Alert button
Picture for Damian Kaloni Mayorga Pena

Damian Kaloni Mayorga Pena

Alert button

Neural Network Approximations for Calabi-Yau Metrics

Jan 27, 2021
Vishnu Jejjala, Damian Kaloni Mayorga Pena, Challenger Mishra

Figure 1 for Neural Network Approximations for Calabi-Yau Metrics
Figure 2 for Neural Network Approximations for Calabi-Yau Metrics
Figure 3 for Neural Network Approximations for Calabi-Yau Metrics
Figure 4 for Neural Network Approximations for Calabi-Yau Metrics

Ricci flat metrics for Calabi-Yau threefolds are not known analytically. In this work, we employ techniques from machine learning to deduce numerical flat metrics for the Fermat quintic, for the Dwork quintic, and for the Tian-Yau manifold. This investigation employs a single neural network architecture that is capable of approximating Ricci flat Kaehler metrics for several Calabi-Yau manifolds of dimensions two and three. We show that measures that assess the Ricci flatness of the geometry decrease after training by three orders of magnitude. This is corroborated on the validation set, where the improvement is more modest. Finally, we demonstrate that discrete symmetries of manifolds can be learned in the process of learning the metric.

* v2: 42 pages, figures improved, discrete symmetries section added, discussions enhanced, references added 
Viaarxiv icon

Baryons from Mesons: A Machine Learning Perspective

Mar 23, 2020
Yarin Gal, Vishnu Jejjala, Damian Kaloni Mayorga Pena, Challenger Mishra

Figure 1 for Baryons from Mesons: A Machine Learning Perspective
Figure 2 for Baryons from Mesons: A Machine Learning Perspective
Figure 3 for Baryons from Mesons: A Machine Learning Perspective
Figure 4 for Baryons from Mesons: A Machine Learning Perspective

Quantum chromodynamics (QCD) is the theory of the strong interaction. The fundamental particles of QCD, quarks and gluons, carry colour charge and form colourless bound states at low energies. The hadronic bound states of primary interest to us are the mesons and the baryons. From knowledge of the meson spectrum, we use neural networks and Gaussian processes to predict the masses of baryons with 90.3% and 96.6% accuracy, respectively. These results compare favourably to the constituent quark model. We as well predict the masses of pentaquarks and other exotic hadrons.

* 25 pages, 3 figures, 1 table 
Viaarxiv icon