Fetching the paper…
Reading the bibliography…
A data-driven framework is proposed towards the end of predictive modeling of complex spatio-temporal dynamics, leveraging nested non-linear manifolds.
1903
Earlier work this paper cites.
1906
Earlier work this paper cites.
1907
Earlier work this paper cites.
1907
Earlier work this paper cites.
1907
Earlier work this paper cites.
1908
Earlier work this paper cites.
1911
Earlier work this paper cites.
G. A. Sod, A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws, Journal of computational physics 27 (1) (1978) 1–31
1978
Earlier work this paper cites.
B. Moore, Principal component analysis in linear systems: Controllability, observability, and model reduction, IEEE transactions on automatic control 26 (1) (1981) 17–32
1981
Earlier work this paper cites.
D. E. Rumelhart, G. E. Hinton, R. J. Williams, et al., Learning representations by back-propagating errors, Cognitive modeling 5 (3) (1988) 1
1988
Earlier work this paper cites.
D. C. Wilcox, Reassessment of the scale-determining equation for advanced turbulence models, AIAA journal 26 (11) (1988) 1299–1310
1988
Earlier work this paper cites.
M. G. Safonov, R. Chiang, A Schur method for balanced-truncation model reduction, IEEE Transactions on Automatic Control 34 (7) (1989) 729–733
1989
Earlier work this paper cites.
J. S. Peterson, The reduced basis method for incompressible viscous flow calculations, SIAM Journal on Scientific and Statistical Computing 10 (4) (1989) 777–786
1989
Earlier work this paper cites.
J. L. Elman, Finding structure in time, Cognitive science 14 (2) (1990) 179–211
1990
Earlier work this paper cites.
G. Berkooz, P. Holmes, J. L. Lumley, The proper orthogonal decomposition in the analysis of turbulent flows, Annual review of fluid mechanics 25 (1) (1993) 539–575
1993
Earlier work this paper cites.
D. DeMers, G. W. Cottrell, Non-linear dimensionality reduction, in: Advances in neural information processing systems, 580–587, 1993
1993
Earlier work this paper cites.
V. Barthelmann, E. Novak, K. Ritter, High dimensional polynomial interpolation on sparse grids, Advances in Computational Mathematics 12 (4) (2000) 273–288
2000
Earlier work this paper cites.
C. Prud’Homme, D. V. Rovas, K. Veroy, L. Machiels, Y. Maday, A. T. Patera, G. Turinici, Reliable real-time solution of parametrized partial differential equations: Reduced-basis output bound methods, J. Fluids Eng. 124 (1) (2001) 70–80
2001
Earlier work this paper cites.
D. Eck, J. Schmidhuber, A first look at music composition using lstm recurrent neural networks, Istituto Dalle Molle Di Studi Sull Intelligenza Artificiale 103 (2002) 48
2002
Earlier work this paper cites.
C. W. Rowley, T. Colonius, R. M. Murray, Model reduction for compressible flows using POD and Galerkin projection, Physica D: Nonlinear Phenomena 189 (1-2) (2004) 115–129
2004
Earlier work this paper cites.
P. Astrid, Reduction of process simulation models: a proper orthogonal decomposition approach, Technische Universiteit Eindhoven Eindhoven, Netherlands, 2004
2004
Earlier work this paper cites.
M. Barrault, Y. Maday, N. C. Nguyen, A. T. Patera, An ‘empirical interpolation’method: application to efficient reduced-basis discretization of partial differential equations, Comptes Rendus Mathematique 339 (9) (2004) 667–672
2004
Earlier work this paper cites.
C. W. Rowley, Model reduction for fluids, using balanced proper orthogonal decomposition, International Journal of Bifurcation and Chaos 15 (03) (2005) 997–1013
2005
Cited alongside, same era.
M. Couplet, C. Basdevant, P. Sagaut, Calibrated reduced-order POD-Galerkin system for fluid flow modelling, Journal of Computational Physics 207 (1) (2005) 192–220
2005
Cited alongside, same era.
D. Lee, N. Sezer-Uzol, J. F. Horn, L. N. Long, Simulation of helicopter shipboard launch and recovery with time-accurate airwakes, Journal of Aircraft 42 (2) (2005) 448–461
2005
Cited alongside, same era.
G. Rozza, D. B. P. Huynh, A. T. Patera, Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations, Archives of Computational Methods in Engineering 15 (3) (2007) 1
2007
Cited alongside, same era.
X. Guo, W. Li, F. Iorio, Convolutional neural networks for steady flow approximation, in: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, ACM, 481–490, 2016
2016
Later among the works it cites.
Z. Drmac, S. Gugercin, A new selection operator for the discrete empirical interpolation method—Improved a priori error bound and extensions, SIAM Journal on Scientific Computing 38 (2) (2016) A631–A648
2016
Later among the works it cites.
S. L. Brunton, J. L. Proctor, J. N. Kutz, Discovering governing equations from data by sparse identification of nonlinear dynamical systems, Proceedings of the National Academy of Sciences 113 (15) (2016) 3932–3937
2016
Later among the works it cites.
