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Predicting the behaviors of Hamiltonian systems has been drawing increasing attention in scientific machine learning.
On the conservation of conditionally periodic motions under small perturbation of the Hamiltonian
A. N. Kolmogorov · 1954
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Hamiltonian fluid mechanics
R. Salmon · 1988
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Hamiltonian dynamics and celestial mechanics
D. G. Saari and Z. Xia · 1996
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Performance of variable step size methods for solving model separable hamiltonian systems
V. Antohe and I. Gladwell · 2004
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Convex optimization
S. Boyd, S. P Boyd, and L. Vandenberghe · 2004
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Hamiltonian and action principle formulations of plasma physics
P. J. Morrison · 2005
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Hamiltonian moving-particle semi-implicit (hmps) method for incompressible fluid flows
Y. Suzuki, S. Koshizuka, and Y. Oka · 2007
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Analytical mechanics
L. N. Hand and J. D. Finch · 2008
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Observer-based Hamiltonian identification for quantum systems
S. Bonnabel, M. Mirrahimi, and P. Rouchon · 2009
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Understanding the difficulty of training deep feedforward neural networks
X. Glorot and Y. Bengio · 2010
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Introduction to topological manifolds
John Lee · 2010
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Adam: A method for stochastic optimization
D. P. Kingma and J. Ba · 2015
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Classifying orbits in the classical hénon–heiles hamiltonian system
E. E. Zotos · 2015
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Interaction networks for learning about objects, relations and physics
P. Battaglia, R. Pascanu, M. Lai, D. J. Rezende, et al · 2016
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Machine learning strategies for systems with invariance properties
J. Ling, R. Jones, and J. Templeton · 2016
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Explicit symplectic approximation of nonseparable Hamiltonians: algorithm and long time performance
M. Tao · 2016
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Explicit symplectic algorithms based on generating functions for charged particle dynamics
R. Zhang, H. Qin, Y. Tang, J. Liu, Y. He, and J. Xiao · 2016
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Splitting k-symplectic methods for non-canonical separable hamiltonian problems
B. Zhu, R. Zhang, Y. Tang, X. Tu, and Y. Zhao · 2016
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A parallel Hamiltonian formulation for forward dynamics of closed-loop multibody systems
K. Chadaj, P. Malczyk, and J. Frączek · 2017
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A class of energy-conserving Hamiltonian boundary value methods for nonlinear Schrödinger equation with wave operator
Signed particles and neural networks, towards efficient simulations of quantum systems
J. M. Sellier, G. M. Caron, and J. Leygonie · 2019
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Machine learning materials physics: Integrable deep neural networks enable scale bridging by learning free energy functions
G. H. Teicherta, A. R. Natarajanc, A. Van der Venc, and K. Garikipati · 2019
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Machine learning for fluid mechanics
S. L. Brunton, B. R. Noack, and P. Koumoutsakos · 2020
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Symplectic recurrent neural networks
Z. Chen, J. Zhang, M. Arjovsky, and L. Bottou · 2020
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M. Cranmer, S. Greydanus, S. Hoyer, P. Battaglia, D. Spergel, and S. Ho · 2020
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Sparse symplectically integrated neural networks
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L. Brugnano, C. Zhang, and D. Li · 2018
Cited alongside, same era.
Neural ordinary differential equations
R. T. Q. Chen, Y. Rubanova, J. Bettencourt, and D. Duvenaud · 2018
Cited alongside, same era.
Physics enhanced neural networks predict order and chaos
A. Choudhary, J. F. Lindner, E. G. Holliday, S. T. Miller, S. Sinha, and W. L. Ditto · 2019
Cited alongside, same era.
Hamiltonian neural networks
S. Greydanus, M. Dzamba, and J. Yosinski · 2019
Cited alongside, same era.
Wave physics as an analog recurrent neural network
T. W. Hughes, I. A. D. Williamson, M. Minkov, and S. Fan · 2019
Cited alongside, same era.
Solving the vlasov–maxwell equations using hamiltonian splitting
Y. Li, Y. He, J. Niesen Y. Sun, H. Qin, and J. Liu · 2019
Cited alongside, same era.
Pytorch: An imperative style, high-performance deep learning library
A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, et al · 2019
Cited alongside, same era.
D. DiPietro, S. Xiong, and B. Zhu · 2020
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Coercing machine learning to output physically accurate results
Z. Geng, D. Johnson, and R. Fedkiw · 2020
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Structure-preserving neural networks
Q. Hernandez, A. Badias, D. Gonzalez, F. Chinesta, and E. Cueto · 2020
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Symplectic networks: intrinsic structure-preserving networks for identifying Hamiltonian systems
P. Jin, A. Zhu, G. E. Karniadakis, and Y. Tang · 2020
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Embedding hard physical constraints in convolutional neural networks for 3D turbulence
A. T. Mohan, N. Lubbers, D. Livescu, and M. Chertkov · 2020
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Symplectic neural networks in Taylor series form for Hamiltonian systems
Y. Tong, S. Xiong, X. He, G. Pan, and Bo Zhu · 2020
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Hamiltonian generative networks
P. Toth, D. J. Rezende, A. Jaegle, S. Racaniére, A. Botev, and I. Higgins · 2020
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Symplectic ODE-Net: learning Hamiltonian dynamics with control
Y. D. Zhong, B. Dey, and A. Chakraborty · 2020
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