Abstract

Coherent beam combining is a method to scale the peak and average power levels of laser systems beyond the limit of a single emitter system. This is achieved by stabilizing the relative optical phase of multiple lasers and combining them. We investigated the use of reinforcement learning (RL) and neural networks (NN) in this domain. Starting from a randomly initialized neural network, the system converged to a phase stabilization policy, which was comparable to a software implemented proportional-integral-derivative (PID) controller. Furthermore, we demonstrate the capability of neural networks to predict relative phase noise, which is one potential advantage of this method.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11, 567–577 (2005).
    [Crossref]
  2. M. Müller, M. Kienel, A. Klenke, T. Gottschall, E. Shestaev, M. Plötner, J. Limpert, and A. Tünnermann, “1 kW 1 mJ eight-channel ultrafast fiber laser,” Opt. Lett. 41, 3439–3442 (2016).
    [Crossref]
  3. A. Klenke, M. Müller, H. Stark, M. Kienel, C. Jauregui, A. Tünnermann, and J. Limpert, “Coherent beam combination of ultrafast fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 24, 1–9 (2018).
    [Crossref]
  4. T. Hansch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
    [Crossref]
  5. T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486(2007).
    [Crossref]
  6. S. B. Weiss, M. E. Weber, and G. D. Goodno, “Group delay locking of coherently combined broadband lasers,” Opt. Lett. 37, 455–457 (2012).
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  7. J. B. Rawlings, “Tutorial overview of model predictive control,” IEEE Control. Syst. Mag. 20, 38–52 (2000).
    [Crossref]
  8. R. S. Sutton and A. G. Barto, Reinforcement learning: An introduction (MIT, 2018).
  9. A. Y. Ng, A. Coates, M. Diel, V. Ganapathi, J. Schulte, B. Tse, E. Berger, and E. Liang, “Autonomous inverted helicopter flight via reinforcement learning,” in Experimental Robotics IX, (Springer, 2006), pp. 363–372.
  10. V. Mnih, K. Kavukcuoglu, D. Silver, A. Graves, I. Antonoglou, D. Wierstra, and M. Riedmiller, “Playing atari with deep reinforcement learning,” arXiv preprint arXiv:1312.5602 (2013).
  11. D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, D. Sander, G. Dominik, N. John, K. Nal, S. Ilya, L. Timothy, L. Madeleine, K. Koray, G. Thore, and H. Demis, “Mastering the game of go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
    [Crossref] [PubMed]
  12. D. G. Sandler, T. K. Barrett, D. A. Palmer, R. Q. Fugate, and W. J. Wild, “Use of a neural network to control an adaptive optics system for an astronomical telescope,” Nature 351, 300–302 (1991).
    [Crossref]
  13. F. C. Hoppensteadt and E. M. Izhikevich, “Pattern recognition via synchronization in phase-locked loop neural networks,” IEEE Transactions on Neural Networks 11, 734–738 (2000).
    [Crossref]
  14. T. Hou, Y. An, Q. Chang, P. Ma, J. Li, L. Huang, D. Zhi, J. Wu, R. Su, Y. Ma, and P. Zhou, “Deep learning-based phase control method for coherent beam combining and its application in generating orbital angular momentum beams,” arXiv preprint arXiv:1903.03983 (2019).
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  18. T. P. Lillicrap, J. J. Hunt, A. Pritzel, N. Heess, T. Erez, Y. Tassa, D. Silver, and D. Wierstra, “Continuous control with deep reinforcement learning,” arXiv preprint arXiv:1509.02971 (2015).
  19. S. J. Augst, T. Fan, and A. Sanchez, “Coherent beam combining and phase noise measurements of ytterbium fiber amplifiers,” Opt. Lett. 29, 474–476 (2004).
    [Crossref] [PubMed]
  20. H. Tünnermann, J. H. Pöld, J. Neumann, D. Kracht, B. Willke, and P. Weßels, “Beam quality and noise properties of coherently combined ytterbium doped single frequency fiber amplifiers,” Opt. Express 19, 19600–19606 (2011).
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  21. J. Chung, C. Gulcehre, K. Cho, and Y. Bengio, “Empirical evaluation of gated recurrent neural networks on sequence modeling,” arXiv preprint arXiv:1412.3555 (2014).
  22. T. Schaul, J. Quan, I. Antonoglou, and D. Silver, “Prioritized experience replay,” arXiv preprint arXiv:1511.05952 (2015).
  23. E. Liang, R. Liaw, P. Moritz, R. Nishihara, R. Fox, K. Goldberg, J. E. Gonzalez, M. I. Jordan, and I. Stoica, “Rllib: Abstractions for distributed reinforcement learning,” arXiv preprint arXiv:1712.09381 (2017).
  24. N. Wahlström, T. B. Schön, and M. P. Deisenroth, “From pixels to torques: Policy learning with deep dynamical models,” arXiv preprint arXiv:1502.02251 (2015).

