Built on

Karl Pearson, “LIII. On lines and planes of closest fit to systems of points in space,” Philosophical Magazine 2
1901
Earlier work this paper cites.
Hong-Ye Hu, Shuo-Hui Li, Lei Wang, and Yi-Zhuang You, “Machine Learning Holographic Mapping by Neural Network Renormalization Group,” (2019) , arXiv:1903.00804
Original
1903
Earlier work this paper cites.
M Mattheakis, P Protopapas, D Sondak, M Di Giovanni, and E Kaxiras, “Physical Symmetries Embedded in Neural Networks,” arXiv (2019) , arXiv:1904.08991v1
Original
1904
Earlier work this paper cites.
M. S. Albergo, G. Kanwar, and P. E. Shanahan, “Flow-based generative models for Markov chain Monte Carlo in lattice field theory,” Phys. Rev. D 100
Original
1904
Earlier work this paper cites.
Sam Greydanus, Misko Dzamba, and Jason Yosinski, “Hamiltonian Neural Networks,” (2019) , arXiv:1906.01563
Original
1906
Earlier work this paper cites.
Roberto Bondesan and Austen Lamacraft, “Learning Symmetries of Classical Integrable Systems,” (2019) , arXiv:1906.04645
Original
1906
Earlier work this paper cites.
Shakir Mohamed, Mihaela Rosca, Michael Figurnov, and Andriy Mnih, “Monte Carlo Gradient Estimation in Machine Learning,” (2019) , arXiv:1906.10652
Original
1906
Earlier work this paper cites.
Ivan Kobyzev, Simon Prince, and Marcus A. Brubaker, “Normalizing Flows: Introduction and Ideas,” (2019) , arXiv:1908.09257
Original
1908
Earlier work this paper cites.
Hari Prasanna Das, Pieter Abbeel, and Costas J Spanos, “Dimensionality Reduction Flows,” (2019) , arXiv:1908.01686
Original
1908
Earlier work this paper cites.
Yihang Wang, Joao Marcelo Lamim Ribeiro, and Pratyush Tiwary, “Machine learning approaches for analyzing and enhancing molecular dynamics simulations,” (2019) , arXiv:1909.11748
Original
1909
Earlier work this paper cites.
Alvaro Sanchez-Gonzalez, Victor Bapst, Kyle Cranmer, and Peter Battaglia, “Hamiltonian Graph Networks with ODE Integrators,” (2019) , arXiv:1909.12790
Original
1909
Earlier work this paper cites.
Yaofeng Desmond Zhong, Biswadip Dey, and Amit Chakraborty, “Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control,” (2019) , arXiv:1909.12077
Original
1909
Earlier work this paper cites.
Zhengdao Chen, Jianyu Zhang, Martin Arjovsky, and Léon Bottou, “Symplectic Recurrent Neural Networks,” (2019) , arXiv:1909.13334
Original
1909
Earlier work this paper cites.
Danilo J. Rezende, Sébastien Racanière, Irina Higgins, and Peter Toth, “Equivariant Hamiltonian Flows,” (2019) , arXiv:1909.13739
Original
1909
Earlier work this paper cites.
Peter Toth, Danilo Jimenez Rezende, Andrew Jaegle, Sébastien Racanière, Aleksandar Botev, and Irina Higgins, “Hamiltonian Generative Networks,” (2019) , arXiv:1909.13789
Original
1909
Earlier work this paper cites.
Mario Lezcano-Casado, “Trivializations for Gradient-Based Optimization on Manifolds,” (2019) , arXiv:1909.09501
Original
1909
Earlier work this paper cites.
Jonas Köhler, Leon Klein, and Frank Noé, “Equivariant Flows: sampling configurations for multi-body systems with symmetric energies,” (2019) , arXiv:1910.00753
Original
1910
Earlier work this paper cites.
George Papamakarios, Eric Nalisnick, Danilo Jimenez Rezende, Shakir Mohamed, and Balaji Lakshminarayanan, “Normalizing Flows for Probabilistic Modeling and Inference,” (2019) , arXiv:1912.02762
Original
1912
Earlier work this paper cites.
V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer, 1989)
1989
Earlier work this paper cites.
L. Molgedey and H. G. Schuster, “Separation of a Mixture of Independent Signals Using Time Delayed Correlations,” Phys. Rev. Lett. 72
1994
Earlier work this paper cites.
A. Belouchrani, K. Abed-Meraim, J. . Cardoso, and E. Moulines, “A blind source separation technique using second-order statistics,” IEEE Transactions on Signal Processing 45
1997
Earlier work this paper cites.
Andreas Ziehe and Klaus-Robert Müller, ICANN 98 , edited by Lars Niklasson, Mikael Bodén, and Tom Ziemke (Springer London, London, 1998) pp. 675–680
1998
Earlier work this paper cites.
Bernhard Schölkopf, Alexander Smola, and Klaus-Robert Müller, “Nonlinear component analysis as a kernel eigenvalue problem,” Neural Computation 10
1998
Earlier work this paper cites.
Gavin S. Hartnett and Masoud Mohseni, “Self-supervised learning of generative spin-glasses with normalizing flows,” CoRR (2020) , arXiv:2001.00585 [cs.LG]
Original
2001
Earlier work this paper cites.
Laurenz Wiskott and Terrence J. Sejnowski, “Slow feature analysis: Unsupervised learning of invariances,” Neural Comput. 14
2002
Earlier work this paper cites.
Alessandro Laio and Michele Parrinello, “Escaping free-energy minima,” PNAS 99
2002
Earlier work this paper cites.

