Abstract

In this work, we demonstrate the efficacy of neural networks in the characterization of dispersive media. We also develop a neural network to make predictions for input probe pulses that propagate through a nonlinear dispersive medium, which may be applied to predicting optimal pulse shapes for a desired output. The setup requires only a single pulse for the probe, providing considerable simplification of the current method of dispersion characterization that requires frequency scanning across the entirety of the gain and absorption features. We show that the trained networks are able to predict pulse profiles as well as dispersive features that are nearly identical to their experimental counterparts. We anticipate that the use of machine learning in conjunction with optical communication and sensing methods, both classical and quantum, can provide signal enhancement and experimental simplifications even in the face of highly complex, layered non-linear light-matter interactions.

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

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References

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2019 (6)

W. Diao, C. Cai, W. Yang, X. Song, and C. Duan, “Theoretical Aspects of Continuous Variables Quantum Teleportation Based on Phase-Sensitive Four-Wave Mixing,” Int. J. Theor. Phys. 58(1), 323–331 (2019).
[Crossref]

A. Karpatne, I. Ebert-Uphoff, S. Ravela, H. A. Babaie, and V. Kumar, “Machine Learning for the Geosciences: Challenges and Opportunities,” IEEE Trans. Knowl. Data Eng. 31(8), 1544–1554 (2019).
[Crossref]

W. Huang, Y. Mao, C. Xie, and D. Huang, “Quantum hacking of free-space continuous-variable quantum key distribution by using a machine-learning technique,” Phys. Rev. A 100(1), 012316 (2019).
[Crossref]

G. R. Steinbrecher, J. P. Olson, D. Englund, and J. Carolan, “Quantum optical neural networks,” npj Quantum Inf. 5(1), 60 (2019).
[Crossref]

T. Tanimura, T. Hoshida, T. Kato, S. Watanabe, and H. Morikawa, “Convolutional Neural Network-Based Optical Performance Monitoring for Optical Transport Networks,” J. Opt. Commun. Netw. 11(1), A52–A59 (2019).
[Crossref]

Y. Ismail, I. Sinayskiy, and F. Petruccione, “Integrating machine learning techniques in quantum communication to characterize the quantum channel,” J. Opt. Soc. Am. B 36(3), B116–B121 (2019).
[Crossref]

2018 (11)

S. Lohani, E. M. Knutson, M. O’Donnell, S. D. Huver, and R. T. Glasser, “On the use of deep neural networks in optical communications,” Appl. Opt. 57(15), 4180–4190 (2018).
[Crossref]

T. Zahavy, A. Dikopoltsev, D. Moss, G. I. Haham, O. Cohen, S. Mannor, and M. Segev, “Deep learning reconstruction of ultrashort pulses,” Optica 5(5), 666–673 (2018).
[Crossref]

S. Lohani and R. T. Glasser, “Turbulence correction with artificial neural networks,” Opt. Lett. 43(11), 2611–2614 (2018).
[Crossref]

M. M. Lotfinejad, R. Hafezi, M. Khanali, S. S. Hosseini, M. Mehrpooya, and S. Shamshirband, “A Comparative Assessment of Predicting Daily Solar Radiation Using Bat Neural Network (BNN), Generalized Regression Neural Network (GRNN), and Neuro-Fuzzy (NF) System: A Case Study,” Energies 11(5), 1188 (2018).
[Crossref]

H. Ye, Q. Ren, X. Hu, T. Lin, L. Shi, G. Zhang, and X. Li, “Modeling energy-related CO2 emissions from office buildings using general regression neural network,” Resour. Conserv. Recycl. 129, 168–174 (2018).
[Crossref]

B. Rahmani, D. Loterie, G. Konstantinou, D. Psaltis, and C. Moser, “Multimode optical fiber transmission with a deep learning network,” Light: Sci. Appl. 7(1), 69 (2018).
[Crossref]

K. T. Butler, D. W. Davies, H. Cartwright, O. Isayev, and A. Walsh, “Machine learning for molecular and materials science,” Nature 559(7715), 547–555 (2018).
[Crossref]

M.-A. T. Vu, T. Adalı, D. Ba, G. Buzsáki, D. Carlson, K. Heller, C. Liston, C. Rudin, V. S. Sohal, A. S. Widge, H. S. Mayberg, G. Sapiro, and K. Dzirasa, “A Shared Vision for Machine Learning in Neuroscience,” J. Neurosci. 38(7), 1601–1607 (2018).
[Crossref]

A. D. Tranter, H. J. Slatyer, M. R. Hush, A. C. Leung, J. L. Everett, K. V. Paul, P. Vernaz-Gris, P. K. Lam, B. C. Buchler, and G. T. Campbell, “Multiparameter optimisation of a magneto-optical trap using deep learning,” Nat. Commun. 9(1), 4360 (2018).
[Crossref]

S. Liu, H. Wang, and J. Jing, “Two-beam pumped cascaded four-wave-mixing process for producing multiple-beam quantum correlation,” Phys. Rev. A 97(4), 043846 (2018).
[Crossref]

E. M. Knutson, J. D. Swaim, S. Wyllie, and R. T. Glasser, “Optimal mode configuration for multiple phase-matched four-wave-mixing processes,” Phys. Rev. A 98(1), 013828 (2018).
[Crossref]

