Neurons on Amoebae

We use the machine learning technique to search the polytope which can result in an orientifold Calabi-Yau hypersurface and the "naive Type IIB string vacua". We show that neural networks can be trained to give a high accuracy for classifying the orientifold property and vacua based on the newly generated orientifold Calabi-Yau database with $h^{1,1}(X) \leq 6$ arXiv:2111.03078. This indicates the orientifold symmetry may already be encoded in the polytope structure. In the e...

This survey consists of two parts. Part 1 is devoted to amoebas. These are images of algebraic subvarieties in the complex torus under the logarithmic moment map. The amoebas have essentially piecewise-linear shape if viewed at large. Furthermore, they degenerate to certain piecewise-linear objects called tropical varieties whose behavior is governed by algebraic geometry over the so-called tropical semifield. Geometric aspects of tropical algebraic geometry are the content o...

We introduce unsupervised machine learning techniques in order to identify toric phases of 4d N=1 supersymmetric gauge theories corresponding to the same toric Calabi-Yau 3-fold. These 4d N=1 supersymmetric gauge theories are worldvolume theories of a D3-brane probing a toric Calabi-Yau 3-fold and are realized in terms of a Type IIB brane configuration known as a brane tiling. It corresponds to the skeleton graph of the coamoeba projection of the mirror curve associated to th...

Generalized Complete Intersection Calabi-Yau Manifold (gCICY) is a new construction of Calabi-Yau manifolds established recently. However, the generation of new gCICYs using standard algebraic method is very laborious. Due to this complexity, the number of gCICYs and their classification still remain unknown. In this paper, we try to make some progress in this direction using neural network. The results showed that our trained models can have a high precision on the existing ...

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.

We describe how simple machine learning methods successfully predict geometric properties from Hilbert series (HS). Regressors predict embedding weights in projective space to ${\sim}1$ mean absolute error, whilst classifiers predict dimension and Gorenstein index to $>90\%$ accuracy with ${\sim}0.5\%$ standard error. Binary random forest classifiers managed to distinguish whether the underlying HS describes a complete intersection with high accuracies exceeding $95\%$. Neura...

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 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...

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...

On the long-established classification problems in general relativity we take a novel perspective by adopting fruitful techniques from machine learning and modern data-science. In particular, we model Petrov's classification of spacetimes, and show that a feed-forward neural network can achieve high degree of success. We also show how data visualization techniques with dimensionality reduction can help analyze the underlying patterns in the structure of the different types of...