2018 (1)

A. Klenke, M. Müller, H. Stark, M. Kienel, C. Jauregui, A. Tünnermann, and J. Limpert, “Coherent beam combination of ultrafast fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 24, 1–9 (2018).
[Crossref]

2016 (2)

M. Müller, M. Kienel, A. Klenke, T. Gottschall, E. Shestaev, M. Plötner, J. Limpert, and A. Tünnermann, “1 kW 1 mJ eight-channel ultrafast fiber laser,” Opt. Lett. 41, 3439–3442 (2016).
[Crossref]

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, D. Sander, G. Dominik, N. John, K. Nal, S. Ilya, L. Timothy, L. Madeleine, K. Koray, G. Thore, and H. Demis, “Mastering the game of go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

2012 (1)

2011 (1)

2007 (1)

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486(2007).
[Crossref]

2005 (1)

T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11, 567–577 (2005).
[Crossref]

2004 (1)

2000 (2)

F. C. Hoppensteadt and E. M. Izhikevich, “Pattern recognition via synchronization in phase-locked loop neural networks,” IEEE Transactions on Neural Networks 11, 734–738 (2000).
[Crossref]

J. B. Rawlings, “Tutorial overview of model predictive control,” IEEE Control. Syst. Mag. 20, 38–52 (2000).
[Crossref]

1991 (1)

D. G. Sandler, T. K. Barrett, D. A. Palmer, R. Q. Fugate, and W. J. Wild, “Use of a neural network to control an adaptive optics system for an astronomical telescope,” Nature 351, 300–302 (1991).
[Crossref]

1980 (1)

T. Hansch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[Crossref]

Abadi, M.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: A system for large-scale machine learning,” in 12th Symposium on Operating Systems Design and Implementation, (2016), pp. 265–283.

An, Y.

T. Hou, Y. An, Q. Chang, P. Ma, J. Li, L. Huang, D. Zhi, J. Wu, R. Su, Y. Ma, and P. Zhou, “Deep learning-based phase control method for coherent beam combining and its application in generating orbital angular momentum beams,” arXiv preprint arXiv:1903.03983 (2019).

Antonoglou, I.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, D. Sander, G. Dominik, N. John, K. Nal, S. Ilya, L. Timothy, L. Madeleine, K. Koray, G. Thore, and H. Demis, “Mastering the game of go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

V. Mnih, K. Kavukcuoglu, D. Silver, A. Graves, I. Antonoglou, D. Wierstra, and M. Riedmiller, “Playing atari with deep reinforcement learning,” arXiv preprint arXiv:1312.5602 (2013).

T. Schaul, J. Quan, I. Antonoglou, and D. Silver, “Prioritized experience replay,” arXiv preprint arXiv:1511.05952 (2015).

Augst, S. J.

Baker, J. T.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486(2007).
[Crossref]

Barham, P.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: A system for large-scale machine learning,” in 12th Symposium on Operating Systems Design and Implementation, (2016), pp. 265–283.

Barrett, T. K.

D. G. Sandler, T. K. Barrett, D. A. Palmer, R. Q. Fugate, and W. J. Wild, “Use of a neural network to control an adaptive optics system for an astronomical telescope,” Nature 351, 300–302 (1991).
[Crossref]

Barto, A. G.

R. S. Sutton and A. G. Barto, Reinforcement learning: An introduction (MIT, 2018).

Bengio, Y.

J. Chung, C. Gulcehre, K. Cho, and Y. Bengio, “Empirical evaluation of gated recurrent neural networks on sequence modeling,” arXiv preprint arXiv:1412.3555 (2014).

Benham, V.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486(2007).
[Crossref]

Berger, E.

A. Y. Ng, A. Coates, M. Diel, V. Ganapathi, J. Schulte, B. Tse, E. Berger, and E. Liang, “Autonomous inverted helicopter flight via reinforcement learning,” in Experimental Robotics IX, (Springer, 2006), pp. 363–372.

Chang, Q.

T. Hou, Y. An, Q. Chang, P. Ma, J. Li, L. Huang, D. Zhi, J. Wu, R. Su, Y. Ma, and P. Zhou, “Deep learning-based phase control method for coherent beam combining and its application in generating orbital angular momentum beams,” arXiv preprint arXiv:1903.03983 (2019).

Chen, J.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: A system for large-scale machine learning,” in 12th Symposium on Operating Systems Design and Implementation, (2016), pp. 265–283.

