Machine Learning String Standard Models

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 revisit the question of predicting both Hodge numbers $h^{1,1}$ and $h^{2,1}$ of complete intersection Calabi-Yau (CICY) 3-folds using machine learning (ML), considering both the old and new datasets built respectively by Candelas-Dale-Lutken-Schimmrigk / Green-H\"ubsch-Lutken and by Anderson-Gao-Gray-Lee. In real world applications, implementing a ML system rarely reduces to feed the brute data to the algorithm. Instead, the typical workflow starts with an exploratory dat...

We survey some recent applications of machine learning to problems in geometry and theoretical physics. Pure mathematical data has been compiled over the last few decades by the community and experiments in supervised, semi-supervised and unsupervised machine learning have found surprising success. We thus advocate the programme of machine learning mathematical structures, and formulating conjectures via pattern recognition, in other words using artificial intelligence to hel...

Amidst all candidates of physics beyond the Standard Model, string theory provides a unique proposal for incorporating gauge and gravitational interactions. In string theory, a four-dimensional theory that unifies quantum mechanics and gravity is obtained automatically if one posits that the additional dimensions predicted by the theory are small and curled up, a concept known as compactification. The gauge sector of the theory is specified by the topology and geometry of the...

We review some recent applications of machine learning to algebraic geometry and physics. Since problems in algebraic geometry can typically be reformulated as mappings between tensors, this makes them particularly amenable to supervised learning. Additionally, unsupervised methods can provide insight into the structure of such geometrical data. At the heart of this programme is the question of how geometry can be machine learned, and indeed how AI helps one to do mathematics...

Machine learning techniques are increasingly powerful, leading to many breakthroughs in the natural sciences, but they are often stochastic, error-prone, and blackbox. How, then, should they be utilized in fields such as theoretical physics and pure mathematics that place a premium on rigor and understanding? In this Perspective we discuss techniques for obtaining rigor in the natural sciences with machine learning. Non-rigorous methods may lead to rigorous results via conjec...

MSSM-like string models from the compactification of the heterotic string on toroidal orbifolds (of the kind $T^6/P$) have distinct phenomenological properties, like the spectrum of vector-like exotics, the scale of supersymmetry breaking, and the existence of non-Abelian flavor symmetries. We show that these characteristics depend crucially on the choice of the underlying orbifold point group $P$. In detail, we use boosted decision trees to predict $P$ from phenomenological ...

We propose a novel approach toward the vacuum degeneracy problem of the string landscape, by finding an efficient measure of similarity amongst compactification scenarios. Using a class of some one million Calabi-Yau manifolds as concrete examples, the paradigm of few-shot machine-learning and Siamese Neural Networks represents them as points in R(3) where the similarity score between two manifolds is the Euclidean distance between their R(3) representatives. Using these meth...

We use machine learning to classify rational two-dimensional conformal field theories. We first use the energy spectra of these minimal models to train a supervised learning algorithm. We find that the machine is able to correctly predict the nature and the value of critical points of several strongly correlated spin models using only their energy spectra. This is in contrast to previous works that use machine learning to classify different phases of matter, but do not reveal...

We review recent efforts to machine learn relations between knot invariants. Because these knot invariants have meaning in physics, we explore aspects of Chern-Simons theory and higher dimensional gauge theories. The goal of this work is to translate numerical experiments with Big Data to new analytic results.