2017 (7)

H. Wang, C. Fabre, and J. Jing, “Single-step fabrication of scalable multimode quantum resources using four-wave mixing with a spatially structured pump,” Phys. Rev. A 95(5), 051802 (2017).
[Crossref]

C. Hegde and K. E. Gray, “Use of machine learning and data analytics to increase drilling efficiency for nearby wells,” J. Nat. Gas Sci. Eng. 40, 327–335 (2017).
[Crossref]

L. K. Tan, Y. M. Liew, E. Lim, and R. A. McLaughlin, “Convolutional neural network regression for short-axis left ventricle segmentation in cardiac cine MR sequences,” Med. Image Anal. 39, 78–86 (2017).
[Crossref]

L. Cao, J. Du, J. Feng, Z. Qin, A. M. Marino, M. I. Kolobov, and J. Jing, “Experimental observation of quantum correlations in four-wave mixing with a conical pump,” Opt. Lett. 42(7), 1201–1204 (2017).
[Crossref]

T. Doster and A. T. Watnik, “Machine learning approach to OAM beam demultiplexing via convolutional neural networks,” Appl. Opt. 56(12), 3386–3396 (2017).
[Crossref]

L. Wang, S. Lv, and J. Jing, “Quantum steering in cascaded four-wave mixing processes,” Opt. Express 25(15), 17457 (2017).
[Crossref]

J. Shi, G. Patera, M. I. Kolobov, and S. Han, “Quantum temporal imaging by four-wave mixing,” Opt. Lett. 42(16), 3121–3124 (2017).
[Crossref]

2016 (1)

O. Danaci, C. Rios, and R. T. Glasser, “All-optical mode conversion via spatially multimode four-wave mixing,” New J. Phys. 18(7), 073032 (2016).
[Crossref]

2015 (4)

Y. Cai, J. Feng, H. Wang, G. Ferrini, X. Xu, J. Jing, and N. Treps, “Quantum-network generation based on four-wave mixing,” Phys. Rev. A 91(1), 013843 (2015).
[Crossref]

Z. Qin, L. Cao, and J. Jing, “Experimental characterization of quantum correlated triple beams generated by cascaded four-wave mixing processes,” Appl. Phys. Lett. 106(21), 211104 (2015).
[Crossref]

R. C. Deo, “Machine Learning in Medicine,” Circulation 132(20), 1920–1930 (2015).
[Crossref]

Y. Xu, J. Du, L. Dai, and C. Lee, “A Regression Approach to Speech Enhancement Based on Deep Neural Networks,” IEEE/ACM Trans. Audio Speech Lang. Process. 23(1), 7–19 (2015).
[Crossref]

2014 (2)

Z. Qin, L. Cao, H. Wang, A. M. Marino, W. Zhang, and J. Jing, “Experimental Generation of Multiple Quantum Correlated Beams from Hot Rubidium Vapor,” Phys. Rev. Lett. 113(2), 023602 (2014).
[Crossref]

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5(1), 3049 (2014).
[Crossref]

2012 (1)

A. MacRae, T. Brannan, R. Achal, and A. I. Lvovsky, “Tomography of a High-Purity Narrowband Photon from a Transient Atomic Collective Excitation,” Phys. Rev. Lett. 109(3), 033601 (2012).
[Crossref]

2011 (1)

2009 (1)

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009).
[Crossref]

2008 (1)

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled Images from Four-Wave Mixing,” Science 321(5888), 544–547 (2008).
[Crossref]

2007 (1)

Abadi, M.

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). Software available from tensorflow.org.

Achal, R.

A. MacRae, T. Brannan, R. Achal, and A. I. Lvovsky, “Tomography of a High-Purity Narrowband Photon from a Transient Atomic Collective Excitation,” Phys. Rev. Lett. 109(3), 033601 (2012).
[Crossref]

Adali, T.

M.-A. T. Vu, T. Adalı, D. Ba, G. Buzsáki, D. Carlson, K. Heller, C. Liston, C. Rudin, V. S. Sohal, A. S. Widge, H. S. Mayberg, G. Sapiro, and K. Dzirasa, “A Shared Vision for Machine Learning in Neuroscience,” J. Neurosci. 38(7), 1601–1607 (2018).
[Crossref]

Agarwal, A.

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). Software available from tensorflow.org.

Arimondo, E.

Ba, D.

M.-A. T. Vu, T. Adalı, D. Ba, G. Buzsáki, D. Carlson, K. Heller, C. Liston, C. Rudin, V. S. Sohal, A. S. Widge, H. S. Mayberg, G. Sapiro, and K. Dzirasa, “A Shared Vision for Machine Learning in Neuroscience,” J. Neurosci. 38(7), 1601–1607 (2018).
[Crossref]

Babaie, H. A.

A. Karpatne, I. Ebert-Uphoff, S. Ravela, H. A. Babaie, and V. Kumar, “Machine Learning for the Geosciences: Challenges and Opportunities,” IEEE Trans. Knowl. Data Eng. 31(8), 1544–1554 (2019).
[Crossref]

Barham, P.

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). Software available from tensorflow.org.

Boyer, V.

