Built on

Y.-H. He and M. Kim, “Learning Algebraic Structures: Preliminary Investigations”, arXiv:1905.02263 [cs.LG]
Original
1905
Earlier work this paper cites.
A. Ashmore, Y.-H. He, and B. A. Ovrut, “Machine Learning Calabi–Yau Metrics”, Fortsch. Phys
Original
1910
Earlier work this paper cites.
L. Alessandretti, A. Baronchelli, and Y.-H. He, “Machine Learning meets Number Theory: The Data Science of Birch-Swinnerton-Dyer”, arXiv:1911.02008 [math.NT]
Original
1911
Earlier work this paper cites.
E. Calabi and K. On, “On kähler manifolds with vanishing canonical class”, Princeton Mathematical Series
1957
Earlier work this paper cites.
S. T. Yau, “On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation.I.”, Commun. Pure Appl. Math
1978
Earlier work this paper cites.
G. Tian, “On a set of polarized Kähler metrics on algebraic manifolds”, Journal of Differential Geometry
1990
Earlier work this paper cites.
P. Horava and E. Witten, “Heterotic and type I string dynamics from eleven-dimensions”, Nucl. Phys. B
1996
Earlier work this paper cites.
P. Horava and E. Witten, “Eleven-dimensional supergravity on a manifold with boundary”, Nucl. Phys. B
1996
Earlier work this paper cites.
A. Lukas, B. A. Ovrut, and D. Waldram, “On the four-dimensional effective action of strongly coupled heterotic string theory”, Nucl. Phys. B
1998
Earlier work this paper cites.
A. Lukas, B. A. Ovrut, K. S. Stelle, and D. Waldram, “The Universe as a domain wall”, Phys. Rev. D
1999
Earlier work this paper cites.
A. Lukas, B. A. Ovrut, K. S. Stelle, and D. Waldram, “Heterotic M theory in five-dimensions”, Nucl. Phys. B
1999
Earlier work this paper cites.
V. Braun, Y.-H. He, B. A. Ovrut, and T. Pantev, “A Standard model from the E(8) x E(8) heterotic superstring”, JHEP
2005
Earlier work this paper cites.
V. Braun, Y.-H. He, B. A. Ovrut, and T. Pantev, “A Heterotic standard model”, Phys. Lett. B
2005
Earlier work this paper cites.
M. Headrick and T. Wiseman, “Numerical Ricci-flat metrics on K3”, Class. Quant. Grav
2005
Earlier work this paper cites.

Similar

V. Braun, Y.-H. He, B. A. Ovrut, and T. Pantev, “The Exact MSSM spectrum from string theory”, JHEP
2006
Cited alongside, same era.
V. Bouchard and R. Donagi, “An SU(5) heterotic standard model”, Phys. Lett. B
2006
Cited alongside, same era.
M. R. Douglas, R. L. Karp, S. Lukic, and R. Reinbacher, “Numerical Calabi-Yau metrics”, J. Math. Phys
2008
Cited alongside, same era.
V. Braun, T. Brelidze, M. R. Douglas, and B. A. Ovrut, “Calabi-Yau Metrics for Quotients and Complete Intersections”, JHEP
Original
2008
Cited alongside, same era.
V. Braun, T. Brelidze, M. R. Douglas, and B. A. Ovrut, “Eigenvalues and Eigenfunctions of the Scalar Laplace Operator on Calabi-Yau Manifolds”, JHEP
Original
2008
Cited alongside, same era.

Then

L. B. Anderson, A. Constantin, J. Gray, A. Lukas, and E. Palti, “A Comprehensive Scan for Heterotic SU(5) GUT models”, JHEP
Original
2014
Later among the works it cites.
S. Groot Nibbelink, O. Loukas, F. Ruehle, and P. K. S. Vaudrevange, “Infinite number of MSSMs from heterotic line bundles?”, Phys. Rev. D
Original
2015
Later among the works it cites.
S. Groot Nibbelink, O. Loukas, and F. Ruehle, “(MS)SM-like models on smooth Calabi-Yau manifolds from all three heterotic string theories”, Fortsch. Phys
Original
2015
Later among the works it cites.
http://tensorflow.org/ . Software available from tensorflow.org
M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-scale machine learning on heterogeneous systems”, 2015 · 2015
Later among the works it cites.

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2021

Calabi-Yau Metrics, Energy Functionals and Machine-Learning

Ashmore, Anthony, Calmon, Lucille, He, Yang-Hui et al.

Understand

We apply machine learning to the problem of finding numerical Calabi-Yau metrics.

