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There has been a wave of interest in applying machine learning to study dynamical systems.
Hamiltonian Graph Networks with ODE Integrators
Alvaro Sanchez-Gonzalez, Victor Bapst, Kyle Cranmer, and Peter Battaglia · 1909
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Invariante variationsprobleme
Emmy Noether · 1918
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The applicability of the third integral of motion: Some numerical experiments
Michel Hénon and Carl Heiles · 1964
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Approximation capabilities of multilayer feedforward networks
Kurt Hornik · 1991
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Symplectic numerical integrators in constrained hamiltonian systems
Benedict J Leimkuhler and Robert D Skeel · 1994
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Artificial neural networks for solving ordinary and partial differential equations
Isaac E. Lagaris, Aristidis Likas, and Dimitrios I. Fotiadis · 1998
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Lyapunov exponents in the hénon-heiles problem
I. I. Shevchenko and A. V. Mel’Nikov · 2003
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Python for scientific computing
Travis E. Oliphant · 2007
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Adam: A method for stochastic optimization
Diederik P. Kingma and Jimmy Ba · 2014
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50 years of time parallel time integration
Martin J. Gander · 2015
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Machine learning strategies for systems with invariance properties
Julia Ling, Reese Jones, and Jeremy Templeton · 2016
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Reynolds averaged turbulence modelling using deep neural networks with embedded invariance
Julia Ling, Andrew Kurzawski, and Jeremy Templeton · 2016
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Reservoir observers: Model-free inference of unmeasured variables in chaotic systems
Zhixin Lu, Jaideep Pathak, Brian Hunt, Michelle Girvan, Roger Brockett, and Edward Ott · 2017
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Inferring solutions of differential equations using noisy multi-fidelity data
Maziar Raissi, Paris Perdikaris, and George Em Karniadakis · 2017
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Machine learning of linear differential equations using Gaussian processes
Maziar Raissi, Paris Perdikaris, and George Em Karniadakis · 2017
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Data-driven discovery of partial differential equations
Samuel H. Rudy, Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz · 2017
Earlier work this paper cites.
Data-driven discovery of governing physical laws and their parametric dependencies in engineering, physics and biology
J. Nathan Kutz, Samuel H. Rudy, Alessandro Alla, and Steven L. Brunton · 2017
Cited alongside, same era.
Solving high-dimensional partial differential equations using deep learning
Jiequn Han, Arnulf Jentzen, and E Weinan · 2017
Cited alongside, same era.
Automatic differentiation in pytorch
Adam Paszke, Sam Gross, Soumith Chintala, Gregory Chanan, Edward Yang, Zachary Devito, Zeming Lin, Alban Desmaison, Luca Antiga, and Adam Lerer · 2017
Cited alongside, same era.
Deep learning for universal linear embeddings of nonlinear dynamics
Bethany Lusch, J. Nathan Kutz, and Steven L. Brunton · 2018
Cited alongside, same era.
Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks
Pantelis R. Vlachas, Wonmin Byeon, Zhong Y. Wan, Themistoklis P. Sapsis, and Petros Koumoutsakos · 2018
Cited alongside, same era.
Hamiltonian neural networks
Sam Greydanus, Misko Dzamba, and Jason Yosinski · 2019
Later among the works it cites.
On learning hamiltonian systems from data
Tom Bertalan, Felix Dietrich, Igor Mezic, and Ioannis G. Kevrekidis · 2019
Later among the works it cites.
Layer-parallel training of deep residual neural networks
Stefanie Gunther, Lars Ruthotto, Jacob B. Schroder, Eric C. Cyr, and Nicolas R. Gauger · 2020
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Physics-enhanced neural networks learn order and chaos
Anshul Choudhary, John F. Lindner, Elliott G. Holliday, Scott T. Miller, Sudeshna Sinha, and William L. Ditto · 2020
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Hamiltonian generative networks
Peter Toth, Danilo Jimenez Rezende, Andrew Jaegle, Sebastien Racaniere, Aleksandar Botev, and Irina Higgins · 2020
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Neural networks fail to learn periodic functions and how to fix it
Liu Ziyin, Tilman Hartwig, and Masahito Ueda · 2020
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Model-free prediction of large spatiotemporally chaotic systems from data: A reservoir computing approach
Jaideep Pathak, Brian Hunt, Michelle Girvan, Zhixin Lu, and Edward Ott · 2018
Cited alongside, same era.
Dgm: A deep learning algorithm for solving partial differential equations
Justin A. Sirignano and Konstantinos Spiliopoulos · 2018
Cited alongside, same era.
Neural networks trained to solve differential equations learn general representations
Martin Magill, Faisal Qureshi, and Hendrick W. de Haan · 2018
Cited alongside, same era.
Identifiability and predictability of integer- and fractional-order epidemiological models using physics-informed neural networks
Ehsan Kharazmi, Min Cai, Xiaoning Zheng, Zhen Zhang, Guang Lin, and George Em Karniadakis · 2018
Cited alongside, same era.
Machine Learning With Observers Predicts Complex Spatiotemporal Behavior
George Neofotistos, Marios Mattheakis, Georgios D. Barmparis, Johanne Hizanidis, Giorgos P. Tsironis, and Efthimios Kaxiras · 2019
Cited alongside, same era.
Recent advances in physical reservoir computing: A review
Gouhei Tanaka, Toshiyuki Yamane, Jean Benoit Héroux, Ryosho Nakane, Naoki Kanazawa, Seiji Takeda, Hidetoshi Numata, Daiju Nakano, and Akira Hirose · 2019
Cited alongside, same era.
Multivariate lstm-fcns for time series classification
Fazle Karim, Somshubra Majumdar, Houshang Darabi, and Samuel Harford · 2019
Cited alongside, same era.
Neural-network-based multistate solver for a static schrödinger equation
Hong Li, Qilong Zhai, and Jeff Z. Y. Chen · 2021
Closest in time.
Physics-informed machine learning
George Em Karniadakis, Ioannis G. Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang · 2021
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Deep learning of free boundary and stefan problems
Sifan Wang and Paris Perdikaris · 2021
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Fourier neural operator for parametric partial differential equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar · 2021
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Characterizing possible failure modes in physics-informed neural networks
Aditi S. Krishnapriyan, Amir Gholami, Shandian Zhe, Robert M. Kirby, and Michael W. Mahoney · 2021
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Variational integrator graph networks for learning energy-conserving dynamical systems
Shaan A. Desai, Marios Mattheakis, and Stephen J. Roberts · 2021
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Adaptable hamiltonian neural networks
Chen-Di Han, Bryan Glaz, Mulugeta Haile, and Ying-Cheng Lai · 2021
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Learning hamiltonian dynamics with reservoir computing
Han Zhang, Huawei Fan, Liang Wang, and Xingang Wang · 2021
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Port-hamiltonian neural networks for learning explicit time-dependent dynamical systems
Shaan A. Desai, Marios Mattheakis, David Sondak, Pavlos Protopapas, and Stephen J. Roberts · 2021
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Chaos, Solitons & \& Fractals
Modeling the effect of the vaccination campaign on the covid-19 pandemic · 2022
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