Chen, Z.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: A system for large-scale machine learning,” in 12th Symposium on Operating Systems Design and Implementation, (2016), pp. 265–283.

Cho, K.

J. Chung, C. Gulcehre, K. Cho, and Y. Bengio, “Empirical evaluation of gated recurrent neural networks on sequence modeling,” arXiv preprint arXiv:1412.3555 (2014).

Chung, J.

J. Chung, C. Gulcehre, K. Cho, and Y. Bengio, “Empirical evaluation of gated recurrent neural networks on sequence modeling,” arXiv preprint arXiv:1412.3555 (2014).

Coates, A.

A. Y. Ng, A. Coates, M. Diel, V. Ganapathi, J. Schulte, B. Tse, E. Berger, and E. Liang, “Autonomous inverted helicopter flight via reinforcement learning,” in Experimental Robotics IX, (Springer, 2006), pp. 363–372.

Couillaud, B.

T. Hansch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[Crossref]

Davis, A.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: A system for large-scale machine learning,” in 12th Symposium on Operating Systems Design and Implementation, (2016), pp. 265–283.

Dean, J.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: A system for large-scale machine learning,” in 12th Symposium on Operating Systems Design and Implementation, (2016), pp. 265–283.

Deisenroth, M. P.

N. Wahlström, T. B. Schön, and M. P. Deisenroth, “From pixels to torques: Policy learning with deep dynamical models,” arXiv preprint arXiv:1502.02251 (2015).

Demis, H.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, D. Sander, G. Dominik, N. John, K. Nal, S. Ilya, L. Timothy, L. Madeleine, K. Koray, G. Thore, and H. Demis, “Mastering the game of go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Devin, M.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: A system for large-scale machine learning,” in 12th Symposium on Operating Systems Design and Implementation, (2016), pp. 265–283.

Diel, M.

A. Y. Ng, A. Coates, M. Diel, V. Ganapathi, J. Schulte, B. Tse, E. Berger, and E. Liang, “Autonomous inverted helicopter flight via reinforcement learning,” in Experimental Robotics IX, (Springer, 2006), pp. 363–372.

Dominik, G.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, D. Sander, G. Dominik, N. John, K. Nal, S. Ilya, L. Timothy, L. Madeleine, K. Koray, G. Thore, and H. Demis, “Mastering the game of go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Erez, T.

T. P. Lillicrap, J. J. Hunt, A. Pritzel, N. Heess, T. Erez, Y. Tassa, D. Silver, and D. Wierstra, “Continuous control with deep reinforcement learning,” arXiv preprint arXiv:1509.02971 (2015).

Fan, T.

Fan, T. Y.

T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11, 567–577 (2005).
[Crossref]

Fox, R.

E. Liang, R. Liaw, P. Moritz, R. Nishihara, R. Fox, K. Goldberg, J. E. Gonzalez, M. I. Jordan, and I. Stoica, “Rllib: Abstractions for distributed reinforcement learning,” arXiv preprint arXiv:1712.09381 (2017).

Fugate, R. Q.

D. G. Sandler, T. K. Barrett, D. A. Palmer, R. Q. Fugate, and W. J. Wild, “Use of a neural network to control an adaptive optics system for an astronomical telescope,” Nature 351, 300–302 (1991).
[Crossref]

Ganapathi, V.

A. Y. Ng, A. Coates, M. Diel, V. Ganapathi, J. Schulte, B. Tse, E. Berger, and E. Liang, “Autonomous inverted helicopter flight via reinforcement learning,” in Experimental Robotics IX, (Springer, 2006), pp. 363–372.

Ghemawat, S.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: A system for large-scale machine learning,” in 12th Symposium on Operating Systems Design and Implementation, (2016), pp. 265–283.

Goldberg, K.

E. Liang, R. Liaw, P. Moritz, R. Nishihara, R. Fox, K. Goldberg, J. E. Gonzalez, M. I. Jordan, and I. Stoica, “Rllib: Abstractions for distributed reinforcement learning,” arXiv preprint arXiv:1712.09381 (2017).

Gonzalez, J. E.

E. Liang, R. Liaw, P. Moritz, R. Nishihara, R. Fox, K. Goldberg, J. E. Gonzalez, M. I. Jordan, and I. Stoica, “Rllib: Abstractions for distributed reinforcement learning,” arXiv preprint arXiv:1712.09381 (2017).

Goodno, G. D.

Gottschall, T.

Graves, A.

V. Mnih, K. Kavukcuoglu, D. Silver, A. Graves, I. Antonoglou, D. Wierstra, and M. Riedmiller, “Playing atari with deep reinforcement learning,” arXiv preprint arXiv:1312.5602 (2013).