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled Images from Four-Wave Mixing,” Science 321(5888), 544–547 (2008).
[Crossref]

C. F. McCormick, V. Boyer, E. Arimondo, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32(2), 178–180 (2007).
[Crossref]

Brannan, T.

A. MacRae, T. Brannan, R. Achal, and A. I. Lvovsky, “Tomography of a High-Purity Narrowband Photon from a Transient Atomic Collective Excitation,” Phys. Rev. Lett. 109(3), 033601 (2012).
[Crossref]

Brevdo, E.

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). Software available from tensorflow.org.

Buchler, B. C.

A. D. Tranter, H. J. Slatyer, M. R. Hush, A. C. Leung, J. L. Everett, K. V. Paul, P. Vernaz-Gris, P. K. Lam, B. C. Buchler, and G. T. Campbell, “Multiparameter optimisation of a magneto-optical trap using deep learning,” Nat. Commun. 9(1), 4360 (2018).
[Crossref]

Butler, K. T.

K. T. Butler, D. W. Davies, H. Cartwright, O. Isayev, and A. Walsh, “Machine learning for molecular and materials science,” Nature 559(7715), 547–555 (2018).
[Crossref]

Buzsáki, G.

M.-A. T. Vu, T. Adalı, D. Ba, G. Buzsáki, D. Carlson, K. Heller, C. Liston, C. Rudin, V. S. Sohal, A. S. Widge, H. S. Mayberg, G. Sapiro, and K. Dzirasa, “A Shared Vision for Machine Learning in Neuroscience,” J. Neurosci. 38(7), 1601–1607 (2018).
[Crossref]

Cai, C.

W. Diao, C. Cai, W. Yang, X. Song, and C. Duan, “Theoretical Aspects of Continuous Variables Quantum Teleportation Based on Phase-Sensitive Four-Wave Mixing,” Int. J. Theor. Phys. 58(1), 323–331 (2019).
[Crossref]

Cai, Y.

Y. Cai, J. Feng, H. Wang, G. Ferrini, X. Xu, J. Jing, and N. Treps, “Quantum-network generation based on four-wave mixing,” Phys. Rev. A 91(1), 013843 (2015).
[Crossref]

Camacho, R. M.

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009).
[Crossref]

Campbell, G. T.

A. D. Tranter, H. J. Slatyer, M. R. Hush, A. C. Leung, J. L. Everett, K. V. Paul, P. Vernaz-Gris, P. K. Lam, B. C. Buchler, and G. T. Campbell, “Multiparameter optimisation of a magneto-optical trap using deep learning,” Nat. Commun. 9(1), 4360 (2018).
[Crossref]

Cao, L.

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Z. Qin, L. Cao, and J. Jing, “Experimental characterization of quantum correlated triple beams generated by cascaded four-wave mixing processes,” Appl. Phys. Lett. 106(21), 211104 (2015).
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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). Software available from tensorflow.org.

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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). Software available from tensorflow.org.

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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). Software available from tensorflow.org.

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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). Software available from tensorflow.org.

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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). Software available from tensorflow.org.

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L. Cao, J. Du, J. Feng, Z. Qin, A. M. Marino, M. I. Kolobov, and J. Jing, “Experimental observation of quantum correlations in four-wave mixing with a conical pump,” Opt. Lett. 42(7), 1201–1204 (2017).
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Y. Xu, J. Du, L. Dai, and C. Lee, “A Regression Approach to Speech Enhancement Based on Deep Neural Networks,” IEEE/ACM Trans. Audio Speech Lang. Process. 23(1), 7–19 (2015).
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Duan, C.

W. Diao, C. Cai, W. Yang, X. Song, and C. Duan, “Theoretical Aspects of Continuous Variables Quantum Teleportation Based on Phase-Sensitive Four-Wave Mixing,” Int. J. Theor. Phys. 58(1), 323–331 (2019).
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M.-A. T. Vu, T. Adalı, D. Ba, G. Buzsáki, D. Carlson, K. Heller, C. Liston, C. Rudin, V. S. Sohal, A. S. Widge, H. S. Mayberg, G. Sapiro, and K. Dzirasa, “A Shared Vision for Machine Learning in Neuroscience,” J. Neurosci. 38(7), 1601–1607 (2018).
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A. Karpatne, I. Ebert-Uphoff, S. Ravela, H. A. Babaie, and V. Kumar, “Machine Learning for the Geosciences: Challenges and Opportunities,” IEEE Trans. Knowl. Data Eng. 31(8), 1544–1554 (2019).
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G. R. Steinbrecher, J. P. Olson, D. Englund, and J. Carolan, “Quantum optical neural networks,” npj Quantum Inf. 5(1), 60 (2019).
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A. D. Tranter, H. J. Slatyer, M. R. Hush, A. C. Leung, J. L. Everett, K. V. Paul, P. Vernaz-Gris, P. K. Lam, B. C. Buchler, and G. T. Campbell, “Multiparameter optimisation of a magneto-optical trap using deep learning,” Nat. Commun. 9(1), 4360 (2018).
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H. Wang, C. Fabre, and J. Jing, “Single-step fabrication of scalable multimode quantum resources using four-wave mixing with a spatially structured pump,” Phys. Rev. A 95(5), 051802 (2017).
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L. Cao, J. Du, J. Feng, Z. Qin, A. M. Marino, M. I. Kolobov, and J. Jing, “Experimental observation of quantum correlations in four-wave mixing with a conical pump,” Opt. Lett. 42(7), 1201–1204 (2017).
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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). Software available from tensorflow.org.

