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The development of data-informed predictive models for dynamical systems is of widespread interest in many disciplines.
AntisymmetricRNN: A Dynamical System View on Recurrent Neural Networks
Bo Chang, Minmin Chen, Eldad Haber, and Ed H. Chi · 1902
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EM-like Learning Chaotic Dynamics from Noisy and Partial Observations
Duong Nguyen, Said Ouala, Lucas Drumetz, and Ronan Fablet · 1903
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Recurrent Neural Networks in the Eye of Differential Equations
Murphy Yuezhen Niu, Lior Horesh, and Isaac Chuang · 1904
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Peter A. G. Watson · 1904
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Modeling of Missing Dynamical Systems: Deriving Parametric Models using a Nonparametric Framework
Shixiao W. Jiang and John Harlim · 1905
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Latent ODEs for Irregularly-Sampled Time Series
Yulia Rubanova, Ricky T. Q. Chen, and David Duvenaud · 1907
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Learning Discrepancy Models From Experimental Data
Kadierdan Kaheman, Eurika Kaiser, Benjamin Strom, J. Nathan Kutz, and Steven L. Brunton · 1909
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Blending Diverse Physical Priors with Neural Networks
Yunhao Ba, Guangyuan Zhao, and Achuta Kadambi · 1910
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Lu Lu, Pengzhan Jin, and George Em Karniadakis · 1910
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Physics-Guided Machine Learning for Scientific Discovery: An Application in Simulating Lake Temperature Profiles
Xiaowei Jia, Jared Willard, Anuj Karpatne, Jordan S. Read, Jacob A. Zwart, Michael Steinbach, and Vipin Kumar · 1922
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Data-Driven Super-Parameterization Using Deep Learning: Experimentation With Multiscale Lorenz 96 Systems and Transfer Learning
Ashesh Chattopadhyay, Adam Subel, and Pedram Hassanzadeh · 1942
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Using Machine Learning to Parameterize Moist Convection: Potential for Modeling of Climate, Climate Change, and Extreme Events
Paul A. O’Gorman and John G. Dwyer · 1942
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Prognostic Validation of a Neural Network Unified Physics Parameterization
N. D. Brenowitz and C. S. Bretherton · 1944
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A cloud resolving model as a cloud parameterization in the NCAR Community Climate System Model: Preliminary results
Marat F. Khairoutdinov and David A. Randall · 1944
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On Information and Sufficiency
S. Kullback and R. A. Leibler · 1951
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Deterministic Nonperiodic Flow
Edward N. Lorenz · 1963
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Smoothing noisy data with spline functions
Peter Craven and Grace Wahba · 1978
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A family of embedded Runge-Kutta formulae
J. R. Dormand and P. J. Prince · 1980
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Detecting strange attractors in turbulence
Floris Takens · 1981
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Learning representations by back-propagating errors
David E Rumelhart, Geoffrey E Hinton, and Ronald J Williams · 1986
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Approximation by superpositions of a sigmoidal function
G. Cybenko · 1989
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Bayesian Approach to Global Optimization: Theory and Applications
Jonas Mockus · 1989
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The strength of weak learnability
Robert E. Schapire · 1990
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Neural networks and dynamical systems
Kumpati S. Narendra and Kannan Parthasarathy · 1992
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DISCRETE- vs. CONTINUOUS-TIME NONLINEAR SIGNAL PROCESSING OF Cu ELECTRODISSOLUTION DATA
R. Rico-Martínez, K. Krischer, I.G. Kevrekidis, M.C. Kube, and J.L. Hudson · 1992
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Stacked generalization
David H. Wolpert · 1992
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Constructive Approximation
Ronald A. DeVore and George G. Lorentz · 1993
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Approximation of dynamical systems by continuous time recurrent neural networks
Ken-ichi Funahashi and Yuichi Nakamura · 1993
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Model identification of a spatiotemporally varying catalytic reaction
K. Krischer, R. Rico-Martínez, I. G. Kevrekidis, H. H. Rotermund, G. Ertl, and J. L. Hudson · 1993
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Discrete- vs. Continuous-Time Nonlinear Signal Processing: Attractors, Transitions and Parallel Implementation Issues
R. Rico-Martines, I. G. Kevrekidis, M. C. Kube, and J. L. Hudson · 1993
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Continuous-time nonlinear signal processing: a neural network based approach for gray box identification
