AdS/CFT Correspondence with Machine Learning

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姓名

黃建隆(Chien-Lung Huang) 查詢紙本館藏

畢業系所

物理學系

論文名稱

(AdS/CFT Correspondence with Machine Learning)

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摘要(中)

在2018年的時候，Koji Hashimoto教授發表了一篇期刊[1]，在期刊中他們用深度神經網絡(DNN)的結構來建構一個模型與AdS/CFT對偶性質做連結。在這篇論文中我們將以重建他們的模型為出發點，並討論在原模型下產生的諸多問題；接著在第三章節中，為了解決這些問題我們嘗試利用其他機械學習的模型來建構新的學習架構，在這個架構下我們期望能擺脫使用負面資料(negative data；因為我們發現這些資料並不能在實際面上被使用)，因此使用強化學習(RL)的方式並以其他近似函數來作配合(深度神經網絡(DNN)、神經微分方程(Neural ODE)、或其他近似函數)。然而從一直以來的結果中我們發現:在這個問題框架下會有複數對應解的問題，也因此我們在後記中在不同的兩個層面上討論對未來發展上的改進。

摘要(英)

In 2018 [1], Koji Hashimoto had presented a deep-neural-like model to connect with AdS/CFT correspondence. We tried to reconstruct his model, and found some problems about uncertainty. Therefore, we attempted to use other learning models to solve these problems. The alternate models consist of using the concepts from reinforcement learning, Neural ODE, and Deep Neural Network. For our goal, we expect to keep from using the negative data in learning because the acquisition will come across problems in experimental. However, the result shows that the problem is actually about the uniqueness of solution, and we provide further discussion and improvement.

關鍵字(中)

★ 反德西特/共形場論對偶
★ 機器學習
★ 強化學習

關鍵字(英)

★ AdS/CFT Correspondence
★ Machine Learning
★ Reinforcement Learning

論文目次

1 Introduction 1
1.1 AdS/CFT correspondence . . . . . . . . . . . . . .2
1.2 Anti-de Sitter space and Conformal Theory . . . . 2
1.3 Machine Learning . . . . . . . . . . . . . . . . .4
2 First step from AdS/CFT to Neural Network 5
2.1 Bulk Metric . . . . . . . . . . . . . . . . . . . 6
2.2 Equation of Motion . . . . . . . . . . . . . . . .6
2.3 Boundary condition . . . . . . . . . . . . . . . .7
2.4 Data and Results . . . . . . . . . . . . . . . . .8
2.5 Problems and Discussion . . . . . . . . . . . . .10
3 Reinforcement learning model 12
3.1 Markov Decision Process . . . . . . . . . . . . .12
3.2 Function Approximation . . . . . . . . . . . . . 15
3.3 Algorithm . . . . . . . . . . . . . . . . . . . .17
3.4 Result and Discussion . . . . . . . . . . . . . .17
4 Epilogue: Improvements 20
5 Conclusion 22

參考文獻

[1] Koji Hashimoto, Sotaro Sugishita, Akinori Tanaka, and Akio Tomiya. Deep learning and the AdS/CFT
correspondence. Phys. Rev. D, 98:046019, Aug 2018.
[2] Juan Maldacena. International Journal of Theoretical Physics, 38(4):1113:1133, 1999.
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[11] Vincent Francois-Lavet, Peter Henderson, Riashat Islam, Marc G. Bellemare, and Joelle Pineau. An
introduction to deep reinforcement learning. CoRR, abs/1811.12560, 2018.
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Alex Graves, Martin Riedmiller, Andreas K. Fidjeland, Georg Ostrovski, Stig Petersen, Charles Beattie,
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decision processes with neural odes. CoRR, abs/2006.16210, 2020.
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equations. CoRR, abs/1806.07366, 2018.
[15] Patrick Kidger, James Morrill, James Foster, and Terry Lyons. Neural controlled dierential equations for
irregular time series, 2020.
[16] Koji Hashimoto. Ads/cft correspondence as a deep boltzmann machine. Physical Review D, 99(10), May
2019.
[17] Tetsuya Akutagawa, Koji Hashimoto, and Takayuki Sumimoto. Deep learning and ads/qcd. Physical
Review D, 102(2), Jul 2020.
[18] Koji Hashimoto, Hong-Ye Hu, and Yi-Zhuang You. Neural ode and holographic qcd, 2020.

指導教授

陳江梅(Chiang-Mei Chen)

審核日期

2021-7-27

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