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We consider the learning and prediction of nonlinear time series generated by a latent symplectic map.
The applicability of the third integral of motion: some numerical experiments
Hénon, M. and Heiles, C · 1964
Earlier work this paper cites.
A universal instability of many-dimensional oscillator systems
Chirikov, B. V · 1979
Earlier work this paper cites.
Classical mechanics, 1980
Goldstein, H · 1980
Earlier work this paper cites.
Integrability of Hamiltonian systems on cantor sets
Pöschel, J · 1982
Earlier work this paper cites.
Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks
Hornik, K., Stinchcombe, M., and White, H · 1990
Earlier work this paper cites.
Fitting ordinary differential equations to chaotic data
Baake, E., Baake, M., Bock, H., and Briggs, K · 1992
Earlier work this paper cites.
A recurrent neural network for modelling dynamical systems
Bailer-Jones, C. A., MacKay, D. J., and Withers, P. J · 1998
Earlier work this paper cites.
Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics
Koon, W. S., Lo, M. W., Marsden, J. E., and Ross, S. D · 2000
Earlier work this paper cites.
Modern celestial mechanics: aspects of solar system dynamics
Morbidelli, A · 2002
Earlier work this paper cites.
Nonlinear time series analysis , volume 7
Kantz, H. and Schreiber, T · 2004
Earlier work this paper cites.
Geometric numerical integration: structure-preserving algorithms for ordinary differential equations , volume 31
Hairer, E., Lubich, C., and Wanner, G · 2006
Earlier work this paper cites.
Automated reverse engineering of nonlinear dynamical systems
Bongard, J. and Lipson, H · 2007
Earlier work this paper cites.
Lectures on symplectic geometry , volume 3575
Da Silva, A. C · 2008
Earlier work this paper cites.
Distilling free-form natural laws from experimental data
Schmidt, M. and Lipson, H · 2009
Earlier work this paper cites.
Complex analysis , volume 2
Stein, E. M. and Shakarchi, R · 2010
Earlier work this paper cites.
Analysis of observed chaotic data
Abarbanel, H · 2012
Earlier work this paper cites.
Mathematical methods of classical mechanics , volume GTM 60
Arnol’d, V. I · 2013
Earlier work this paper cites.
Time series analysis: forecasting and control
Box, G. E., Jenkins, G. M., Reinsel, G. C., and Ljung, G. M · 2015
Cited alongside, same era.
Nonlinear time-series analysis revisited
Bradley, E. and Kantz, H · 2015
Cited alongside, same era.
The many facets of chaos
Sander, E. and Yorke, J. A · 2015
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Discovering governing equations from data by sparse identification of nonlinear dynamical systems
Brunton, S. L., Proctor, J. L., and Kutz, J. N · 2016
Cited alongside, same era.
Uncovering circumbinary planetary architectural properties from selection biases
Li, G., Holman, M. J., and Tao, M · 2016
Cited alongside, same era.
Explicit symplectic approximation of nonseparable hamiltonians: Algorithm and long time performance
Tao, M · 2016
Cited alongside, same era.
Nonparametric inference of interaction laws in systems of agents from trajectory data
Lu, F., Zhong, M., Tang, S., and Maggioni, M · 2019
Later among the works it cites.
Deep lagrangian networks: Using physics as model prior for deep learning
Lutter, M., Ritter, C., and Peters, J · 2019
Later among the works it cites.
Data driven governing equations approximation using deep neural networks
Qin, T., Wu, K., and Xiu, D · 2019
Later among the works it cites.
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Raissi, M., Perdikaris, P., and Karniadakis, G. E · 2019
Later among the works it cites.
Deep learning of dynamics and signal-noise decomposition with time-stepping constraints
Rudy, S. H., Kutz, J. N., and Brunton, S. L · 2019
Later among the works it cites.
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Tran, G. and Ward, R · 2017
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Yarotsky, D · 2017
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Cited alongside, same era.
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Tensorized transformer for dynamical systems modeling
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Toth, P., Rezende, D. J., Jaegle, A., Racanière, S., Botev, A., and Higgins, I · 2020
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Learning molecular dynamics with simple language model built upon long short-term memory neural network
Tsai, S.-T., Kuo, E.-J., and Tiwary, P · 2020
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