R. Rico-Martinez, J.S. Anderson, and I.G. Kevrekidis · 1994
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On the Dynamics of Small Continuous-Time Recurrent Neural Networks
Randall D. Beer · 1995
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Bagging predictors
Leo Breiman · 1996
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Predictability-A problem partly solved
E. Lorenz · 1996
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Long Short-term Memory
Sepp Hochreiter and Jürgen Schmidhuber · 1997
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The em algorithm—an old folk-song sung to a fast new tune
Xiao-Li Meng and David Van Dyk · 1997
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A generalised approach to process state estimation using hybrid artificial neural network/mechanistic models
J.A. Wilson and L.F.M. Zorzetto · 1997
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Identification of distributed parameter systems: A neural net based approach
R. González-García, R. Rico-Martínez, and I.G. Kevrekidis · 1998
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Artificial Neural Networks for Solving Ordinary and Partial Differential Equations
I. E. Lagaris, A. Likas, and D. I. Fotiadis · 1998
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Optimal prediction and the Mori–Zwanzig representation of irreversible processes
Alexandre J Chorin, Ole H Hald, and Raz Kupferman · 2000
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An adaptive variational method for data assimilation with imperfect models
Jian Zhu and Masafumi Kamachi · 2000
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Julien Brajard, Alberto Carassi, Marc Bocquet, and Laurent Bertino · 2001
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Coupling Cloud Processes with the Large-Scale Dynamics Using the Cloud-Resolving Convection Parameterization (CRCP)
Wojciech W. Grabowski · 2001
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The” echo state” approach to analysing and training recurrent neural networks-with an erratum note’
Herbert Jaeger · 2001
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Universal Differential Equations for Scientific Machine Learning
Christopher Rackauckas, Yingbo Ma, Julius Martensen, Collin Warner, Kirill Zubov, Rohit Supekar, Dominic Skinner, Ali Ramadhan, and Alan Edelman · 2001
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A hybrid model based on deep LSTM for predicting high-dimensional chaotic systems
Youming Lei, Jian Hu, and Jianpeng Ding · 2002
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Fast communications: Numerical techniques for multi-scale dynamical systems with stochastic effects
Eric Vanden-Eijnden and others · 2003
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Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems
Jared Willard, Xiaowei Jia, Shaoming Xu, Michael Steinbach, and Vipin Kumar · 2003
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A computational strategy for multiscale systems with applications to Lorenz 96 model
Ibrahim Fatkullin and Eric Vanden-Eijnden · 2004
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Statistical Inference for Ergodic Diffusion Processes
Yury A. Kutoyants · 2004
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The inverse crime
Armand Wirgin · 2004
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Model Reduction and Neural Networks for Parametric PDEs
Kaushik Bhattacharya, Bamdad Hosseini, Nikola B. Kovachki, and Andrew M. Stuart · 2005
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Kernel Analog Forecasting: Multiscale Test Problems
Dmitry Burov, Dimitrios Giannakis, Krithika Manohar, and Andrew Stuart · 2005
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Statistical and Computational Inverse Problems
Jari Kaipio and E. Somersalo · 2005
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The Random Feature Model for Input-Output Maps between Banach Spaces
Nicholas H. Nelsen and Andrew M. Stuart · 2005
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Gaussian Process Dynamical Models
Jack Wang, Aaron Hertzmann, and David J. Fleet · 2005
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Reservoir Computing meets Recurrent Kernels and Structured Transforms
Jonathan Dong, Ruben Ohana, Mushegh Rafayelyan, and Florent Krzakala · 2006
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Lipschitz Recurrent Neural Networks
N. Benjamin Erichson, Omri Azencot, Alejandro Queiruga, Liam Hodgkinson, and Michael W. Mahoney · 2006
Cited alongside, same era.
Gaussian processes for machine learning
Carl Edward Rasmussen and Christopher K. I. Williams · 2006
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Modeling Large Dynamical Systems with Dynamical Consistent Neural Networks
Simon Haykin, Jose C. Principe, Terrence J. Sejnowski, and John Mcwhirter · 2007
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Central limit theorems and invariance principles for Lorenz attractors
Mark Holland and Ian Melbourne · 2007
Cited alongside, same era.
Random Features for Large-Scale Kernel Machines
Ali Rahimi and Benjamin Recht · 2007
Cited alongside, same era.