Guez, A.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, D. Sander, G. Dominik, N. John, K. Nal, S. Ilya, L. Timothy, L. Madeleine, K. Koray, G. Thore, and H. Demis, “Mastering the game of go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Gulcehre, C.

J. Chung, C. Gulcehre, K. Cho, and Y. Bengio, “Empirical evaluation of gated recurrent neural networks on sequence modeling,” arXiv preprint arXiv:1412.3555 (2014).

Hansch, T.

T. Hansch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35, 441–444 (1980).
[Crossref]

Heess, N.

T. P. Lillicrap, J. J. Hunt, A. Pritzel, N. Heess, T. Erez, Y. Tassa, D. Silver, and D. Wierstra, “Continuous control with deep reinforcement learning,” arXiv preprint arXiv:1509.02971 (2015).

Hoppensteadt, F. C.

F. C. Hoppensteadt and E. M. Izhikevich, “Pattern recognition via synchronization in phase-locked loop neural networks,” IEEE Transactions on Neural Networks 11, 734–738 (2000).
[Crossref]

Hou, T.

T. Hou, Y. An, Q. Chang, P. Ma, J. Li, L. Huang, D. Zhi, J. Wu, R. Su, Y. Ma, and P. Zhou, “Deep learning-based phase control method for coherent beam combining and its application in generating orbital angular momentum beams,” arXiv preprint arXiv:1903.03983 (2019).

Huang, A.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, D. Sander, G. Dominik, N. John, K. Nal, S. Ilya, L. Timothy, L. Madeleine, K. Koray, G. Thore, and H. Demis, “Mastering the game of go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Huang, L.

T. Hou, Y. An, Q. Chang, P. Ma, J. Li, L. Huang, D. Zhi, J. Wu, R. Su, Y. Ma, and P. Zhou, “Deep learning-based phase control method for coherent beam combining and its application in generating orbital angular momentum beams,” arXiv preprint arXiv:1903.03983 (2019).

Hunt, J. J.

T. P. Lillicrap, J. J. Hunt, A. Pritzel, N. Heess, T. Erez, Y. Tassa, D. Silver, and D. Wierstra, “Continuous control with deep reinforcement learning,” arXiv preprint arXiv:1509.02971 (2015).

Ilya, S.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, D. Sander, G. Dominik, N. John, K. Nal, S. Ilya, L. Timothy, L. Madeleine, K. Koray, G. Thore, and H. Demis, “Mastering the game of go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Irving, G.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: A system for large-scale machine learning,” in 12th Symposium on Operating Systems Design and Implementation, (2016), pp. 265–283.

Isard, M.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: A system for large-scale machine learning,” in 12th Symposium on Operating Systems Design and Implementation, (2016), pp. 265–283.

Izhikevich, E. M.

F. C. Hoppensteadt and E. M. Izhikevich, “Pattern recognition via synchronization in phase-locked loop neural networks,” IEEE Transactions on Neural Networks 11, 734–738 (2000).
[Crossref]

Jauregui, C.

A. Klenke, M. Müller, H. Stark, M. Kienel, C. Jauregui, A. Tünnermann, and J. Limpert, “Coherent beam combination of ultrafast fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 24, 1–9 (2018).
[Crossref]

John, N.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, D. Sander, G. Dominik, N. John, K. Nal, S. Ilya, L. Timothy, L. Madeleine, K. Koray, G. Thore, and H. Demis, “Mastering the game of go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Jordan, M. I.

E. Liang, R. Liaw, P. Moritz, R. Nishihara, R. Fox, K. Goldberg, J. E. Gonzalez, M. I. Jordan, and I. Stoica, “Rllib: Abstractions for distributed reinforcement learning,” arXiv preprint arXiv:1712.09381 (2017).

Kavukcuoglu, K.

V. Mnih, K. Kavukcuoglu, D. Silver, A. Graves, I. Antonoglou, D. Wierstra, and M. Riedmiller, “Playing atari with deep reinforcement learning,” arXiv preprint arXiv:1312.5602 (2013).

Kienel, M.

A. Klenke, M. Müller, H. Stark, M. Kienel, C. Jauregui, A. Tünnermann, and J. Limpert, “Coherent beam combination of ultrafast fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 24, 1–9 (2018).
[Crossref]

M. Müller, M. Kienel, A. Klenke, T. Gottschall, E. Shestaev, M. Plötner, J. Limpert, and A. Tünnermann, “1 kW 1 mJ eight-channel ultrafast fiber laser,” Opt. Lett. 41, 3439–3442 (2016).
[Crossref]

Klenke, A.

