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We present a new machine learning library for computing metrics of string compactification spaces.
Machine Learning Calabi–Yau Metrics
Anthony Ashmore, Yang-Hui He, and Burt A. Ovrut · 1910
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On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
Shing-Tung Yau · 1978
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Anti self-dual yang-mills connections over complex algebraic surfaces and stable vector bundles
Simon K Donaldson · 1985
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On the existence of hermitian-yang-mills connections in stable vector bundles
Karen Uhlenbeck and Shing-Tung Yau · 1986
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Complete Intersection Calabi-Yau Manifolds
P. Candelas, A. M. Dale, C. A. Lutken, and R. Schimmrigk · 1988
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All Hodge Numbers of All Complete Intersection Calabi-Yau Manifolds
Paul S. Green, Tristan Hubsch, and Carsten A. Lutken · 1989
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Mirror symmetry is T duality
Andrew Strominger, Shing-Tung Yau, and Eric Zaslow · 1996
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Distribution of Zeros of Random and Quantum Chaotic Sections of Positive Line Bundles
Bernard Shiffman and Steve Zelditch · 1999
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Complete classification of reflexive polyhedra in four-dimensions
Maximilian Kreuzer and Harald Skarke · 2000
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Scaling laws for neural language models
Jared Kaplan, Sam McCandlish, Tom Henighan, Tom B. Brown, Benjamin Chess, Rewon Child, Scott Gray, Alec Radford, Jeffrey Wu, and Dario Amodei · 2001
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The String landscape and the swampland
Cumrun Vafa · 2005
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Some numerical results in complex differential geometry
S. K. Donaldson · 2005
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Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic
Michael R. Douglas, Robert L. Karp, Sergio Lukic, and Rene Reinbacher · 2007
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Numerical Calabi-Yau metrics
Michael R. Douglas, Robert L. Karp, Sergio Lukic, and Rene Reinbacher · 2008
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Calabi-Yau Metrics for Quotients and Complete Intersections
Volker Braun, Tamaz Brelidze, Michael R. Douglas, and Burt A. Ovrut · 2008
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Eigenvalues and Eigenfunctions of the Scalar Laplace Operator on Calabi-Yau Manifolds
Neural Network Approximations for Calabi-Yau Metrics
Vishnu Jejjala, Damian Kaloni Mayorga Pena, and Challenger Mishra · 2012
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Energy functionals for Calabi-Yau metrics
Matthew Headrick and Ali Nassar · 2013
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The no-u-turn sampler: adaptively setting path lengths in hamiltonian monte carlo
Matthew D Hoffman, Andrew Gelman, et al · 2014
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TensorFlow: Large-scale machine learning on heterogeneous systems, 2015
Martín Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng Chen, Craig Citro, Greg S. Corrado, Andy Davis, Jeffrey Dean, Matthieu Devin, Sanjay Ghemawat, Ian Goodfellow, Andrew Harp, Geoffrey Irving, Michael Isard, Yangqing Jia, Rafal Jozefowicz, Lukasz Kaiser, Manjunath Kudlur, Josh Levenberg, Dandelion Mané, Rajat Monga, Sherry Moore, Derek Murray, Chris Olah, Mike Schuster, Jonathon Shlens, Benoit Steiner, Ilya Sutskever, Kunal Talwar, Paul Tucker, Vincent Vanhoucke, Vijay Vasudevan, Fernanda Viégas, Oriol Vinyals, Pete Warden, Martin Wattenberg, Martin Wicke, Yuan Yu, and Xiaoqiang Zheng · 2015
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Volker Braun, Tamaz Brelidze, Michael R. Douglas, and Burt A. Ovrut · 2008
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Numerical Hermitian Yang-Mills Connections and Vector Bundle Stability in Heterotic Theories
Lara B. Anderson, Volker Braun, Robert L. Karp, and Burt A. Ovrut · 2010
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Unsupervised neural networks for quantum eigenvalue problems
Henry Jin, Marios Mattheakis, and Pavlos Protopapas · 2010
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Numerical Hermitian Yang-Mills Connections and Kahler Cone Substructure
Lara B. Anderson, Volker Braun, and Burt A. Ovrut · 2012
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Numerical Calabi-Yau metrics from holomorphic networks
Michael R. Douglas, Subramanian Lakshminarasimhan, and Yidi Qi · 2012
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On Kähler Manifolds with Vanishing Canonical Class:
Eugenio Calabi · 2015
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Maziar Raissi, Paris Perdikaris, and George E Karniadakis · 2019
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Numerical Metrics, Curvature Expansions and Calabi-Yau Manifolds
Wei Cui and James Gray · 2020
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Array programming with NumPy
Charles R. Harris, K. Jarrod Millman, Stéfan J. van der Walt, Ralf Gommers, Pauli Virtanen, David Cournapeau, Eric Wieser, Julian Taylor, Sebastian Berg, Nathaniel J. Smith, Robert Kern, Matti Picus, Stephan Hoyer, Marten H. van Kerkwijk, Matthew Brett, Allan Haldane, Jaime Fernández del Río, Mark Wiebe, Pearu Peterson, Pierre Gérard-Marchant, Kevin Sheppard, Tyler Reddy, Warren Weckesser, Hameer Abbasi, Christoph Gohlke, and Travis E. Oliphant · 2020
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Moduli-dependent KK towers and the swampland distance conjecture on the quintic Calabi-Yau manifold
Anthony Ashmore and Fabian Ruehle · 2021
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Moduli-dependent Calabi-Yau and SU(3)-structure metrics from Machine Learning
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