Recurrent Neural Networks are universal approximators
Anton Maximilian Schäfer and Hans-Georg Zimmermann · 2007
Stochastic parameterization identification using ensemble Kalman filtering combined with maximum likelihood methods
Manuel Pulido, Pierre Tandeo, Marc Bocquet, Alberto Carrassi, and Magdalena Lucini · 2018
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
M. Raissi, P. Perdikaris, and G. E. Karniadakis · 2018
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Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems
Maziar Raissi, Paris Perdikaris, and George Em Karniadakis · 2018
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Deep learning to represent subgrid processes in climate models
Stephan Rasp, Michael S. Pritchard, and Pierre Gentine · 2018
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Extracting sparse high-dimensional dynamics from limited data
Hayden Schaeffer, Giang Tran, and Rachel Ward · 2018
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Cited alongside, same era.
Learning Insulin-Glucose Dynamics in the Wild
Andrew C. Miller, Nicholas J. Foti, and Emily Fox · 2008
Cited alongside, same era.
Multiscale methods: averaging and homogenization
Grigoris Pavliotis and Andrew Stuart · 2008
Cited alongside, same era.
Continuous-in-Depth Neural Networks
Alejandro F. Queiruga, N. Benjamin Erichson, Dane Taylor, and Michael W. Mahoney · 2008
Cited alongside, same era.
Uniform approximation of functions with random bases
Ali Rahimi and Benjamin Recht · 2008
Cited alongside, same era.
Computing generalized Langevin equations and generalized Fokker–Planck equations
Eric Darve, Jose Solomon, and Amirali Kia · 2009
Cited alongside, same era.
On the Curse of Memory in Recurrent Neural Networks: Approximation and Optimization Analysis
Zhong Li, Jiequn Han, Weinan E, and Qianxiao Li · 2009
Cited alongside, same era.
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Neural Lander: Stable Drone Landing Control using Learned Dynamics
Guanya Shi, Xichen Shi, Michael O’Connell, Rose Yu, Kamyar Azizzadenesheli, Animashree Anandkumar, Yisong Yue, and Soon-Jo Chung · 2018
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An extended eddy-diffusivity mass-flux scheme for unified representation of subgrid-scale turbulence and convection
Zhihong Tan, Colleen M Kaul, Kyle G Pressel, Yair Cohen, Tapio Schneider, and João Teixeira · 2018
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On the estimation of the Mori-Zwanzig memory integral
Yuanran Zhu, Jason M Dominy, and Daniele Venturi · 2018
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Learning Dynamical Systems from Partial Observations, February 2019
Ibrahim Ayed, Emmanuel de Bézenac, Arthur Pajot, Julien Brajard, and Patrick Gallinari · 2019
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Data-driven discovery of coordinates and governing equations
Kathleen Champion, Bethany Lusch, J. Nathan Kutz, and Steven L. Brunton · 2019
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Turbulence modeling in the age of data
Karthik Duraisamy, Gianluca Iaccarino, and Heng Xiao · 2019
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A Priori Estimates of the Population Risk for Two-layer Neural Networks
Weinan E, Chao Ma, and Lei Wu · 2019
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Machine-learning error models for approximate solutions to parameterized systems of nonlinear equations
Brian A. Freno and Kevin T. Carlberg · 2019
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Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) network
Alex Sherstinsky · 2019
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Operator-theoretic framework for forecasting nonlinear time series with kernel analog techniques
Romeo Alexander and Dimitrios Giannakis · 2020
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Variance continuity for Lorenz flows
Wael Bahsoun, Ian Melbourne, and Marks Ruziboev · 2020
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Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization
Marc Bocquet, Julien Brajard, Alberto Carrassi, and Laurent Bertino · 2020
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Effective models and predictability of chaotic multiscale systems via machine learning
Francesco Borra, Angelo Vulpiani, and Massimo Cencini · 2020
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Combining data assimilation and machine learning to infer unresolved scale parametrization
Julien Brajard, Alberto Carrassi, Marc Bocquet, and Laurent Bertino · 2020
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Data-driven predictions of a multiscale Lorenz 96 chaotic system using machine-learning methods: reservoir computing, artificial neural network, and long short-term memory network
