請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/73827完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳俊瑋(Jiunn-Wei Chen) | |
| dc.contributor.author | Chung-Chun Hsieh | en |
| dc.contributor.author | 謝仲鈞 | zh_TW |
| dc.date.accessioned | 2021-06-17T08:11:14Z | - |
| dc.date.available | 2021-02-22 | |
| dc.date.copyright | 2021-02-22 | |
| dc.date.issued | 2021 | |
| dc.date.submitted | 2021-02-01 | |
| dc.identifier.citation | M. S. Albergo, G. Kanwar, and P. E. Shanahan. Flowbased generative models for Markov chain Monte Carlo in lattice field theory. Phys.Rev.D, 100:034515, Aug 2019. A. Alexandru, G. m. c. Başar, P. F. Bedaque, and N. C. Warrington. Tempered transitions between thimbles.Phys.Rev.D, 96:034513, Aug 2017. B. Apolloni, C. Carvalho, and D. de Falco. Quantum stochastic optimization. Stochastic Processes and their Applications, 33(2):233 – 244, 1989. J.D. Benamou and Y. Brenier. A computational fluid mechanics solution to the Monge Kantorovich mass transfer problem. Numerische Mathematik, 84:375–393,2000. C. M. Bishop. Pattern Recognition and Machine Learning (Information Scienceand Statistics). Springer Verlag, Berlin, Heidelberg, 2006. D. Boyda, G. Kanwar, S. Racanière, D. J. Rezende, M. S. Albergo, K. Cranmer, D. C. Hackett, and P. E. Shanahan. Sampling using SU(N) gauge equivariant flows, 2020. L. Dinh, J. SohlDickstein, and S. Bengio. Density estimation using real nvp, 2017.49 S.Duane, A.Kennedy, B.J.Pendleton, and D.Roweth. Hybrid Monte Carlo. Physics Letters B, 195(2):216 – 222, 1987. C. Finlay, J.H. Jacobsen, L. Nurbekyan, and A. M. Oberman. How to train your neural ode: the world of jacobian and kinetic regularization, 2020. A. Finnila, M. Gomez, C. Sebenik, C. Stenson, and J. Doll. Quantum annealing: Anew method for minimizing multidimensional functions. Chemical Physics Letters, 219(5):343 – 348, 1994. M.Fukuma, N.Matsumoto, and N.Umeda. Applying the tempered Lefschetz thimble method to the Hubbard model away from half filling. Phys.Rev.D, 100:114510, Dec2019. A. Gepperth and B. Pfülb. Gradientbased training of gaussian mixture models in high dimensional spaces, 2020. W.Grathwohl, R.T.Q.Chen, J.Bettencourt, I.Sutskever, and D.Duvenaud. Ffjord: Freeform continuous dynamics for scalable reversible generative models, 2018. W. K. Hastings. Monte Carlo sampling methods using Markov chains and their applications.Biometrika, 57(1):97–109, 1970. T. Kadowaki and H. Nishimori. Quantum annealing in the transverse Ising model. Phys.Rev.E, 58:5355–5363, Nov 1998. G.Kanwar, M.S.Albergo, D.Boyda, K.Cranmer, D.C.Hackett, S.Racanière, D.J.Rezende, and P. E. Shanahan. Equivariant flowbased sampling for lattice gauge theory. Phys.Rev.Lett., 125:121601, Sep 2020. D. P. Kingma and J. Ba. Adam: A method for stochastic optimization, 2017.50 S.Kirkpatrick, C.D.Gelatt, andM.P.Vecchi. Optimization by simulated annealing. SCIENCE, 220(4598):671–680, 1983. J. Köhler, L. Klein, and F. Noé. Equivariant flows: sampling configurations formultibody systems with symmetric energies, 2019. L. Landau. On the theory of phase transitions. Zh.Eksp.Teor.Fiz., 7:19–32, 1937. Y. Matsuda, H. Nishimori, and H. G. Katzgraber. Quantum annealing for problems with groundstate degeneracy. Journal of Physics: Conference Series, 143:012003, Jan 2009. P. Mehta, M. Bukov, C.H. Wang, A. G. Day, C. Richardson, C. K. Fisher, and D. J. Schwab. A highbias, lowvariance introduction to machine learning for physicists. Physics Reports, 810:1 – 124, 2019. A high bias, low variance introduction to Machine Learning for physicists. C. Meng, Y. Song, J. Song, and S. Ermon. Gaussianization flows, 2020. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller. Equation of state calculations by fast computing machines. The Journal of Chemical Physics, 21(6):1087–1092, 1953. R. M. Neal. Sampling from multimodal distributions using tempered transitions. Statistics and Computing, 6(4598):353–366, 1996. D. Ormoneit and V. Tresp. Averaging, maximum penalized likelihood and bayesian estimation for improving Gaussian mixture probability density estimates.IEEE Transactions on Neural Networks, 9(4):639–650, 1998.51 N. Prokof’ev and B. Svistunov. Worm algorithms for classical statistical models. Phys.Rev.Lett., 87:160601, Sep 2001. D. J. Rezendeand S. Mohamed. Variational inference with normalizing flows, 2016. D. Rudoy