Similar

Zhongwei Zhu, Mark E. Tuckerman, Shane O. Samuelson, and Glenn J. Martyna, “Using Novel Variable Transformations to Enhance Conformational Sampling in Molecular Dynamics,” Phys. Rev. Lett. 88
2002
Cited alongside, same era.
Stefan Harmeling, Andreas Ziehe, Motoaki Kawanabe, and Klaus-Robert Müller, “Kernel-based nonlinear blind source separation,” Neural Computation 15
2003
Cited alongside, same era.
Alexander Kraskov, Harald Stögbauer, and Peter Grassberger, “Estimating mutual information,” Phys. Rev. E 69
2004
Cited alongside, same era.
Juan A. Acebrón, L. L. Bonilla, Conrad J. Pérez Vicente, Félix Ritort, and Renato Spigler, “The kuramoto model: A simple paradigm for synchronization phenomena,” Rev. Mod. Phys. 77
2005
Cited alongside, same era.
Jörg Behler and Michele Parrinello, “Generalized neural-network representation of high-dimensional potential-energy surfaces,” Physical Review Letters 98

Then

Stefan Chmiela, Alexandre Tkatchenko, Huziel E. Sauceda, Igor Poltavsky, Kristof T. Schütt, and Klaus-Robert Müller, “Machine learning of accurate energy-conserving molecular force fields,” Science Advances 3
2017
Later among the works it cites.
Jiaming Song, Shengjia Zhao, and Stefano Ermon, “A-NICE-MC: Adversarial Training for MCMC,” (2017) , arXiv:1706.07561
Original
2017
Later among the works it cites.
Daniel Levy, Matthew D. Hoffman, and Jascha Sohl-Dickstein, “Generalizing Hamiltonian Monte Carlo with Neural Networks,” (2017) , arXiv:1711.09268
Original
2017
Later among the works it cites.
Weinan E, “A Proposal on Machine Learning via Dynamical Systems,” Commun. Math. Stat. 5
2017
Later among the works it cites.
Aaron van den Oord, Yazhe Li, Igor Babuschkin, Karen Simonyan, Oriol Vinyals, Koray Kavukcuoglu, George van den Driessche, Edward Lockhart, Luis C. Cobo, Florian Stimberg, Norman Casagrande, Dominik Grewe, Seb Noury, Sander Dieleman, Erich Elsen, Nal Kalchbrenner, Heiga Zen, Alex Graves, Helen King, Tom Walters, Dan Belov, and Demis Hassabis, “Parallel WaveNet: Fast High-Fidelity Speech Synthesis,” (2017) , arXiv:1711.10433

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2019

Neural Canonical Transformation with Symplectic Flows

Li, Shuo-Hui, Dong, Chen-Xiao, Zhang, Linfeng et al.

Understand

Canonical transformation plays a fundamental role in simplifying and solving classical Hamiltonian systems.

We construct flexible and powerful canonical transformations as generative models using symplectic neural networks.
The model transforms physical variables towards a latent representation with an independent harmonic oscillator Hamiltonian.
Correspondingly, the phase space density of the physical system flows towards a factorized Gaussian distribution in the latent space.