A. Klenke, M. Müller, H. Stark, M. Kienel, C. Jauregui, A. Tünnermann, and J. Limpert, “Coherent beam combination of ultrafast fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 24, 1–9 (2018).
[Crossref]

M. Müller, M. Kienel, A. Klenke, T. Gottschall, E. Shestaev, M. Plötner, J. Limpert, and A. Tünnermann, “1 kW 1 mJ eight-channel ultrafast fiber laser,” Opt. Lett. 41, 3439–3442 (2016).
[Crossref]

Koray, K.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, D. Sander, G. Dominik, N. John, K. Nal, S. Ilya, L. Timothy, L. Madeleine, K. Koray, G. Thore, and H. Demis, “Mastering the game of go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Kracht, D.

Kudlur, M.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: A system for large-scale machine learning,” in 12th Symposium on Operating Systems Design and Implementation, (2016), pp. 265–283.

Lanctot, M.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, D. Sander, G. Dominik, N. John, K. Nal, S. Ilya, L. Timothy, L. Madeleine, K. Koray, G. Thore, and H. Demis, “Mastering the game of go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Levenberg, J.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: A system for large-scale machine learning,” in 12th Symposium on Operating Systems Design and Implementation, (2016), pp. 265–283.

Li, J.

T. Hou, Y. An, Q. Chang, P. Ma, J. Li, L. Huang, D. Zhi, J. Wu, R. Su, Y. Ma, and P. Zhou, “Deep learning-based phase control method for coherent beam combining and its application in generating orbital angular momentum beams,” arXiv preprint arXiv:1903.03983 (2019).

Liang, E.

A. Y. Ng, A. Coates, M. Diel, V. Ganapathi, J. Schulte, B. Tse, E. Berger, and E. Liang, “Autonomous inverted helicopter flight via reinforcement learning,” in Experimental Robotics IX, (Springer, 2006), pp. 363–372.

E. Liang, R. Liaw, P. Moritz, R. Nishihara, R. Fox, K. Goldberg, J. E. Gonzalez, M. I. Jordan, and I. Stoica, “Rllib: Abstractions for distributed reinforcement learning,” arXiv preprint arXiv:1712.09381 (2017).

Liaw, R.

E. Liang, R. Liaw, P. Moritz, R. Nishihara, R. Fox, K. Goldberg, J. E. Gonzalez, M. I. Jordan, and I. Stoica, “Rllib: Abstractions for distributed reinforcement learning,” arXiv preprint arXiv:1712.09381 (2017).

Lillicrap, T. P.

T. P. Lillicrap, J. J. Hunt, A. Pritzel, N. Heess, T. Erez, Y. Tassa, D. Silver, and D. Wierstra, “Continuous control with deep reinforcement learning,” arXiv preprint arXiv:1509.02971 (2015).

Limpert, J.

A. Klenke, M. Müller, H. Stark, M. Kienel, C. Jauregui, A. Tünnermann, and J. Limpert, “Coherent beam combination of ultrafast fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 24, 1–9 (2018).
[Crossref]

M. Müller, M. Kienel, A. Klenke, T. Gottschall, E. Shestaev, M. Plötner, J. Limpert, and A. Tünnermann, “1 kW 1 mJ eight-channel ultrafast fiber laser,” Opt. Lett. 41, 3439–3442 (2016).
[Crossref]

Lu, C. A.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486(2007).
[Crossref]

Ma, P.

T. Hou, Y. An, Q. Chang, P. Ma, J. Li, L. Huang, D. Zhi, J. Wu, R. Su, Y. Ma, and P. Zhou, “Deep learning-based phase control method for coherent beam combining and its application in generating orbital angular momentum beams,” arXiv preprint arXiv:1903.03983 (2019).

Ma, Y.

T. Hou, Y. An, Q. Chang, P. Ma, J. Li, L. Huang, D. Zhi, J. Wu, R. Su, Y. Ma, and P. Zhou, “Deep learning-based phase control method for coherent beam combining and its application in generating orbital angular momentum beams,” arXiv preprint arXiv:1903.03983 (2019).

Maddison, C. J.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, D. Sander, G. Dominik, N. John, K. Nal, S. Ilya, L. Timothy, L. Madeleine, K. Koray, G. Thore, and H. Demis, “Mastering the game of go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Madeleine, L.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, D. Sander, G. Dominik, N. John, K. Nal, S. Ilya, L. Timothy, L. Madeleine, K. Koray, G. Thore, and H. Demis, “Mastering the game of go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Mnih, V.

V. Mnih, K. Kavukcuoglu, D. Silver, A. Graves, I. Antonoglou, D. Wierstra, and M. Riedmiller, “Playing atari with deep reinforcement learning,” arXiv preprint arXiv:1312.5602 (2013).

Monga, R.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: A system for large-scale machine learning,” in 12th Symposium on Operating Systems Design and Implementation, (2016), pp. 265–283.