Y. Wang, M. Huang, X. Zhu, L. Zhao, Attention-based LSTM for aspect-level sentiment classification, in: Proceedings of the 2016 conference on empirical methods in natural language processing, 606–615, 2016
2016
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
I. Danaila, P. Joly, S. M. Kaber, M. Postel, Gas Dynamics: The Riemann Problem and Discontinuous Solutions: Application to the Shock Tube Problem, in: Introduction to scientific computing, Springer, New York, NY, 213–233, 2007
2007
Cited alongside, same era.
P. Astrid, S. Weiland, K. Willcox, T. Backx, Missing point estimation in models described by proper orthogonal decomposition, IEEE Transactions on Automatic Control 53 (10) (2008) 2237–2251
2008
Cited alongside, same era.
S. Chaturantabut, D. C. Sorensen, Discrete empirical interpolation for nonlinear model reduction, in: Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on, IEEE, 4316–4321, 2009
2009
Cited alongside, same era.
U. Baur, C. Beattie, P. Benner, S. Gugercin, Interpolatory projection methods for parameterized model reduction, SIAM Journal on Scientific Computing 33 (5) (2011) 2489–2518
2011
Cited alongside, same era.
K. Carlberg, C. Bou-Mosleh, C. Farhat, Efficient non-linear model reduction via a least-squares Petrov–Galerkin projection and compressive tensor approximations, International Journal for Numerical Methods in Engineering 86 (2) (2011) 155–181
2011
Cited alongside, same era.
Z. Wang, I. Akhtar, J. Borggaard, T. Iliescu, Two-level discretizations of nonlinear closure models for proper orthogonal decomposition, Journal of Computational Physics 230 (1) (2011) 126–146
2011
Cited alongside, same era.
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.
C. Gu, QLMOR: A projection-based nonlinear model order reduction approach using quadratic-linear representation of nonlinear systems, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 30 (9) (2011) 1307–1320
2011
Cited alongside, same era.
K. Carlberg, M. Barone, H. Antil, Galerkin v. least-squares Petrov–Galerkin projection in nonlinear model reduction, Journal of Computational Physics 330 (2017) 693–734
2017
Later among the works it cites.
A. Gouasmi, E. J. Parish, K. Duraisamy, A priori estimation of memory effects in reduced-order models of nonlinear systems using the Mori–Zwanzig formalism, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473 (2205) (2017) 20170385
2017
Later among the works it cites.
D. Hartman, L. K. Mestha, A deep learning framework for model reduction of dynamical systems, in: 2017 IEEE Conference on Control Technology and Applications (CCTA), IEEE, 1917–1922, 2017
2017
Later among the works it cites.
C. Lea, M. D. Flynn, R. Vidal, A. Reiter, G. D. Hager, Temporal convolutional networks for action segmentation and detection, in: proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 156–165, 2017
2017
Later among the works it cites.
Y. N. Dauphin, A. Fan, M. Auli, D. Grangier, Language modeling with gated convolutional networks, in: International conference on machine learning, 933–941, 2017
2017
Later among the works it cites.
C. Huang, J. Xu, K. Duraisamy, C. Merkle, Exploration of reduced-order models for rocket combustion applications, in: 2018 AIAA Aerospace Sciences Meeting, 1183, 2018
2018
Later among the works it cites.
S. C. Puligilla, B. Jayaraman, Deep multilayer convolution frameworks for data-driven learning of fluid flow dynamics, in: 2018 Fluid Dynamics Conference, 3091, 2018
2018
Later among the works it cites.
M. Guo, J. S. Hesthaven, Reduced order modeling for nonlinear structural analysis using gaussian process regression, Computer Methods in Applied Mechanics and Engineering 341 (2018) 807–826
2018
Later among the works it cites.
J. S. Hesthaven, S. Ubbiali, Non-intrusive reduced order modeling of nonlinear problems using neural networks, Journal of Computational Physics 363 (2018) 55–78
2018
Later among the works it cites.
X. Qing, Y. Niu, Hourly day-ahead solar irradiance prediction using weather forecasts by LSTM, Energy 148 (2018) 461–468
2018
Later among the works it cites.
J. Xu, C. Huang, K. Duraisamy, Reduced-Order Modeling Framework for Combustor Instabilities Using Truncated Domain Training, AIAA Journal (2019) 1–15
2019
Closest in time.
N. Omata, S. Shirayama, A novel method of low-dimensional representation for temporal behavior of flow fields using deep autoencoder, AIP Advances 9 (1) (2019) 015006
2019
Closest in time.
Q. Wang, J. S. Hesthaven, D. Ray, Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem, Journal of computational physics 384 (2019) 289–307
2019
Closest in time.
C. Huang, K. Duraisamy, C. L. Merkle, Investigations and improvement of robustness of reduced-order models of reacting flow, AIAA Journal 57 (12) (2019) 5377–5389
2019
Closest in time.
M. Raissi, P. Perdikaris, G. E. Karniadakis, Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, Journal of Computational Physics 378 (2019) 686–707
2019
Closest in time.
R. Maulik, A. Mohan, B. Lusch, S. Madireddy, P. Balaprakash, D. Livescu, Time-series learning of latent-space dynamics for reduced-order model closure, Physica D: Nonlinear Phenomena (2020) 132368
2020
Closest in time.
C. Huang, K. Duraisamy, C. Merkle, Data-Informed Species Limiters for Local Robustness Control of Reduced-Order Models of Reacting Flow, in: AIAA Scitech 2020 Forum, 2141, 2020
2020
Closest in time.