Built on

Karl Pearson, “LIII. On lines and planes of closest fit to systems of points in space,” Philosophical Magazine 2
1901
Earlier work this paper cites.
Hong-Ye Hu, Shuo-Hui Li, Lei Wang, and Yi-Zhuang You, “Machine Learning Holographic Mapping by Neural Network Renormalization Group,” (2019) , arXiv:1903.00804
Original
1903
Earlier work this paper cites.
M Mattheakis, P Protopapas, D Sondak, M Di Giovanni, and E Kaxiras, “Physical Symmetries Embedded in Neural Networks,” arXiv (2019) , arXiv:1904.08991v1
Original
1904
Earlier work this paper cites.
M. S. Albergo, G. Kanwar, and P. E. Shanahan, “Flow-based generative models for Markov chain Monte Carlo in lattice field theory,” Phys. Rev. D 100
Original
1904
Earlier work this paper cites.
Sam Greydanus, Misko Dzamba, and Jason Yosinski, “Hamiltonian Neural Networks,” (2019) , arXiv:1906.01563
Original
1906
Earlier work this paper cites.
Roberto Bondesan and Austen Lamacraft, “Learning Symmetries of Classical Integrable Systems,” (2019) , arXiv:1906.04645
Original
1906
Earlier work this paper cites.
Shakir Mohamed, Mihaela Rosca, Michael Figurnov, and Andriy Mnih, “Monte Carlo Gradient Estimation in Machine Learning,” (2019) , arXiv:1906.10652
Original
1906
Earlier work this paper cites.
Ivan Kobyzev, Simon Prince, and Marcus A. Brubaker, “Normalizing Flows: Introduction and Ideas,” (2019) , arXiv:1908.09257
Original
1908
Earlier work this paper cites.
Hari Prasanna Das, Pieter Abbeel, and Costas J Spanos, “Dimensionality Reduction Flows,” (2019) , arXiv:1908.01686
Original
1908
Earlier work this paper cites.
Yihang Wang, Joao Marcelo Lamim Ribeiro, and Pratyush Tiwary, “Machine learning approaches for analyzing and enhancing molecular dynamics simulations,” (2019) , arXiv:1909.11748
Original
1909
Earlier work this paper cites.
Alvaro Sanchez-Gonzalez, Victor Bapst, Kyle Cranmer, and Peter Battaglia, “Hamiltonian Graph Networks with ODE Integrators,” (2019) , arXiv:1909.12790
Original
1909
Earlier work this paper cites.
Yaofeng Desmond Zhong, Biswadip Dey, and Amit Chakraborty, “Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control,” (2019) , arXiv:1909.12077
Original
1909
Earlier work this paper cites.
Zhengdao Chen, Jianyu Zhang, Martin Arjovsky, and Léon Bottou, “Symplectic Recurrent Neural Networks,” (2019) , arXiv:1909.13334
Original
1909
Earlier work this paper cites.
Danilo J. Rezende, Sébastien Racanière, Irina Higgins, and Peter Toth, “Equivariant Hamiltonian Flows,” (2019) , arXiv:1909.13739
Original
1909
Earlier work this paper cites.
Peter Toth, Danilo Jimenez Rezende, Andrew Jaegle, Sébastien Racanière, Aleksandar Botev, and Irina Higgins, “Hamiltonian Generative Networks,” (2019) , arXiv:1909.13789
Original
1909
Earlier work this paper cites.
Mario Lezcano-Casado, “Trivializations for Gradient-Based Optimization on Manifolds,” (2019) , arXiv:1909.09501
Original
1909
Earlier work this paper cites.
Jonas Köhler, Leon Klein, and Frank Noé, “Equivariant Flows: sampling configurations for multi-body systems with symmetric energies,” (2019) , arXiv:1910.00753
Original
1910
Earlier work this paper cites.
George Papamakarios, Eric Nalisnick, Danilo Jimenez Rezende, Shakir Mohamed, and Balaji Lakshminarayanan, “Normalizing Flows for Probabilistic Modeling and Inference,” (2019) , arXiv:1912.02762
Original
1912
Earlier work this paper cites.
V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer, 1989)
1989
Earlier work this paper cites.
L. Molgedey and H. G. Schuster, “Separation of a Mixture of Independent Signals Using Time Delayed Correlations,” Phys. Rev. Lett. 72
1994
Earlier work this paper cites.
A. Belouchrani, K. Abed-Meraim, J. . Cardoso, and E. Moulines, “A blind source separation technique using second-order statistics,” IEEE Transactions on Signal Processing 45
1997
Earlier work this paper cites.
Andreas Ziehe and Klaus-Robert Müller, ICANN 98 , edited by Lars Niklasson, Mikael Bodén, and Tom Ziemke (Springer London, London, 1998) pp. 675–680
1998
Earlier work this paper cites.
Bernhard Schölkopf, Alexander Smola, and Klaus-Robert Müller, “Nonlinear component analysis as a kernel eigenvalue problem,” Neural Computation 10
1998
Earlier work this paper cites.
Gavin S. Hartnett and Masoud Mohseni, “Self-supervised learning of generative spin-glasses with normalizing flows,” CoRR (2020) , arXiv:2001.00585 [cs.LG]
Original
2001
Earlier work this paper cites.
Laurenz Wiskott and Terrence J. Sejnowski, “Slow feature analysis: Unsupervised learning of invariances,” Neural Comput. 14
2002
Earlier work this paper cites.
Alessandro Laio and Michele Parrinello, “Escaping free-energy minima,” PNAS 99
2002
Earlier work this paper cites.