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S. Lohani, E. M. Knutson, M. O’Donnell, S. D. Huver, and R. T. Glasser, “On the use of deep neural networks in optical communications,” Appl. Opt. 57(15), 4180–4190 (2018).
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S. Lohani and R. T. Glasser, “Turbulence correction with artificial neural networks,” Opt. Lett. 43(11), 2611–2614 (2018).
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E. M. Knutson, J. D. Swaim, S. Wyllie, and R. T. Glasser, “Optimal mode configuration for multiple phase-matched four-wave-mixing processes,” Phys. Rev. A 98(1), 013828 (2018).
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O. Danaci, C. Rios, and R. T. Glasser, “All-optical mode conversion via spatially multimode four-wave mixing,” New J. Phys. 18(7), 073032 (2016).
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J. D. Swaim, E. M. Knutson, O. Danaci, and R. T. Glasser, “Multi-mode four-wave mixing with a spatially-structured pump,” arXiv:1802.03412 [physics, physics:quant-ph] (2018).

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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). Software available from tensorflow.org.

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Han, S.

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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). Software available from tensorflow.org.

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C. Hegde and K. E. Gray, “Use of machine learning and data analytics to increase drilling efficiency for nearby wells,” J. Nat. Gas Sci. Eng. 40, 327–335 (2017).
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M.-A. T. Vu, T. Adalı, D. Ba, G. Buzsáki, D. Carlson, K. Heller, C. Liston, C. Rudin, V. S. Sohal, A. S. Widge, H. S. Mayberg, G. Sapiro, and K. Dzirasa, “A Shared Vision for Machine Learning in Neuroscience,” J. Neurosci. 38(7), 1601–1607 (2018).
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W. Huang, Y. Mao, C. Xie, and D. Huang, “Quantum hacking of free-space continuous-variable quantum key distribution by using a machine-learning technique,” Phys. Rev. A 100(1), 012316 (2019).
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F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5(1), 3049 (2014).
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Hush, M. R.

A. D. Tranter, H. J. Slatyer, M. R. Hush, A. C. Leung, J. L. Everett, K. V. Paul, P. Vernaz-Gris, P. K. Lam, B. C. Buchler, and G. T. Campbell, “Multiparameter optimisation of a magneto-optical trap using deep learning,” Nat. Commun. 9(1), 4360 (2018).
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Huver, S. D.

Irving, G.

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). Software available from tensorflow.org.

Isard, M.

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). Software available from tensorflow.org.

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K. T. Butler, D. W. Davies, H. Cartwright, O. Isayev, and A. Walsh, “Machine learning for molecular and materials science,” Nature 559(7715), 547–555 (2018).
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Jia, Y.

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). Software available from tensorflow.org.

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L. Cao, J. Du, J. Feng, Z. Qin, A. M. Marino, M. I. Kolobov, and J. Jing, “Experimental observation of quantum correlations in four-wave mixing with a conical pump,” Opt. Lett. 42(7), 1201–1204 (2017).
[Crossref]

H. Wang, C. Fabre, and J. Jing, “Single-step fabrication of scalable multimode quantum resources using four-wave mixing with a spatially structured pump,” Phys. Rev. A 95(5), 051802 (2017).
[Crossref]

Y. Cai, J. Feng, H. Wang, G. Ferrini, X. Xu, J. Jing, and N. Treps, “Quantum-network generation based on four-wave mixing,” Phys. Rev. A 91(1), 013843 (2015).
[Crossref]

Z. Qin, L. Cao, and J. Jing, “Experimental characterization of quantum correlated triple beams generated by cascaded four-wave mixing processes,” Appl. Phys. Lett. 106(21), 211104 (2015).
[Crossref]

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5(1), 3049 (2014).
[Crossref]

Z. Qin, L. Cao, H. Wang, A. M. Marino, W. Zhang, and J. Jing, “Experimental Generation of Multiple Quantum Correlated Beams from Hot Rubidium Vapor,” Phys. Rev. Lett. 113(2), 023602 (2014).
[Crossref]

Jones, K. M.

Jozefowicz, R.

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). Software available from tensorflow.org.

Kaiser, L.

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). Software available from tensorflow.org.

Karpatne, A.

A. Karpatne, I. Ebert-Uphoff, S. Ravela, H. A. Babaie, and V. Kumar, “Machine Learning for the Geosciences: Challenges and Opportunities,” IEEE Trans. Knowl. Data Eng. 31(8), 1544–1554 (2019).
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Kato, T.

Khanali, M.

M. M. Lotfinejad, R. Hafezi, M. Khanali, S. S. Hosseini, M. Mehrpooya, and S. Shamshirband, “A Comparative Assessment of Predicting Daily Solar Radiation Using Bat Neural Network (BNN), Generalized Regression Neural Network (GRNN), and Neuro-Fuzzy (NF) System: A Case Study,” Energies 11(5), 1188 (2018).
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Knutson, E. M.