Moore, S.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: A system for large-scale machine learning,” in 12th Symposium on Operating Systems Design and Implementation, (2016), pp. 265–283.

Moritz, P.

E. Liang, R. Liaw, P. Moritz, R. Nishihara, R. Fox, K. Goldberg, J. E. Gonzalez, M. I. Jordan, and I. Stoica, “Rllib: Abstractions for distributed reinforcement learning,” arXiv preprint arXiv:1712.09381 (2017).

Müller, M.

A. Klenke, M. Müller, H. Stark, M. Kienel, C. Jauregui, A. Tünnermann, and J. Limpert, “Coherent beam combination of ultrafast fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 24, 1–9 (2018).
[Crossref]

M. Müller, M. Kienel, A. Klenke, T. Gottschall, E. Shestaev, M. Plötner, J. Limpert, and A. Tünnermann, “1 kW 1 mJ eight-channel ultrafast fiber laser,” Opt. Lett. 41, 3439–3442 (2016).
[Crossref]

Murray, D. G.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: A system for large-scale machine learning,” in 12th Symposium on Operating Systems Design and Implementation, (2016), pp. 265–283.

Nal, K.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, D. Sander, G. Dominik, N. John, K. Nal, S. Ilya, L. Timothy, L. Madeleine, K. Koray, G. Thore, and H. Demis, “Mastering the game of go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Neumann, J.

Ng, A. Y.

A. Y. Ng, A. Coates, M. Diel, V. Ganapathi, J. Schulte, B. Tse, E. Berger, and E. Liang, “Autonomous inverted helicopter flight via reinforcement learning,” in Experimental Robotics IX, (Springer, 2006), pp. 363–372.

Nishihara, R.

E. Liang, R. Liaw, P. Moritz, R. Nishihara, R. Fox, K. Goldberg, J. E. Gonzalez, M. I. Jordan, and I. Stoica, “Rllib: Abstractions for distributed reinforcement learning,” arXiv preprint arXiv:1712.09381 (2017).

Palmer, D. A.

D. G. Sandler, T. K. Barrett, D. A. Palmer, R. Q. Fugate, and W. J. Wild, “Use of a neural network to control an adaptive optics system for an astronomical telescope,” Nature 351, 300–302 (1991).
[Crossref]

Panneershelvam, V.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, D. Sander, G. Dominik, N. John, K. Nal, S. Ilya, L. Timothy, L. Madeleine, K. Koray, G. Thore, and H. Demis, “Mastering the game of go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Pilkington, D.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486(2007).
[Crossref]

Plötner, M.

Pöld, J. H.

Pritzel, A.

T. P. Lillicrap, J. J. Hunt, A. Pritzel, N. Heess, T. Erez, Y. Tassa, D. Silver, and D. Wierstra, “Continuous control with deep reinforcement learning,” arXiv preprint arXiv:1509.02971 (2015).

Quan, J.

T. Schaul, J. Quan, I. Antonoglou, and D. Silver, “Prioritized experience replay,” arXiv preprint arXiv:1511.05952 (2015).

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J. B. Rawlings, “Tutorial overview of model predictive control,” IEEE Control. Syst. Mag. 20, 38–52 (2000).
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V. Mnih, K. Kavukcuoglu, D. Silver, A. Graves, I. Antonoglou, D. Wierstra, and M. Riedmiller, “Playing atari with deep reinforcement learning,” arXiv preprint arXiv:1312.5602 (2013).

Sanchez, A.

Sanchez, A. D.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486(2007).
[Crossref]

Sander, D.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, D. Sander, G. Dominik, N. John, K. Nal, S. Ilya, L. Timothy, L. Madeleine, K. Koray, G. Thore, and H. Demis, “Mastering the game of go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Sandler, D. G.

D. G. Sandler, T. K. Barrett, D. A. Palmer, R. Q. Fugate, and W. J. Wild, “Use of a neural network to control an adaptive optics system for an astronomical telescope,” Nature 351, 300–302 (1991).
[Crossref]

Schaul, T.

T. Schaul, J. Quan, I. Antonoglou, and D. Silver, “Prioritized experience replay,” arXiv preprint arXiv:1511.05952 (2015).

Schön, T. B.

N. Wahlström, T. B. Schön, and M. P. Deisenroth, “From pixels to torques: Policy learning with deep dynamical models,” arXiv preprint arXiv:1502.02251 (2015).

Schrittwieser, J.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, D. Sander, G. Dominik, N. John, K. Nal, S. Ilya, L. Timothy, L. Madeleine, K. Koray, G. Thore, and H. Demis, “Mastering the game of go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Schulte, J.