Similar

Zhongwei Zhu, Mark E. Tuckerman, Shane O. Samuelson, and Glenn J. Martyna, “Using Novel Variable Transformations to Enhance Conformational Sampling in Molecular Dynamics,” Phys. Rev. Lett. 88
2002
Cited alongside, same era.
Stefan Harmeling, Andreas Ziehe, Motoaki Kawanabe, and Klaus-Robert Müller, “Kernel-based nonlinear blind source separation,” Neural Computation 15
2003
Cited alongside, same era.
Alexander Kraskov, Harald Stögbauer, and Peter Grassberger, “Estimating mutual information,” Phys. Rev. E 69
2004
Cited alongside, same era.
Juan A. Acebrón, L. L. Bonilla, Conrad J. Pérez Vicente, Félix Ritort, and Renato Spigler, “The kuramoto model: A simple paradigm for synchronization phenomena,” Rev. Mod. Phys. 77
2005
Cited alongside, same era.
Jörg Behler and Michele Parrinello, “Generalized neural-network representation of high-dimensional potential-energy surfaces,” Physical Review Letters 98

Then

Stefan Chmiela, Alexandre Tkatchenko, Huziel E. Sauceda, Igor Poltavsky, Kristof T. Schütt, and Klaus-Robert Müller, “Machine learning of accurate energy-conserving molecular force fields,” Science Advances 3
2017
Later among the works it cites.
Jiaming Song, Shengjia Zhao, and Stefano Ermon, “A-NICE-MC: Adversarial Training for MCMC,” (2017) , arXiv:1706.07561
Original
2017
Later among the works it cites.
Daniel Levy, Matthew D. Hoffman, and Jascha Sohl-Dickstein, “Generalizing Hamiltonian Monte Carlo with Neural Networks,” (2017) , arXiv:1711.09268
Original
2017
Later among the works it cites.
Weinan E, “A Proposal on Machine Learning via Dynamical Systems,” Commun. Math. Stat. 5
2017
Later among the works it cites.
Aaron van den Oord, Yazhe Li, Igor Babuschkin, Karen Simonyan, Oriol Vinyals, Koray Kavukcuoglu, George van den Driessche, Edward Lockhart, Luis C. Cobo, Florian Stimberg, Norman Casagrande, Dominik Grewe, Seb Noury, Sander Dieleman, Erich Elsen, Nal Kalchbrenner, Heiga Zen, Alex Graves, Helen King, Tom Walters, Dan Belov, and Demis Hassabis, “Parallel WaveNet: Fast High-Fidelity Speech Synthesis,” (2017) , arXiv:1711.10433

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

2007

Cited alongside, same era.

David E Shaw, Paul Maragakis, Kresten Lindorff-Larsen, Stefano Piana, Ron O Dror, Michael P Eastwood, Joseph A Bank, John M Jumper, John K Salmon, Yibing Shan, and Willy Wriggers, “Atomic-level characterization of the structural dynamics of proteins,” Science 330

2010

Cited alongside, same era.

Peter J. Schmid, “Dynamic mode decomposition of numerical and experimental data,” J. Fluid Mech. 656

2010

Cited alongside, same era.

Kang Feng and Mengzhao Qin, Symplectic Geometric Algorithms for Hamiltonian Systems (Springer, 2011)

2011

Cited alongside, same era.

Guillermo Pérez-Hernández, Fabian Paul, Toni Giorgino, Gianni De Fabritiis, and Frank Noé, “Identification of slow molecular order parameters for Markov model construction,” J. Chem. Phys. 139

2013

Cited alongside, same era.

Christian R. Schwantes and Vijay S. Pande, “Improvements in Markov State Model construction reveal many non-native interactions in the folding of NTL9,” J. Chem. Theory Comput. 9

2013

Cited alongside, same era.

Diederik P Kingma and Max Welling, “Auto-Encoding Variational Bayes,” (2013) , arXiv:1312.6114