Fetching the paper…
Reading the bibliography…
The modeling and simulation of high-dimensional multiscale systems is a critical challenge across all areas of science and engineering.
B. O. Koopman, Hamiltonian Systems and Transformations in Hilbert Space , Proceedings of the National Academy of Sciences of the United States of America 17 (5) (1931) 315–318. URL https://www.jstor.org/stable/86114
1931
Earlier work this paper cites.
H. Mori, Transport, collective motion, and brownian motion, Progress of theoretical physics 33 (3) (1965) 423–455
1965
Earlier work this paper cites.
R. Zwanzig, Nonlinear generalized langevin equations, Journal of Statistical Physics 9 (3) (1973) 215–220
1973
Earlier work this paper cites.
J. M. Hyman, B. Nicolaenko, The kuramoto-sivashinsky equation: a bridge between pde’s and dynamical systems, Physica D: Nonlinear Phenomena 18 (1-3) (1986) 113–126
1986
Earlier work this paper cites.
D. C. Wilcox, Multiscale model for turbulent flows, AIAA journal 26 (11) (1988) 1311–1320
1988
Earlier work this paper cites.
J. C. Robinson, Inertial manifolds for the kuramoto-sivashinsky equation, Physics Letters A 184 (2) (1994) 190–193
1994
Earlier work this paper cites.
T. Chen, H. Chen, Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems, IEEE Transactions on Neural Networks 6 (4) (1995) 911–917
1995
Earlier work this paper cites.
S. Hochreiter, J. Schmidhuber, Long short-term memory, Neural computation 9 (8) (1997) 1735–1780
1997
Earlier work this paper cites.
A. T. Mohan, N. Lubbers, D. Livescu, M. Chertkov, Embedding hard physical constraints in neural network coarse-graining of 3d turbulence (2020) · 2002
Earlier work this paper cites.
I. G. Kevrekidis, C. W. Gear, J. M. Hyman, P. G. Kevrekidis, O. Runborg, C. Theodoropoulos, et al., Equation-free, coarse-grained multiscale computation: enabling microscopic simulators to perform system-level analysis, Commun. Math. Sci 1 (4) (2003) 715–762
2003
Earlier work this paper cites.
E. Weinan, B. Engquist, Z. Huang, Heterogeneous multiscale method: a general methodology for multiscale modeling, Physical Review B 67 (9) (2003) 092101
2003
Earlier work this paper cites.
doi:10.1002/0470013850
K. Falconer, Fractal Geometry: Mathematical Foundations and Applications, 2003 · 2003
Earlier work this paper cites.
I. G. Kevrekidis, C. W. Gear, G. Hummer, Equation-free: The computer-aided analysis of complex multiscale systems, AIChE Journal 50 (7) (2004) 1346–1355
2004
Earlier work this paper cites.
D. Givon, R. Kupferman, A. Stuart, Extracting Macroscopic Dynamics: Model Problems and Algorithms, Nonlinearity (2004)
2004
Earlier work this paper cites.
I. Mezić, Spectral properties of dynamical systems, model reduction and decompositions, Nonlinear Dynamics 41 (2005) 309–325
2005
Earlier work this paper cites.
doi:10.1175/MWR3214.1
S. K. Kar, A semi-implicit runge–kutta time-difference scheme for the two-dimensional shallow-water equations, Monthly Weather Review 134 (10) (2006) 2916–2926 · 2006
Earlier work this paper cites.
doi:https://doi.org/
K. I. V., S. Ansumali, F. C. E., C. S. S., Elements of the lattice boltzmann method i: Linear advection equation , Communications in Computational Physics 1 (4) (2006) 616–655 · 2006
Earlier work this paper cites.
E. Weinan, B. Engquist, X. Li, W. Ren, E. Vanden-Eijnden, Heterogeneous multiscale methods: a review, Communications in computational physics 2 (3) (2007) 367–450
2007
Earlier work this paper cites.
A. Chorin, P. Stinis, Problem reduction, renormalization, and memory, Communications in Applied Mathematics and Computational Science 1 (1) (2007) 1–27
2007
Earlier work this paper cites.
E. Darve, J. Solomon, A. Kia, Computing generalized langevin equations and generalized fokker–planck equations, Proceedings of the National Academy of Sciences 106 (27) (2009) 10884–10889
2009
Earlier work this paper cites.
M. Tao, H. Owhadi, J. E. Marsden, Nonintrusive and structure preserving multiscale integration of stiff odes, sdes, and hamiltonian systems with hidden slow dynamics via flow averaging, Multiscale Modeling & Simulation 8 (4) (2010) 1269–1324
2010
Earlier work this paper cites.
P. J. Schmid, Dynamic mode decomposition of numerical and experimental data, Journal of fluid mechanics 656 (2010) 5–28
2010
Earlier work this paper cites.
arXiv:https://doi.org/10.1137/100813051
D. Amsallem, C. Farhat, An online method for interpolating linear parametric reduced-order models , SIAM Journal on Scientific Computing 33 (5) (2011) 2169–2198 · 2011
Cited alongside, same era.
N. R. Council, A National Strategy for Advancing Climate Modeling, The National Academies Press, 2012
2012
Cited alongside, same era.
M. Budišić, R. Mohr, I. Mezić, Applied koopmanism, Chaos: An Interdisciplinary Journal of Nonlinear Science 22 (4) (2012) 047510
2012
Cited alongside, same era.
C. Rocsoreanu, A. Georgescu, N. Giurgiteanu, The FitzHugh-Nagumo model: bifurcation and dynamics, Vol. 10, Springer Science & Business Media, 2012
2012
Cited alongside, same era.
I. Mezić, Analysis of fluid flows via spectral properties of the koopman operator, Annual review of fluid mechanics 45 (2013) 357–378
2013
Cited alongside, same era.