We extend previous work on learning approximate Ricci-flat metrics calculated using Donaldson's algorithm to the much more accurate "optimal" metrics of Headrick and Nassar.
We show that machine learning is able to predict the K\"ahler potential of a Calabi-Yau metric having seen only a small sample of training data.

Built on

Y.-H. He and M. Kim, “Learning Algebraic Structures: Preliminary Investigations”, arXiv:1905.02263 [cs.LG]
Original
1905
Earlier work this paper cites.
A. Ashmore, Y.-H. He, and B. A. Ovrut, “Machine Learning Calabi–Yau Metrics”, Fortsch. Phys
Original
1910
Earlier work this paper cites.
L. Alessandretti, A. Baronchelli, and Y.-H. He, “Machine Learning meets Number Theory: The Data Science of Birch-Swinnerton-Dyer”, arXiv:1911.02008 [math.NT]
Original
1911
Earlier work this paper cites.
E. Calabi and K. On, “On kähler manifolds with vanishing canonical class”, Princeton Mathematical Series
1957
Earlier work this paper cites.
S. T. Yau, “On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation.I.”, Commun. Pure Appl. Math
1978
Earlier work this paper cites.
G. Tian, “On a set of polarized Kähler metrics on algebraic manifolds”, Journal of Differential Geometry
1990
Earlier work this paper cites.
P. Horava and E. Witten, “Heterotic and type I string dynamics from eleven-dimensions”, Nucl. Phys. B
1996
Earlier work this paper cites.
P. Horava and E. Witten, “Eleven-dimensional supergravity on a manifold with boundary”, Nucl. Phys. B
1996
Earlier work this paper cites.
A. Lukas, B. A. Ovrut, and D. Waldram, “On the four-dimensional effective action of strongly coupled heterotic string theory”, Nucl. Phys. B
1998
Earlier work this paper cites.
A. Lukas, B. A. Ovrut, K. S. Stelle, and D. Waldram, “The Universe as a domain wall”, Phys. Rev. D
1999
Earlier work this paper cites.
A. Lukas, B. A. Ovrut, K. S. Stelle, and D. Waldram, “Heterotic M theory in five-dimensions”, Nucl. Phys. B
1999
Earlier work this paper cites.
V. Braun, Y.-H. He, B. A. Ovrut, and T. Pantev, “A Standard model from the E(8) x E(8) heterotic superstring”, JHEP
2005
Earlier work this paper cites.
V. Braun, Y.-H. He, B. A. Ovrut, and T. Pantev, “A Heterotic standard model”, Phys. Lett. B
2005
Earlier work this paper cites.
M. Headrick and T. Wiseman, “Numerical Ricci-flat metrics on K3”, Class. Quant. Grav
2005
Earlier work this paper cites.

Similar

V. Braun, Y.-H. He, B. A. Ovrut, and T. Pantev, “The Exact MSSM spectrum from string theory”, JHEP
2006
Cited alongside, same era.
V. Bouchard and R. Donagi, “An SU(5) heterotic standard model”, Phys. Lett. B
2006
Cited alongside, same era.
M. R. Douglas, R. L. Karp, S. Lukic, and R. Reinbacher, “Numerical Calabi-Yau metrics”, J. Math. Phys
2008
Cited alongside, same era.
V. Braun, T. Brelidze, M. R. Douglas, and B. A. Ovrut, “Calabi-Yau Metrics for Quotients and Complete Intersections”, JHEP
Original
2008
Cited alongside, same era.
V. Braun, T. Brelidze, M. R. Douglas, and B. A. Ovrut, “Eigenvalues and Eigenfunctions of the Scalar Laplace Operator on Calabi-Yau Manifolds”, JHEP
Original
2008
Cited alongside, same era.

Then

L. B. Anderson, A. Constantin, J. Gray, A. Lukas, and E. Palti, “A Comprehensive Scan for Heterotic SU(5) GUT models”, JHEP
Original
2014
Later among the works it cites.
S. Groot Nibbelink, O. Loukas, F. Ruehle, and P. K. S. Vaudrevange, “Infinite number of MSSMs from heterotic line bundles?”, Phys. Rev. D
Original
2015
Later among the works it cites.
S. Groot Nibbelink, O. Loukas, and F. Ruehle, “(MS)SM-like models on smooth Calabi-Yau manifolds from all three heterotic string theories”, Fortsch. Phys
Original
2015
Later among the works it cites.
http://tensorflow.org/ . Software available from tensorflow.org
M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-scale machine learning on heterogeneous systems”, 2015 · 2015
Later among the works it cites.