Machine learning CICY threefolds

Abstract

The latest techniques from Neural Networks and Support Vector Machines (SVM) are used to investigate geometric properties of Complete Intersection Calabi-Yau (CICY) threefolds, a class of manifolds that facilitate string model building. An advanced neural network classifier and SVM are employed to (1) learn Hodge numbers and report a remarkable improvement over previous efforts, (2) query for favourability, and (3) predict discrete symmetries, a highly imbalanced problem to which both Synthetic Minority Oversampling Technique (SMOTE) and permutations of the CICY matrix are used to decrease the class imbalance and improve performance. In each case study, we employ a genetic algorithm to optimise the hyperparameters of the neural network. We demonstrate that our approach provides quick diagnostic tools capable of shortlisting quasi-realistic string models based on compactification over smooth CICYs and further supports the paradigm that classes of problems in algebraic geometry can be machine learned. * kieran.bull@seh.ox.ac.uk † hey@maths.ox.ac.uk ‡ vishnu@neo.phys.wits.ac.za

Branes with brains: exploring string vacua with deep reinforcement learning

“…In mathematical directions that are also relevant for string vacua, supervised learning yielded an estimated upper bound on the number of Calabi-Yau threefolds realized as hypersurfaces in a large class of toric varieties [5], and has also led to accurate predictions for line bundle cohomology [12,14]. See [15][16][17][18][19][20] for additional works in string theory that use supervised learning.…”

“…N max ≥ 3, and the m i 's are chosen non-negative since the their negatives are automatically included as orientifold images. Since each stack is specified by a vector 18) there are N max × (2n + 1) 3 × (m + 1) 3 choices per stack, such that the number of states in the system without taking into account any symmetries is…”

Getting CICY high

“…We briefly summarize the main ideas behind the machine learning tools we have employed in this paper (and its predecessor [21]), namely, neural networks and Support Vector Machines (SVMs). Neural networks and SVMs can function as both classifiers and regressors, and as such have been the subject of active research in the machine learning community for several years.…”

“…In our previous work [21], using the CICY threefolds as a testbed, we answered the following questions. Given the configuration matrix which defines a CICY threefold, can machine learning techniques compute the Hodge numbers of the geometry?…”

Searching the landscape of flux vacua with genetic algorithms

“…The discrete landscape can be viewed as the complement of a continuum of seemingly consistent low-energy effective field theories (EFTs) that cannot descend from a string compactification, deemed the swampland [22,23]. While the latter has received much attention in recent years, progress in data science might allow for systematic studies of [24] and machine learning [25][26][27][28][29][30][31][32][33][34].…”