A. Y. Ng, A. Coates, M. Diel, V. Ganapathi, J. Schulte, B. Tse, E. Berger, and E. Liang, “Autonomous inverted helicopter flight via reinforcement learning,” in Experimental Robotics IX, (Springer, 2006), pp. 363–372.

Shay, T. M.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486(2007).
[Crossref]

Shestaev, E.

Shirakawa, A.

H. Tünnermann and A. Shirakawa, “Reinforcement learning for coherent beam combining,” in Pacific Rim Conference on Lasers and Electro-Optics (CLEO-PR), (2018). W1A.2.

H. Tünnermann and A. Shirakawa, “End-to-end reinforcement learning for coherent beam combination,” in 8th EPS-QEOD Europhoton Conference, (2018). TuP.11.

Sifre, L.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, D. Sander, G. Dominik, N. John, K. Nal, S. Ilya, L. Timothy, L. Madeleine, K. Koray, G. Thore, and H. Demis, “Mastering the game of go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Silver, D.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, D. Sander, G. Dominik, N. John, K. Nal, S. Ilya, L. Timothy, L. Madeleine, K. Koray, G. Thore, and H. Demis, “Mastering the game of go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

V. Mnih, K. Kavukcuoglu, D. Silver, A. Graves, I. Antonoglou, D. Wierstra, and M. Riedmiller, “Playing atari with deep reinforcement learning,” arXiv preprint arXiv:1312.5602 (2013).

T. P. Lillicrap, J. J. Hunt, A. Pritzel, N. Heess, T. Erez, Y. Tassa, D. Silver, and D. Wierstra, “Continuous control with deep reinforcement learning,” arXiv preprint arXiv:1509.02971 (2015).

T. Schaul, J. Quan, I. Antonoglou, and D. Silver, “Prioritized experience replay,” arXiv preprint arXiv:1511.05952 (2015).

Stark, H.

A. Klenke, M. Müller, H. Stark, M. Kienel, C. Jauregui, A. Tünnermann, and J. Limpert, “Coherent beam combination of ultrafast fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 24, 1–9 (2018).
[Crossref]

Steiner, B.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: A system for large-scale machine learning,” in 12th Symposium on Operating Systems Design and Implementation, (2016), pp. 265–283.

Stoica, I.

E. Liang, R. Liaw, P. Moritz, R. Nishihara, R. Fox, K. Goldberg, J. E. Gonzalez, M. I. Jordan, and I. Stoica, “Rllib: Abstractions for distributed reinforcement learning,” arXiv preprint arXiv:1712.09381 (2017).

Su, R.

T. Hou, Y. An, Q. Chang, P. Ma, J. Li, L. Huang, D. Zhi, J. Wu, R. Su, Y. Ma, and P. Zhou, “Deep learning-based phase control method for coherent beam combining and its application in generating orbital angular momentum beams,” arXiv preprint arXiv:1903.03983 (2019).

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R. S. Sutton and A. G. Barto, Reinforcement learning: An introduction (MIT, 2018).

Tassa, Y.

T. P. Lillicrap, J. J. Hunt, A. Pritzel, N. Heess, T. Erez, Y. Tassa, D. Silver, and D. Wierstra, “Continuous control with deep reinforcement learning,” arXiv preprint arXiv:1509.02971 (2015).

Thore, G.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, D. Sander, G. Dominik, N. John, K. Nal, S. Ilya, L. Timothy, L. Madeleine, K. Koray, G. Thore, and H. Demis, “Mastering the game of go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Timothy, L.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, D. Sander, G. Dominik, N. John, K. Nal, S. Ilya, L. Timothy, L. Madeleine, K. Koray, G. Thore, and H. Demis, “Mastering the game of go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Tse, B.

A. Y. Ng, A. Coates, M. Diel, V. Ganapathi, J. Schulte, B. Tse, E. Berger, and E. Liang, “Autonomous inverted helicopter flight via reinforcement learning,” in Experimental Robotics IX, (Springer, 2006), pp. 363–372.

Tucker, P.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: A system for large-scale machine learning,” in 12th Symposium on Operating Systems Design and Implementation, (2016), pp. 265–283.

Tünnermann, A.

A. Klenke, M. Müller, H. Stark, M. Kienel, C. Jauregui, A. Tünnermann, and J. Limpert, “Coherent beam combination of ultrafast fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 24, 1–9 (2018).
[Crossref]

M. Müller, M. Kienel, A. Klenke, T. Gottschall, E. Shestaev, M. Plötner, J. Limpert, and A. Tünnermann, “1 kW 1 mJ eight-channel ultrafast fiber laser,” Opt. Lett. 41, 3439–3442 (2016).
[Crossref]

Tünnermann, H.

