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تسجيل مستخدم جديدMachine Learning CICY Threefolds
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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.
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Supervised machine learning can be used to predict properties of string geometries with previously unknown features. Using the complete intersection Calabi-Yau (CICY) threefold dataset as a theoretical laboratory for this investigation, we use low $h
^{1,1}$ geometries for training and validate on geometries with large $h^{1,1}$. Neural networks and Support Vector Machines successfully predict trends in the number of Kahler parameters of CICY threefolds. The numerical accuracy of machine learning improves upon seeding the training set with a small number of samples at higher $h^{1,1}$.
David Mumford made groundbreaking contributions in many fields, including the pure mathematics of algebraic geometry and the applied mathematics of machine learning and artificial intelligence. His work in both fields influenced my career at several key moments.
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