Ashesh Chattopadhyay, Pedram Hassanzadeh, and Devika Subramanian · 2020
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Kernel-based prediction of non-Markovian time series
Faheem Gilani, Dimitrios Giannakis, and John Harlim · 2020
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Probability and random processes
Geoffrey Grimmett and David Stirzaker · 2020
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Learning dynamical systems from data: A simple cross-validation perspective, part I: Parametric kernel flows
Boumediene Hamzi and Houman Owhadi · 2020
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Machine learning for prediction with missing dynamics
John Harlim, Shixiao W. Jiang, Senwei Liang, and Haizhao Yang · 2020
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Physics-informed machine learning: case studies for weather and climate modelling
K. Kashinath, M. Mustafa, A. Albert, J-L. Wu, C. Jiang, S. Esmaeilzadeh, K. Azizzadenesheli, R. Wang, A. Chattopadhyay, A. Singh, A. Manepalli, D. Chirila, R. Yu, R. Walters, B. White, H. Xiao, H. A. Tchelepi, P. Marcus, A. Anandkumar, P. Hassanzadeh, and null Prabhat · 2020
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Data-driven spectral analysis of the Koopman operator
Milan Korda, Mihai Putinar, and Igor Mezić · 2020
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Data-driven model reduction, Wiener projections, and the Koopman-Mori-Zwanzig formalism
Kevin K. Lin and Fei Lu · 2020
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Partial Observations and Conservation Laws: Gray-Box Modeling in Biotechnology and Optogenetics
Robert J. Lovelett, José L. Avalos, and Ioannis G. Kevrekidis · 2020
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Data-Driven Model Reduction for Stochastic Burgers Equations
Fei Lu · 2020
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Learning latent dynamics for partially observed chaotic systems
S. Ouala, D. Nguyen, L. Drumetz, B. Chapron, A. Pascual, F. Collard, L. Gaultier, and R. Fablet · 2020
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Domain-driven models yield better predictions at lower cost than reservoir computers in Lorenz systems
Ryan Pyle, Nikola Jovanovic, Devika Subramanian, Krishna V. Palem, and Ankit B. Patel · 2020
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Extracting structured dynamical systems using sparse optimization with very few samples
Hayden Schaeffer, Giang Tran, Rachel Ward, and Linan Zhang · 2020
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EikoNet: Solving the Eikonal Equation With Deep Neural Networks
Jonathan D. Smith, Kamyar Azizzadenesheli, and Zachary E. Ross · 2020
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SciPy 1.0: fundamental algorithms for scientific computing in Python
Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, Stéfan J. van der Walt, Matthew Brett, Joshua Wilson, K. Jarrod Millman, Nikolay Mayorov, Andrew R. J. Nelson, Eric Jones, Robert Kern, Eric Larson, C. J. Carey, Ilhan Polat, Yu Feng, Eric W. Moore, Jake VanderPlas, Denis Laxalde, Josef Perktold, Robert Cimrman, Ian Henriksen, E. A. Quintero, Charles R. Harris, Anne M. Archibald, Antônio H. Ribeiro, Fabian Pedregosa, and Paul van Mulbregt · 2020
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Backpropagation algorithms and Reservoir Computing in Recurrent Neural Networks for the forecasting of complex spatiotemporal dynamics
P.R. Vlachas, J. Pathak, B.R. Hunt, T.P. Sapsis, M. Girvan, E. Ott, and P. Koumoutsakos · 2020
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Recurrent neural network closure of parametric POD-Galerkin reduced-order models based on the Mori-Zwanzig formalism
Qian Wang, Nicolò Ripamonti, and Jan S Hesthaven · 2020
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Combining machine learning with knowledge-based modeling for scalable forecasting and subgrid-scale closure of large, complex, spatiotemporal systems
Alexander Wikner, Jaideep Pathak, Brian Hunt, Michelle Girvan, Troy Arcomano, Istvan Szunyogh, Andrew Pomerance, and Edward Ott · 2020
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Bubbles in turbulent flows: Data-driven, kinematic models with history terms
Zhong Yi Wan, Petr Karnakov, Petros Koumoutsakos, and Themistoklis P. Sapsis · 2020
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Estimating linear response statistics using orthogonal polynomials: An RKHS formulation
He Zhang, John Harlim, Xiantao Li, ,Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA, and ,Department of Mathematics, Department of Meteorology and Atmospheric Science, Institute for Computational and Data Sciences, The Pennsylvania State University, University Park, PA 16802, USA · 2020
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