E. M. Knutson, J. D. Swaim, S. Wyllie, and R. T. Glasser, “Optimal mode configuration for multiple phase-matched four-wave-mixing processes,” Phys. Rev. A 98(1), 013828 (2018).
[Crossref]

S. Lohani, E. M. Knutson, M. O’Donnell, S. D. Huver, and R. T. Glasser, “On the use of deep neural networks in optical communications,” Appl. Opt. 57(15), 4180–4190 (2018).
[Crossref]

J. D. Swaim, E. M. Knutson, O. Danaci, and R. T. Glasser, “Multi-mode four-wave mixing with a spatially-structured pump,” arXiv:1802.03412 [physics, physics:quant-ph] (2018).

Kolobov, M. I.

Kong, J.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5(1), 3049 (2014).
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Kudlur, M.

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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). Software available from tensorflow.org.

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H. Ye, Q. Ren, X. Hu, T. Lin, L. Shi, G. Zhang, and X. Li, “Modeling energy-related CO2 emissions from office buildings using general regression neural network,” Resour. Conserv. Recycl. 129, 168–174 (2018).
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L. K. Tan, Y. M. Liew, E. Lim, and R. A. McLaughlin, “Convolutional neural network regression for short-axis left ventricle segmentation in cardiac cine MR sequences,” Med. Image Anal. 39, 78–86 (2017).
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H. Ye, Q. Ren, X. Hu, T. Lin, L. Shi, G. Zhang, and X. Li, “Modeling energy-related CO2 emissions from office buildings using general regression neural network,” Resour. Conserv. Recycl. 129, 168–174 (2018).
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B. Rahmani, D. Loterie, G. Konstantinou, D. Psaltis, and C. Moser, “Multimode optical fiber transmission with a deep learning network,” Light: Sci. Appl. 7(1), 69 (2018).
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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). Software available from tensorflow.org.

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M.-A. T. Vu, T. Adalı, D. Ba, G. Buzsáki, D. Carlson, K. Heller, C. Liston, C. Rudin, V. S. Sohal, A. S. Widge, H. S. Mayberg, G. Sapiro, and K. Dzirasa, “A Shared Vision for Machine Learning in Neuroscience,” J. Neurosci. 38(7), 1601–1607 (2018).
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L. K. Tan, Y. M. Liew, E. Lim, and R. A. McLaughlin, “Convolutional neural network regression for short-axis left ventricle segmentation in cardiac cine MR sequences,” Med. Image Anal. 39, 78–86 (2017).
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M. M. Lotfinejad, R. Hafezi, M. Khanali, S. S. Hosseini, M. Mehrpooya, and S. Shamshirband, “A Comparative Assessment of Predicting Daily Solar Radiation Using Bat Neural Network (BNN), Generalized Regression Neural Network (GRNN), and Neuro-Fuzzy (NF) System: A Case Study,” Energies 11(5), 1188 (2018).
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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). Software available from tensorflow.org.

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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). Software available from tensorflow.org.

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B. Rahmani, D. Loterie, G. Konstantinou, D. Psaltis, and C. Moser, “Multimode optical fiber transmission with a deep learning network,” Light: Sci. Appl. 7(1), 69 (2018).
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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). Software available from tensorflow.org.

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J. Lv, Z. Na, X. Liu, and Z. Deng, “Machine Learning and Its Applications in Wireless Communications,” in Communications, Signal Processing, and Systems, Q. Liang, J. Mu, M. Jia, W. Wang, X. Feng, and B. Zhang, eds. (Springer, Singapore, 2019), Lecture Notes in Electrical Engineering, pp. 2429–2436.

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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). Software available from tensorflow.org.

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G. R. Steinbrecher, J. P. Olson, D. Englund, and J. Carolan, “Quantum optical neural networks,” npj Quantum Inf. 5(1), 60 (2019).
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F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5(1), 3049 (2014).
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Paul, K. V.

A. D. Tranter, H. J. Slatyer, M. R. Hush, A. C. Leung, J. L. Everett, K. V. Paul, P. Vernaz-Gris, P. K. Lam, B. C. Buchler, and G. T. Campbell, “Multiparameter optimisation of a magneto-optical trap using deep learning,” Nat. Commun. 9(1), 4360 (2018).
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Pooser, R. C.