H. Tünnermann, J. H. Pöld, J. Neumann, D. Kracht, B. Willke, and P. Weßels, “Beam quality and noise properties of coherently combined ytterbium doped single frequency fiber amplifiers,” Opt. Express 19, 19600–19606 (2011).
[Crossref] [PubMed]

H. Tünnermann and A. Shirakawa, “End-to-end reinforcement learning for coherent beam combination,” in 8th EPS-QEOD Europhoton Conference, (2018). TuP.11.

H. Tünnermann and A. Shirakawa, “Reinforcement learning for coherent beam combining,” in Pacific Rim Conference on Lasers and Electro-Optics (CLEO-PR), (2018). W1A.2.

Van Den Driessche, G.

D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, D. Sander, G. Dominik, N. John, K. Nal, S. Ilya, L. Timothy, L. Madeleine, K. Koray, G. Thore, and H. Demis, “Mastering the game of go with deep neural networks and tree search,” Nature 529, 484–489 (2016).
[Crossref] [PubMed]

Vasudevan, V.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: A system for large-scale machine learning,” in 12th Symposium on Operating Systems Design and Implementation, (2016), pp. 265–283.

Wahlström, N.

N. Wahlström, T. B. Schön, and M. P. Deisenroth, “From pixels to torques: Policy learning with deep dynamical models,” arXiv preprint arXiv:1502.02251 (2015).

Warden, P.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: A system for large-scale machine learning,” in 12th Symposium on Operating Systems Design and Implementation, (2016), pp. 265–283.

Weber, M. E.

Weiss, S. B.

Weßels, P.

Wicke, M.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: A system for large-scale machine learning,” in 12th Symposium on Operating Systems Design and Implementation, (2016), pp. 265–283.

Wierstra, D.

V. Mnih, K. Kavukcuoglu, D. Silver, A. Graves, I. Antonoglou, D. Wierstra, and M. Riedmiller, “Playing atari with deep reinforcement learning,” arXiv preprint arXiv:1312.5602 (2013).

T. P. Lillicrap, J. J. Hunt, A. Pritzel, N. Heess, T. Erez, Y. Tassa, D. Silver, and D. Wierstra, “Continuous control with deep reinforcement learning,” arXiv preprint arXiv:1509.02971 (2015).

Wild, W. J.

D. G. Sandler, T. K. Barrett, D. A. Palmer, R. Q. Fugate, and W. J. Wild, “Use of a neural network to control an adaptive optics system for an astronomical telescope,” Nature 351, 300–302 (1991).
[Crossref]

Willke, B.

Wu, J.

T. Hou, Y. An, Q. Chang, P. Ma, J. Li, L. Huang, D. Zhi, J. Wu, R. Su, Y. Ma, and P. Zhou, “Deep learning-based phase control method for coherent beam combining and its application in generating orbital angular momentum beams,” arXiv preprint arXiv:1903.03983 (2019).

Yu, Y.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: A system for large-scale machine learning,” in 12th Symposium on Operating Systems Design and Implementation, (2016), pp. 265–283.

Zheng, X.

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard, M. Kudlur, J. Levenberg, R. Monga, S. Moore, D. G. Murray, B. Steiner, P. Tucker, V. Vasudevan, P. Warden, M. Wicke, Y. Yu, and X. Zheng, “Tensorflow: A system for large-scale machine learning,” in 12th Symposium on Operating Systems Design and Implementation, (2016), pp. 265–283.

Zhi, D.

T. Hou, Y. An, Q. Chang, P. Ma, J. Li, L. Huang, D. Zhi, J. Wu, R. Su, Y. Ma, and P. Zhou, “Deep learning-based phase control method for coherent beam combining and its application in generating orbital angular momentum beams,” arXiv preprint arXiv:1903.03983 (2019).

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Figures (7)

Fig. 1
Fig. 1 Setup of the combining system.
Fig. 2
Fig. 2 (a) Training of the RL agent: Average Power and power noise in dependence of training episode. (b) Lock using the trained neural network after training.
Fig. 3
Fig. 3 Comparison of the residual phase noise between PID and NN based CBC. The baseline is the detection noise with just one laser running.
Fig. 4
Fig. 4 Free running phase noise of the setup.
Fig. 5
Fig. 5 Standard deviation of the relative phase assuming random walk noise (last known value) and deep neural network.
Fig. 6
Fig. 6 Simulation of a CBC system with strong oscillation at 1000 Hz. (a) Stabilization using PID and NN Controller in time domain. (b) Power spectral density of the phase noise.
Fig. 7
Fig. 7 Multichannel CBC using a DDPG trained Neural Network and a SPGD algorithm as optimizers. (a) Convergence during training. (b) Power noise relative to the maximum combined power with NN, SPGD and no stabilization.