Intelligent Explorations of the String Theory Landscape

The landscape of low-energy effective field theories stemming from string theory is too vast for a systematic exploration. However, the meadows of the string landscape may be fertile ground for the application of machine learning techniques. Employing neural network learning may allow for inferring novel, undiscovered properties that consistent theories in the landscape should possess, or checking conjectural statements about alleged characteristics thereof. The aim of this w...

We utilize machine learning to study the string landscape. Deep data dives and conjecture generation are proposed as useful frameworks for utilizing machine learning in the landscape, and examples of each are presented. A decision tree accurately predicts the number of weak Fano toric threefolds arising from reflexive polytopes, each of which determines a smooth F-theory compactification, and linear regression generates a previously proven conjecture for the gauge group rank ...

We briefly overview how, historically, string theory led theoretical physics first to precise problems in algebraic and differential geometry, and thence to computational geometry in the last decade or so, and now, in the last few years, to data science. Using the Calabi-Yau landscape -- accumulated by the collaboration of physicists, mathematicians and computer scientists over the last 4 decades -- as a starting-point and concrete playground, we review some recent progress i...

We study machine learning of phenomenologically relevant properties of string compactifications, which arise in the context of heterotic line bundle models. Both supervised and unsupervised learning are considered. We find that, for a fixed compactification manifold, relatively small neural networks are capable of distinguishing consistent line bundle models with the correct gauge group and the correct chiral asymmetry from random models without these properties. The same dis...

The string theory landscape may include a multitude of ultraviolet embeddings of the Standard Model, but identifying these has proven difficult due to the enormous number of available string compactifications. Genetic Algorithms (GAs) represent a powerful class of discrete optimisation techniques that can efficiently deal with the immensity of the string landscape, especially when enhanced with input from quantum annealers. In this letter we focus on geometric compactificatio...

We review the recent programme of using machine-learning to explore the landscape of mathematical problems. With this paradigm as a model for human intuition - complementary to and in contrast with the more formalistic approach of automated theorem proving - we highlight some experiments on how AI helps with conjecture formulation, pattern recognition and computation.

The immensity of the string landscape and the difficulty of identifying solutions that match the observed features of particle physics have raised serious questions about the predictive power of string theory. Modern methods of optimisation and search can, however, significantly improve the prospects of constructing the standard model in string theory. In this paper we scrutinise a corner of the heterotic string landscape consisting of compactifications on Calabi-Yau three-fo...

We study possible applications of artificial neural networks to examine the string landscape. Since the field of application is rather versatile, we propose to dynamically evolve these networks via genetic algorithms. This means that we start from basic building blocks and combine them such that the neural network performs best for the application we are interested in. We study three areas in which neural networks can be applied: to classify models according to a fixed set of...

We apply deep-learning techniques to the string landscape, in particular, $SO(32)$ heterotic string theory on simply-connected Calabi-Yau threefolds with line bundles. It turns out that three-generation models cluster in particular islands specified by deep autoencoder networks and k-means++ clustering. Especially, we explore mutual relations between model parameters and the cluster with densest three-generation models (called "3-generation island"). We find that the 3-genera...

We use deep autoencoder neural networks to draw a chart of the heterotic $\mathbb{Z}_6$-II orbifold landscape. Even though the autoencoder is trained without knowing the phenomenological properties of the $\mathbb{Z}_6$-II orbifold models, we are able to identify fertile islands in this chart where phenomenologically promising models cluster. Then, we apply a decision tree to our chart in order to extract the defining properties of the fertile islands. Based on this informati...