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled Images from Four-Wave Mixing,” Science 321(5888), 544–547 (2008).
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B. Rahmani, D. Loterie, G. Konstantinou, D. Psaltis, and C. Moser, “Multimode optical fiber transmission with a deep learning network,” Light: Sci. Appl. 7(1), 69 (2018).
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L. Cao, J. Du, J. Feng, Z. Qin, A. M. Marino, M. I. Kolobov, and J. Jing, “Experimental observation of quantum correlations in four-wave mixing with a conical pump,” Opt. Lett. 42(7), 1201–1204 (2017).
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Z. Qin, L. Cao, and J. Jing, “Experimental characterization of quantum correlated triple beams generated by cascaded four-wave mixing processes,” Appl. Phys. Lett. 106(21), 211104 (2015).
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Z. Qin, L. Cao, H. Wang, A. M. Marino, W. Zhang, and J. Jing, “Experimental Generation of Multiple Quantum Correlated Beams from Hot Rubidium Vapor,” Phys. Rev. Lett. 113(2), 023602 (2014).
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B. Rahmani, D. Loterie, G. Konstantinou, D. Psaltis, and C. Moser, “Multimode optical fiber transmission with a deep learning network,” Light: Sci. Appl. 7(1), 69 (2018).
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A. Karpatne, I. Ebert-Uphoff, S. Ravela, H. A. Babaie, and V. Kumar, “Machine Learning for the Geosciences: Challenges and Opportunities,” IEEE Trans. Knowl. Data Eng. 31(8), 1544–1554 (2019).
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H. Ye, Q. Ren, X. Hu, T. Lin, L. Shi, G. Zhang, and X. Li, “Modeling energy-related CO2 emissions from office buildings using general regression neural network,” Resour. Conserv. Recycl. 129, 168–174 (2018).
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M.-A. T. Vu, T. Adalı, D. Ba, G. Buzsáki, D. Carlson, K. Heller, C. Liston, C. Rudin, V. S. Sohal, A. S. Widge, H. S. Mayberg, G. Sapiro, and K. Dzirasa, “A Shared Vision for Machine Learning in Neuroscience,” J. Neurosci. 38(7), 1601–1607 (2018).
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M.-A. T. Vu, T. Adalı, D. Ba, G. Buzsáki, D. Carlson, K. Heller, C. Liston, C. Rudin, V. S. Sohal, A. S. Widge, H. S. Mayberg, G. Sapiro, and K. Dzirasa, “A Shared Vision for Machine Learning in Neuroscience,” J. Neurosci. 38(7), 1601–1607 (2018).
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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). Software available from tensorflow.org.

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Shamshirband, S.

M. M. Lotfinejad, R. Hafezi, M. Khanali, S. S. Hosseini, M. Mehrpooya, and S. Shamshirband, “A Comparative Assessment of Predicting Daily Solar Radiation Using Bat Neural Network (BNN), Generalized Regression Neural Network (GRNN), and Neuro-Fuzzy (NF) System: A Case Study,” Energies 11(5), 1188 (2018).
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Shi, L.

H. Ye, Q. Ren, X. Hu, T. Lin, L. Shi, G. Zhang, and X. Li, “Modeling energy-related CO2 emissions from office buildings using general regression neural network,” Resour. Conserv. Recycl. 129, 168–174 (2018).
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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). Software available from tensorflow.org.

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Slatyer, H. J.

A. D. Tranter, H. J. Slatyer, M. R. Hush, A. C. Leung, J. L. Everett, K. V. Paul, P. Vernaz-Gris, P. K. Lam, B. C. Buchler, and G. T. Campbell, “Multiparameter optimisation of a magneto-optical trap using deep learning,” Nat. Commun. 9(1), 4360 (2018).
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M.-A. T. Vu, T. Adalı, D. Ba, G. Buzsáki, D. Carlson, K. Heller, C. Liston, C. Rudin, V. S. Sohal, A. S. Widge, H. S. Mayberg, G. Sapiro, and K. Dzirasa, “A Shared Vision for Machine Learning in Neuroscience,” J. Neurosci. 38(7), 1601–1607 (2018).
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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). Software available from tensorflow.org.

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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). Software available from tensorflow.org.

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Talwar, K.

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). Software available from tensorflow.org.

Tan, L. K.

L. K. Tan, Y. M. Liew, E. Lim, and R. A. McLaughlin, “Convolutional neural network regression for short-axis left ventricle segmentation in cardiac cine MR sequences,” Med. Image Anal. 39, 78–86 (2017).
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A. D. Tranter, H. J. Slatyer, M. R. Hush, A. C. Leung, J. L. Everett, K. V. Paul, P. Vernaz-Gris, P. K. Lam, B. C. Buchler, and G. T. Campbell, “Multiparameter optimisation of a magneto-optical trap using deep learning,” Nat. Commun. 9(1), 4360 (2018).
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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). Software available from tensorflow.org.

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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). Software available from tensorflow.org.

Vasudevan, V.

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). Software available from tensorflow.org.

Vernaz-Gris, P.

A. D. Tranter, H. J. Slatyer, M. R. Hush, A. C. Leung, J. L. Everett, K. V. Paul, P. Vernaz-Gris, P. K. Lam, B. C. Buchler, and G. T. Campbell, “Multiparameter optimisation of a magneto-optical trap using deep learning,” Nat. Commun. 9(1), 4360 (2018).
[Crossref]

Viégas, F.

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). Software available from tensorflow.org.

Vinyals, O.

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). Software available from tensorflow.org.

Vu, M.-A. T.

M.-A. T. Vu, T. Adalı, D. Ba, G. Buzsáki, D. Carlson, K. Heller, C. Liston, C. Rudin, V. S. Sohal, A. S. Widge, H. S. Mayberg, G. Sapiro, and K. Dzirasa, “A Shared Vision for Machine Learning in Neuroscience,” J. Neurosci. 38(7), 1601–1607 (2018).
[Crossref]

Vudyasetu, P. K.

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009).
[Crossref]

Walsh, A.

K. T. Butler, D. W. Davies, H. Cartwright, O. Isayev, and A. Walsh, “Machine learning for molecular and materials science,” Nature 559(7715), 547–555 (2018).
[Crossref]

Wang, H.

