Built on

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B. Carpenter, A. Gelman, M. D. Hoffman, D. Lee, B. Goodrich, M. Betancourt, M. Brubaker, J. Guo, P. Li, and A. Riddell, Journal of statistical software 76
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D. Guest, K. Cranmer, and D. Whiteson, Ann. Rev. Nucl. Part. Sci. 68
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A. Radovic, M. Williams, D. Rousseau, M. Kagan, D. Bonacorsi, A. Himmel, A. Aurisano, K. Terao, and T. Wongjirad, Nature 560
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P. E. Shanahan, D. Trewartha, and W. Detmold, Phys. Rev. D 97

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2019

Spectral Reconstruction with Deep Neural Networks

Kades, Lukas, Pawlowski, Jan M., Rothkopf, Alexander et al.

Understand

We explore artificial neural networks as a tool for the reconstruction of spectral functions from imaginary time Green's functions, a classic ill-conditioned inverse problem.

Our ansatz is based on a supervised learning framework in which prior knowledge is encoded in the training data and the inverse transformation manifold is explicitly parametrised through a neural network.
We systematically investigate this novel reconstruction approach, providing a detailed analysis of its performance on physically motivated mock data, and compare it to established methods of Bayesian inference.
The reconstruction accuracy is found to be at least comparable, and potentially superior in particular at larger noise levels.

Built on

J. Karpie, K. Orginos, A. Rothkopf, and S. Zafeiropoulos, JHEP 04
Original
1901
Earlier work this paper cites.
A. Rothkopf, in 13th Conference on Quark Confinement and the Hadron Spectrum (Confinement XIII) Maynooth, Ireland, July 31-August 6, 2018 (2019) arXiv:1903.02293 [hep-ph]
Original
1903
Earlier work this paper cites.
R. Oehme and W. Zimmermann, Phys. Rev. D21
1980
Earlier work this paper cites.
R. Oehme, Phys. Lett. B252
1990
Earlier work this paper cites.
M. Jarrell and J. E. Gubernatis, Phys. Rept. 269
1996
Earlier work this paper cites.
M. Asakawa, T. Hatsuda, and Y. Nakahara, Prog. Part. Nucl. Phys. 46
2001
Earlier work this paper cites.
G. Cuniberti, E. De Micheli, and G. A. Viano, Commun. Math. Phys. 216
2001
Earlier work this paper cites.
S. Bluecher, L. Kades, J. M. Pawlowski, N. Strodthoff, and J. M. Urban, (2020), arXiv:2003.01504 [hep-lat]
Original
2003
Earlier work this paper cites.
Y. Burnier, M. Laine, and L. Mether, Eur. Phys. J. C71
Original
2011
Earlier work this paper cites.

Similar

Y. Burnier and A. Rothkopf, Phys. Rev. Lett. 111
Original
2013
Cited alongside, same era.
J. Schmidhuber, (2014), 10.1016/j.neunet.2014.09.003 , arXiv:1404.7828
Original
2014
Cited alongside, same era.
Y. LeCun, Y. Bengio, and G. Hinton, Nature 521
2015
Cited alongside, same era.
L. Wang, Phys. Rev. B 94
2016
Cited alongside, same era.
J. Carrasquilla and R. G. Melko, Nature Physics 13
2017
Cited alongside, same era.
G. Carleo and M. Troyer, Science 355
2017
Cited alongside, same era.

Then

L. Huang and L. Wang, Phys. Rev. B 95
2017
Later among the works it cites.
J. Liu, Y. Qi, Z. Y. Meng, and L. Fu, Phys. Rev. B 95
2017
Later among the works it cites.
B. Carpenter, A. Gelman, M. D. Hoffman, D. Lee, B. Goodrich, M. Betancourt, M. Brubaker, J. Guo, P. Li, and A. Riddell, Journal of statistical software 76
Original
2017
Later among the works it cites.
D. Guest, K. Cranmer, and D. Whiteson, Ann. Rev. Nucl. Part. Sci. 68
Original
2018
Later among the works it cites.
A. Radovic, M. Williams, D. Rousseau, M. Kagan, D. Bonacorsi, A. Himmel, A. Aurisano, K. Terao, and T. Wongjirad, Nature 560
2018
Later among the works it cites.
P. E. Shanahan, D. Trewartha, and W. Detmold, Phys. Rev. D 97