and P. J. Wolfe. Monte carlo methods for multimodal distributions. In 2006 Fortieth Asilomar Conference on Signals, Systems and Computers, pages 2019–2023, 2006. R. H. Swendsen and J.S. Wang. Nonuniversal critical dynamics in Monte Carlo simulations.Phys.Rev.Lett., 58:86–88, Jan 1987. L. Tierney. Markov chains for exploring posterior distributions. Ann.Statist., 22(4): 1701–1728, 12 1994. J. Verbeek, N. Vlassis, and B. Kröse. Selforganizing mixture models. Neurocomputing, 63:99 – 123, 2005. New Aspects in Neurocomputing: 11th European Symposium on Artificial Neural Networks. U. Wolff. Collective Monte Carlo updating for spin systems. Phys.Rev.Lett., 62:361–364, Jan 1989. U. Wolff. Nucl.Phys.Proc.Suppl., 17, 1990. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/73827 | - |
| dc.description.abstract | 本文利用機器學習生成性模型建構晶格點量子場論中對於多極值分布的採樣方法。我們釐清了以更新為基礎的採樣演算法與生成流模型在面對多極值分布的問題，透過修正損失函數和訓練模型過程，我們設計了三個改進的演算法，分別為正KL訓練、絕熱訓練以及流距離正則化。我們利用自發對稱性破缺的實純量φ^4理論來驗證這三種方法的成效，以對稱化的混和蒙地卡羅演算法作為基準，檢視諸多物理量來確認模型是否完好的採樣到各極值。我們也探討在作用量顯著對稱性破壞的情況下這些機器學習方法的效果，我們發現流距離正則演算法可以在不知道作用量位移的情況下得到正確的採樣，這是一個機器學習可能超越混和蒙地卡羅的地方。 | zh_TW |
| dc.description.abstract | We proposed a guideline for multimodal sampling in lattice field theory based on machine-learned generative flow models. We identified the problems in update-based and flow-based algorithms in multimodal sampling. With proper manipulation of the loss function and training procedure, one can consistently train the resulting distribution into the desired modes using symmetrized forward KL training, Adiabatic training and flow-distance regularization. These algorithms are tested on the real scalar φ^4 theory in the symmetry-broken phase. Physical quantities, such as average magnetization, are computed and benchmarked by symmetrized Hybrid Monte Carlo (HMC). We also demonstrate that the regularized model is capable of finding both modes in the potentials with an unknown shift, therefore has the potential to outperform HMC. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T08:11:14Z (GMT). No. of bitstreams: 1 U0001-2801202117362900.pdf: 5222520 bytes, checksum: b7a3f464a152451558c1bf1059a9c390 (MD5) Previous issue date: 2021 | en |
| dc.description.tableofcontents | Verification Letter from the Oral Examination Committee i Acknowledgements iii 摘要 v Abstract vii Contents ix List of Figures xi List of Tables xv Chapter 1 Introduction 1 Chapter 2 Challenges in sampling multimodal distributions 5 2.1 Challenges for updatebased sampling methods 6 2.2 Challenges for flowbased generative models 9 2.2.1 Review of flowbased generative models 10 2.2.2 Sampling challenges in flowbased generative models 11 Chapter 3 Approaches to multimodal sampling with flowbased models 15 3.1 Symmetrized forward KL training 15 3.2 Adiabatic training 19 3.3 Flowdistance regularization 21 Chapter 4 Multimodal sampling in scalar field theory 25 4.1 Network structure 26 4.2 Comparison with symmetrized HMC 28 4.3 Training comparison for spontaneously broken symmetry 29 4.4 Explicitly broken symmetry 36 4.4.1 Tilted potential 36 4.4.2 Shifted potential 42 Chapter 5 Summary and outlook 47 References 49 Appendix A — Mixture model 53 | |
| dc.language.iso | en | |
| dc.subject | 機器學習 | zh_TW |
| dc.subject | 多極值 | zh_TW |
| dc.subject | 採樣 | zh_TW |
| dc.subject | 晶格點場論 | zh_TW |
| dc.subject | 流生成模型 | zh_TW |
| dc.subject | Lattice field theory | en |
| dc.subject | Sampling | en |
| dc.subject | Multimodal | en |
| dc.subject | Machine learning | en |
| dc.subject | Flow model | en |
| dc.title | 利用流生成模型進行晶格點場論中多極值採樣 | zh_TW |
| dc.title | Multimodal sampling in lattice field theory using flow-based generative models | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 109-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳凱風(Kai-Feng Chen),高英哲(Ying-Jer Kao),程之寧(Miranda Chih-Ning Cheng) | |
| dc.subject.keyword | 晶格點場論,採樣,多極值,機器學習,流生成模型, | zh_TW |
| dc.subject.keyword | Lattice field theory,Sampling,Multimodal,Machine learning,Flow model, | en |
| dc.relation.page | 56 | |
| dc.identifier.doi | 10.6342/NTU202100234 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2021-02-02 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理學研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| U0001-2801202117362900.pdf 未授權公開取用 | 5.1 MB | Adobe PDF |
系統中的文件，除了特別指名其著作權條款之外，均受到著作權保護，並且保留所有的權利。