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The numerical solution of partial differential equations (PDEs) is challenging because of the need to resolve spatiotemporal features over wide length and timescales.
N. J. Zabusky and M. D. Kruskal, Physical Review Letters 15
1965
Earlier work this paper cites.
M. Van Dyke, NASA STI/Recon Technical Report A 75
1975
Earlier work this paper cites.
A. Harten, B. Engquist, S. Osher, and S. R. Chakravarthy, Journal of computational physics , 231 (1987)
1987
Earlier work this paper cites.
C. Foias, G. R. Sell, and R. Temam, Journal of differential equations 73
1988
Earlier work this paper cites.
B. Fornberg, Mathematics of computation 51
1988
Earlier work this paper cites.
M. Marion, Journal of Dynamics and Differential Equations 1
1989
Earlier work this paper cites.
M. Jolly, I. Kevrekidis, and E. Titi, Physica D: Nonlinear Phenomena 44
1990
Earlier work this paper cites.
E. S. Titi, Journal of mathematical analysis and applications 149
1990
Earlier work this paper cites.
W. E. Schiesser, The numerical method of lines: integration of partial differential equations (Academic Press San Diego, San Diego, 1991)
1991
Earlier work this paper cites.
R. J. LeVeque, Numerical Methods for Conservation Laws (Birkhauser Verlag, 1992)
1992
Earlier work this paper cites.
R. Rico-Martinez, I. Kevrekidis, and K. Krischer, Neural networks for chemical engineers , 409 (1995)
1995
Earlier work this paper cites.
U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, 1996)
1996
Earlier work this paper cites.
C. J. Chen, Fundamentals of turbulence modelling (CRC Press, 1997)
1997
Earlier work this paper cites.
R. Gonzalez-Garcia, R. Rico-Martinez, and I. Kevrekidis, Computers & chemical engineering 22
1998
Earlier work this paper cites.
C.-W. Shu, in Advanced numerical approximation of nonlinear hyperbolic equations (Springer, 1998) pp. 325–432
1998
Cited alongside, same era.
D. Zwillinger, Handbook of differential equations (Gulf Professional Publishing, 1998)
1998
Cited alongside, same era.
J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, 1999)
1999
Cited alongside, same era.
A. Roberts, Applied numerical mathematics 37
2001
Cited alongside, same era.
I. G. Kevrekidis and G. Samaey, Annual Review of Physical Chemistry 60
2009
Cited alongside, same era.
S. Ross and D. Bagnell, in Proceedings of the 13th International Conference on Artificial Intelligence and Statistics , Vol. 9, edited by Y. W. Teh and M. Titterington (PMLR, Chia Laguna Resort, Sardinia, Italy, 2010) pp. 661–668
M. Clay, D. Buaria, T. Gotoh, and P. Yeung, Computer Physics Communications 219
2017
Later among the works it cites.
K. P. Iyer, K. R. Sreenivasan, and P. K. Yeung, Physical Review E 95
2017
Later among the works it cites.
M. Sundararajan, A. Taly, and Q. Yan, arXiv Preprint 1703.01365 (2017)
2017
Later among the works it cites.
2017
Later among the works it cites.
Y. Romano, J. Isidoro, and P. Milanfar, IEEE Transactions on Computational Imaging 3
2017
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
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2010
Cited alongside, same era.
D. Sholl and J. A. Steckel, Density functional theory: a practical introduction (Wiley & Sons, 2011)
2011
Cited alongside, same era.
P. Constantin, C. Foias, B. Nicolaenko, and R. Temam, Integral manifolds and inertial manifolds for dissipative partial differential equations , Vol. 70 (Springer Science & Business Media, 2012)
2012
Cited alongside, same era.
M. Lee and R. D. Moser, Journal of Fluid Mechanics 774
2015
Cited alongside, same era.
S. L. Brunton, J. L. Proctor, and J. N. Kutz, Proceedings of the National Academy of Sciences 113
2016
Cited alongside, same era.
J. Ling, A. Kurzawski, and J. Templeton, Journal of Fluid Mechanics 807
2016
Cited alongside, same era.
I. Goodfellow, Y. Bengio, A. Courville, and Y. Bengio, Deep learning (MIT press Cambridge, 2016)
2016
Cited alongside, same era.
J. Gilmer, S. S. Schoenholz, P. F. Riley, O. Vinyals, and G. E. Dahl, in Proceedings of the 34th International Conference on Machine Learning , Vol. 70 (PMLR, International Convention Centre, Sydney, Australia, 2017) pp. 1263–1272
2017
Later among the works it cites.
C. R. Qi, L. Yi, H. Su, and L. J. Guibas, in Advances in Neural Information Processing Systems , Vol. 30 (2017)
2017
Later among the works it cites.
2018
Closest in time.
S. Rasp, M. S. Pritchard, and P. Gentine, Proceedings of the National Academy of Sciences 115
2018
Closest in time.
E. de Bezenac, A. Pajot, and P. Gallinari, in International Conference on Learning Representations (2018)
2018
Closest in time.
B. Lusch, J. N. Kutz, and S. L. Brunton, Nature Communications 9
2018
Closest in time.
2018
Closest in time.
A. D. Beck, D. G. Flad, and C.-D. Munz, arXiv Preprint 1806.04482 (2018)
2018
Closest in time.
P. Getreuer, I. Garcia-Dorado, J. Isidoro, S. Choi, F. Ong, and P. Milanfar, in 2018 IEEE International Conference on Computational Photography (ICCP) (2018)
2018
Closest in time.