S. Liu, H. Wang, and J. Jing, “Two-beam pumped cascaded four-wave-mixing process for producing multiple-beam quantum correlation,” Phys. Rev. A 97(4), 043846 (2018).
[Crossref]

H. Wang, C. Fabre, and J. Jing, “Single-step fabrication of scalable multimode quantum resources using four-wave mixing with a spatially structured pump,” Phys. Rev. A 95(5), 051802 (2017).
[Crossref]

Y. Cai, J. Feng, H. Wang, G. Ferrini, X. Xu, J. Jing, and N. Treps, “Quantum-network generation based on four-wave mixing,” Phys. Rev. A 91(1), 013843 (2015).
[Crossref]

Z. Qin, L. Cao, H. Wang, A. M. Marino, W. Zhang, and J. Jing, “Experimental Generation of Multiple Quantum Correlated Beams from Hot Rubidium Vapor,” Phys. Rev. Lett. 113(2), 023602 (2014).
[Crossref]

Wang, L.

Warden, P.

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). Software available from tensorflow.org.

Watanabe, S.

Watnik, A. T.

Wattenberg, M.

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). Software available from tensorflow.org.

Wicke, M.

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). Software available from tensorflow.org.

Widge, A. S.

M.-A. T. Vu, T. Adalı, D. Ba, G. Buzsáki, D. Carlson, K. Heller, C. Liston, C. Rudin, V. S. Sohal, A. S. Widge, H. S. Mayberg, G. Sapiro, and K. Dzirasa, “A Shared Vision for Machine Learning in Neuroscience,” J. Neurosci. 38(7), 1601–1607 (2018).
[Crossref]

Wyllie, S.

E. M. Knutson, J. D. Swaim, S. Wyllie, and R. T. Glasser, “Optimal mode configuration for multiple phase-matched four-wave-mixing processes,” Phys. Rev. A 98(1), 013828 (2018).
[Crossref]

Xie, C.

W. Huang, Y. Mao, C. Xie, and D. Huang, “Quantum hacking of free-space continuous-variable quantum key distribution by using a machine-learning technique,” Phys. Rev. A 100(1), 012316 (2019).
[Crossref]

Xu, X.

Y. Cai, J. Feng, H. Wang, G. Ferrini, X. Xu, J. Jing, and N. Treps, “Quantum-network generation based on four-wave mixing,” Phys. Rev. A 91(1), 013843 (2015).
[Crossref]

Xu, Y.

Y. Xu, J. Du, L. Dai, and C. Lee, “A Regression Approach to Speech Enhancement Based on Deep Neural Networks,” IEEE/ACM Trans. Audio Speech Lang. Process. 23(1), 7–19 (2015).
[Crossref]

Yang, W.

W. Diao, C. Cai, W. Yang, X. Song, and C. Duan, “Theoretical Aspects of Continuous Variables Quantum Teleportation Based on Phase-Sensitive Four-Wave Mixing,” Int. J. Theor. Phys. 58(1), 323–331 (2019).
[Crossref]

Ye, H.

H. Ye, Q. Ren, X. Hu, T. Lin, L. Shi, G. Zhang, and X. Li, “Modeling energy-related CO2 emissions from office buildings using general regression neural network,” Resour. Conserv. Recycl. 129, 168–174 (2018).
[Crossref]

Yu, Y.

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). Software available from tensorflow.org.

Zahavy, T.

Zhang, G.

H. Ye, Q. Ren, X. Hu, T. Lin, L. Shi, G. Zhang, and X. Li, “Modeling energy-related CO2 emissions from office buildings using general regression neural network,” Resour. Conserv. Recycl. 129, 168–174 (2018).
[Crossref]

Zhang, W.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5(1), 3049 (2014).
[Crossref]

Z. Qin, L. Cao, H. Wang, A. M. Marino, W. Zhang, and J. Jing, “Experimental Generation of Multiple Quantum Correlated Beams from Hot Rubidium Vapor,” Phys. Rev. Lett. 113(2), 023602 (2014).
[Crossref]

Zheng, X.

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). Software available from tensorflow.org.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

Z. Qin, L. Cao, and J. Jing, “Experimental characterization of quantum correlated triple beams generated by cascaded four-wave mixing processes,” Appl. Phys. Lett. 106(21), 211104 (2015).
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R. C. Deo, “Machine Learning in Medicine,” Circulation 132(20), 1920–1930 (2015).
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M. M. Lotfinejad, R. Hafezi, M. Khanali, S. S. Hosseini, M. Mehrpooya, and S. Shamshirband, “A Comparative Assessment of Predicting Daily Solar Radiation Using Bat Neural Network (BNN), Generalized Regression Neural Network (GRNN), and Neuro-Fuzzy (NF) System: A Case Study,” Energies 11(5), 1188 (2018).
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IEEE Trans. Knowl. Data Eng. (1)

A. Karpatne, I. Ebert-Uphoff, S. Ravela, H. A. Babaie, and V. Kumar, “Machine Learning for the Geosciences: Challenges and Opportunities,” IEEE Trans. Knowl. Data Eng. 31(8), 1544–1554 (2019).
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IEEE/ACM Trans. Audio Speech Lang. Process. (1)