Y. Choi, K. Carlberg, Space–time least-squares petrov–galerkin projection for nonlinear model reduction, SIAM Journal on Scientific Computing 41 (1) (2019) A26–A58
2019
Later among the works it cites.
K. P. Champion, S. L. Brunton, J. N. Kutz, Discovery of nonlinear multiscale systems: Sampling strategies and embeddings, SIAM Journal on Applied Dynamical Systems 18 (1) (2019) 312–333
2019
Later among the works it cites.
J. L. Callaham, K. Maeda, S. L. Brunton, Robust flow reconstruction from limited measurements via sparse representation, Physical Review Fluids 4 (10) (2019) 103907
2019
Later among the works it cites.
K. Lee, K. T. Carlberg, Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders, Journal of Computational Physics 404 (2020) 108973
2020
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
J. Koutnik, K. Greff, F. Gomez, J. Schmidhuber, A clockwork rnn, in: International conference on machine learning, PMLR, 2014, pp. 1863–1871
2014
Cited alongside, same era.
doi:10.1038/526032a
T. Palmer, Modelling: Build imprecise supercomputers , Nature 526 (7571) (2015) 32–33 · 2015
Cited alongside, same era.
doi:https://doi.org/10.1016/j.cma.2015.03.018
B. Peherstorfer, K. Willcox, Dynamic data-driven reduced-order models , Computer Methods in Applied Mechanics and Engineering 291 (2015) 21–41 · 2015
Cited alongside, same era.
M. O. Williams, I. G. Kevrekidis, C. W. Rowley, A data–driven approximation of the koopman operator: Extending dynamic mode decomposition, Journal of Nonlinear Science 25 (2015) 1307–1346
2015
Cited alongside, same era.
N. Srivastava, E. Mansimov, R. Salakhudinov, Unsupervised learning of video representations using lstms, in: International conference on machine learning, PMLR, 2015, pp. 843–852
2015
Cited alongside, same era.
D. Kondrashov, M. D. Chekroun, M. Ghil, Data-driven non-markovian closure models, Physica D: Nonlinear Phenomena 297 (2015) 33–55
2015
Cited alongside, same era.
A. Mahadevan, The impact of submesoscale physics on primary productivity of plankton, Annual review of marine science 8 (2016) 161–184
2016
Cited alongside, same era.
2020
Later among the works it cites.
S. Kaltenbach, P.-S. Koutsourelakis, Incorporating physical constraints in a deep probabilistic machine learning framework for coarse-graining dynamical systems, Journal of Computational Physics 419 (2020) 109673
2020
Later among the works it cites.
2020
Later among the works it cites.
S. Kaltenbach, P. S. Koutsourelakis, Physics-aware, probabilistic model order reduction with guaranteed stability , in: International Conference on Learning Representations (ICLR), 2021. URL https://openreview.net/forum?id=vyY0jnWG-tK
2021
Later among the works it cites.
doi:10.1038/s42256-020-00272-0
G. Novati, H. L. de Laroussilhe, P. Koumoutsakos, Automating turbulence modelling by multi-agent reinforcement learning , Nat. Mach. Intell. 3 (1) (2021) 87–96 · 2021
Later among the works it cites.
2021
Later among the works it cites.
Y. T. Lin, Y. Tian, M. Anghel, D. Livescu, Data-driven learning for the mori-zwanzig formalism: a generalization of the koopman learning framework (2021)
2021
Later among the works it cites.
L. Lu, P. Jin, G. Pang, Z. Zhang, G. E. Karniadakis, Learning nonlinear operators via deeponet based on the universal approximation theorem of operators, Nature machine intelligence 3 (3) (2021) 218–229
2021
Later among the works it cites.
Z. Li, N. B. Kovachki, K. Azizzadenesheli, B. liu, K. Bhattacharya, A. Stuart, A. Anandkumar, Fourier neural operator for parametric partial differential equations , in: International Conference on Learning Representations, 2021. URL https://openreview.net/forum?id=c8P9NQVtmnO
2021
Later among the works it cites.
E. Menier, M. A. Bucci, M. Yagoubi, L. Mathelin, M. Schoenauer, Cd-rom: Complementary deep-reduced order model (2022) · 2022
Later among the works it cites.
P. R. Vlachas, G. Arampatzis, C. Uhler, P. Koumoutsakos, Multiscale simulations of complex systems by learning their effective dynamics, Nature Machine Intelligence 4 (4) (2022) 359–366
2022
Later among the works it cites.
doi:https://doi.org/10.1016/j.cma.2022.115717
R. Geelen, S. Wright, K. Willcox, Operator inference for non-intrusive model reduction with quadratic manifolds , Computer Methods in Applied Mechanics and Engineering 403 (2023) 115717 · 2022
Later among the works it cites.
G. Kissas, J. H. Seidman, L. F. Guilhoto, V. M. Preciado, G. J. Pappas, P. Perdikaris, Learning operators with coupled attention, Journal of Machine Learning Research 23 (215) (2022) 1–63
2022
Later among the works it cites.
doi:10.1007/978-3-030-67902-6_24
M. Bucci, O. Semeraro, A. Allauzen, L. Cordier, L. Mathelin, Nonlinear Optimal Control Using Deep Reinforcement Learning, 2022, pp. 279–290 · 2022
Later among the works it cites.
2023
Closest in time.
M. Mannattil, Nolitsa (nonlinear time series analysis), https://github.com/manu-mannattil/nolitsa (2023)
2023
Closest in time.
I. Kičić, P. R. Vlachas, G. Arampatzis, M. Chatzimanolakis, L. Guibas, P. Koumoutsakos, Adaptive learning of effective dynamics: Adaptive real-time, online modeling for complex systems (2023) · 2023
Closest in time.