Deep learning for K3 fibrations in heterotic/Type IIA string duality

Abstract

The development of Large Language Models, such as the recently released GPT-4, has revolutionized the field of Machine Learning and opened new avenues for interdisciplinary research. Prompt Engineering, a methodology for designing effective input prompts to guide these AI models, will emerge as a powerful tool for accelerating research efforts. In this study, we leverage Prompt Engineering with GPT-4 to address the problem of predicting K3 Fibrations in Calabi-Yau manifolds embedded in toric varieties with a single weight system. Out of the 184,026 weights spaces previously discovered, 101,495 remained unclassified concerning the presence of a K3 projection, thereby providing an opportunity for machine learning to bridge this gap. By utilizing an ensemble of Deep Neural Networks, we are able to predict the existence of the K3 fibration. Furthermore, we assess the potential of these models to predict the spectrum of possible Hodge Numbers and other properties of reflexive polytopes. These results not only demonstrate the utility of AI in studying the heterotic/Type IIA string duality in F-Theory but also serve as a stepping stone for further machine learning integration into traditional scientific workflows.