Y. Xu, J. Du, L. Dai, and C. Lee, “A Regression Approach to Speech Enhancement Based on Deep Neural Networks,” IEEE/ACM Trans. Audio Speech Lang. Process. 23(1), 7–19 (2015).
[Crossref]

Int. J. Theor. Phys. (1)

W. Diao, C. Cai, W. Yang, X. Song, and C. Duan, “Theoretical Aspects of Continuous Variables Quantum Teleportation Based on Phase-Sensitive Four-Wave Mixing,” Int. J. Theor. Phys. 58(1), 323–331 (2019).
[Crossref]

J. Nat. Gas Sci. Eng. (1)

C. Hegde and K. E. Gray, “Use of machine learning and data analytics to increase drilling efficiency for nearby wells,” J. Nat. Gas Sci. Eng. 40, 327–335 (2017).
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J. Neurosci. (1)

M.-A. T. Vu, T. Adalı, D. Ba, G. Buzsáki, D. Carlson, K. Heller, C. Liston, C. Rudin, V. S. Sohal, A. S. Widge, H. S. Mayberg, G. Sapiro, and K. Dzirasa, “A Shared Vision for Machine Learning in Neuroscience,” J. Neurosci. 38(7), 1601–1607 (2018).
[Crossref]

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B. Rahmani, D. Loterie, G. Konstantinou, D. Psaltis, and C. Moser, “Multimode optical fiber transmission with a deep learning network,” Light: Sci. Appl. 7(1), 69 (2018).
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Med. Image Anal. (1)

L. K. Tan, Y. M. Liew, E. Lim, and R. A. McLaughlin, “Convolutional neural network regression for short-axis left ventricle segmentation in cardiac cine MR sequences,” Med. Image Anal. 39, 78–86 (2017).
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Nat. Commun. (2)

A. D. Tranter, H. J. Slatyer, M. R. Hush, A. C. Leung, J. L. Everett, K. V. Paul, P. Vernaz-Gris, P. K. Lam, B. C. Buchler, and G. T. Campbell, “Multiparameter optimisation of a magneto-optical trap using deep learning,” Nat. Commun. 9(1), 4360 (2018).
[Crossref]

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5(1), 3049 (2014).
[Crossref]

Nat. Photonics (1)

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009).
[Crossref]

Nature (1)

K. T. Butler, D. W. Davies, H. Cartwright, O. Isayev, and A. Walsh, “Machine learning for molecular and materials science,” Nature 559(7715), 547–555 (2018).
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Y. Cai, J. Feng, H. Wang, G. Ferrini, X. Xu, J. Jing, and N. Treps, “Quantum-network generation based on four-wave mixing,” Phys. Rev. A 91(1), 013843 (2015).
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H. Wang, C. Fabre, and J. Jing, “Single-step fabrication of scalable multimode quantum resources using four-wave mixing with a spatially structured pump,” Phys. Rev. A 95(5), 051802 (2017).
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S. Liu, H. Wang, and J. Jing, “Two-beam pumped cascaded four-wave-mixing process for producing multiple-beam quantum correlation,” Phys. Rev. A 97(4), 043846 (2018).
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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). Software available from tensorflow.org.

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Figures (5)

Fig. 1.
Fig. 1. (a.) Experimental setup for detecting reference (input) pulses. A Ti:Sapphire laser is locked to a wavelength of approximately 795 nm and passed through a $\lambda /2$ waveplate (WP) then split on a polarizing beam splitter (PBS). A portion of the light is passed through an acoustic-optical modulator (AOM), which is modulated with various pulses and waveforms (inset a-I) from an arbitrary waveform generator. The intensity-modulated and frequency-shifted light (orange) then bypasses a flip mirror (FM) and is incident on a detector (PDA), resulting in the reference probe pulses (a-II). (b.) Experimental setup for detecting gain lines and output probe pulses. The AOM is either scanned in frequency over $\sim$100 MHz (b-I) or pulsed as before (b-II), resulting in a gain line (b-III) or output probe pulses (b-IV) respectively. An energy level diagram for the FWM process is shown in inset b-V.
Fig. 2.
Fig. 2. Architecture of the neural network for unknown probe prediction using gain and desired outputs as the two channel input, or outputs only (without gain) as the single channel input. Here the measured output probe and dispersion profiles are used to predict the input probe pulse. As discussed in the text the scheme is easily altered to predict the dispersion profile using the input and output probe pulses as the two channel input, or the output pulses only (without input pulses) as the single channel input.
Fig. 3.
Fig. 3. (a-d) Input probe (pulse) predictions using, green: FWM output probes and gain profiles as two channels training inputs, and red: FWM output probes only (without gain) as a single channel data to train the network.
Fig. 4.
Fig. 4. Predicting the gain curve of a non-linear medium peaked approximately at a detuning of (a) 3.047 GHz, and (b) 3.071 GHz using FWM output probes and input probes as two channel training inputs (green), and FWM output probes only as single channel training inputs (red) to the network. The mean square loss at each epoch is shown in inset of (b).
Fig. 5.
Fig. 5. Gain curve predictions using the training data with a set of (a) 2, (b) 4, (c) 8, and (d) 16 pulses, respectively.