially large redundancy factors in the map from polytope triangulations to Calabi–Yau hypersurfaces. In particular, this encoding renders the entire Kreuzer–Skarke list amenable to a variety of optimization strategies, including but not limited to Genetic Algorithms. To achieve optimal performance, the hyperparameters of Genetic Algorithm are tuned using Bayesian optimization. The resulting implementation vastly outperforms other sampling and optimization strategies like Markov Chain Monte Carlo or Simulated Annealing. Finally, it is demonstrated that our Genetic Algorithm efficiently performs optimization even for the maximal polytope with Hodge numbers , where it is used to maximize axion–photon couplings.