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This work presents a non-intrusive surrogate modeling scheme based on machine learning technology for predictive modeling of complex systems, described by parametrized time-dependent PDEs.
doi:10.1137/S0036142901389049
M. Rathinam, L. R. Petzold, A new look at proper orthogonal decomposition, SIAM Journal on Numerical Analysis 41 (5) (2003) 1893–1925 · 1925
Earlier work this paper cites.
A. G. Brady, C. Rojahn, V. Perez, P. Carydis, J. Shokos, Seismic engineering data report: Romanian and greek records, 1972-77, U.S. Geological Survey, USGS Numbered Series (1978)
1978
Earlier work this paper cites.
doi:10.1109/TAC.1981.1102568
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.
doi:10.1109/TCOM.1983.1095851
P. Burt, E. Adelson, The laplacian pyramid as a compact image code, IEEE Transactions on Communications 31 (4) (1983) 532–540 · 1983
Earlier work this paper cites.
D. Rumelhart, G. Hinton, R. Williams, Learning representations by back-propagating errors, Nature 323 (1986) 533 – 536
1986
Earlier work this paper cites.
doi:10.1109/9.29399
M. G. Safonov, R. Y. 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.
M. Buscema, Back propagation neural networks, Substance use & misuse 33 (1998) 233–70
1998
Earlier work this paper cites.
doi:https://doi.org/10.1006/jmaa.2000.6994
J. Baker, A. Armaou, P. D. Christofides, Nonlinear control of incompressible fluid flow: Application to burgers’ equation and 2d channel flow, Journal of Mathematical Analysis and Applications 252 (1) (2000) 230 – 255 · 2000
Earlier work this paper cites.
M. Belkin, P. Niyogi, Laplacian eigenmaps for dimensionality reduction and data representation, Neural Comput. 15 (6) (2003) 1373–1396
2003
Earlier work this paper cites.
doi:https://doi.org/10.1016/S0167-4730(02)00039-5
A. Olsson, G. Sandberg, O. Dahlblom, On latin hypercube sampling for structural reliability analysis, Structural Safety 25 (1) (2003) 47 – 68 · 2003
Earlier work this paper cites.
D. J. Lucia, P. S. Beran, W. A. Silva, Reduced-order modeling: new approaches for computational physics, Progress in Aerospace Sciences 40 (1) (2004) 51 – 117
2004
Earlier work this paper cites.
doi:https://doi.org/10.1016/j.compstruc.2004.07.008
T. K. Sengupta, S. Dey, Proper orthogonal decomposition of direct numerical simulation data of by-pass transition, Computers & Structures 82 (31) (2004) 2693–2703, nonlinear Dynamics of Continuous Systems · 2004
Earlier work this paper cites.
doi:10.1137/S1064827502419154
Z. Zhang, H. Zha, Principal manifolds and nonlinear dimensionality reduction via tangent space alignment, SIAM Journal on Scientific Computing 26 (1) (2004) 313–338 · 2004
Earlier work this paper cites.
doi:https://doi.org/10.1016/j.acha.2005.07.005
R. R. Coifman, S. Lafon, Geometric harmonics: A novel tool for multiscale out-of-sample extension of empirical functions, Applied and Computational Harmonic Analysis 21 (1) (2006) 31 – 52, special Issue: Diffusion Maps and Wavelets · 2005
Earlier work this paper cites.
doi:https://doi.org/10.1016/j.acha.2006.04.006
R. R. Coifman, S. Lafon, Diffusion maps, Applied and Computational Harmonic Analysis 21 (1) (2006) 5 – 30, special Issue: Diffusion Maps and Wavelets · 2006
Earlier work this paper cites.
doi:https://doi.org/10.1016/j.compstruc.2007.01.013
A. de Boer, M. van der Schoot, H. Bijl, Mesh deformation based on radial basis function interpolation, Computers & Structures 85 (11) (2007) 784–795, fourth MIT Conference on Computational Fluid and Solid Mechanics · 2007
Earlier work this paper cites.
doi:10.2514/1.35374
D. Amsallem, C. Farhat, Interpolation method for adapting reduced-order models and application to aeroelasticity, American Institute of Aeronautics and Astronautics 46 (7) (2008) 1803–1813 · 2008
Earlier work this paper cites.
N. C. Nguyen, J. Peraire, An efficient reduced-order modeling approach for non-linear parametrized partial differential equations, International Journal for Numerical Methods in Engineering 76 (1) (2008) 27–55
2008
Earlier work this paper cites.
S. Chaturantabut, D. C. Sorensen, Nonlinear model reduction via discrete empirical interpolation, SIAM Journal on Scientific Computing 32 (5) (2010) 2737–2764
2010
Cited alongside, same era.
F. Chinesta, A. Ammar, A. Leygue, R. Keunings, An overview of the proper generalized decomposition with applications in computational rheology, Journal of Non-Newtonian Fluid Mechanics 166 (11) (2011) 578 – 592
2011
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.
J. Masci, U. Meier, D. Ciresan, J. Schmidhuber, Stacked convolutional auto-encoders for hierarchical feature extraction, Proc. 21th International Conference on Artificial Neural Networks (2011) pp 52 – 59
2011
Cited alongside, same era.
doi:10.5815/ijigsp.2016.03.03
O. Oyedotun, K. Dimililer, Pattern recognition: Invariance learning in convolutional auto encoder network, International Journal of Image, Graphics and Signal Processing 8 (2016) 19–27 · 2016
Later among the works it cites.
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, KDD ’16, Association for Computing Machinery, 2016, p. 481–490
2016
Later among the works it cites.
A. van den Oord, S. Dieleman, H. Zen, K. Simonyan, O. Vinyals, A. Graves, N. Kalchbrenner, A. Senior, K. Kavukcuoglu, Wavenet: A generative model for raw audio (2016) · 2016
Later among the works it cites.
M. Hasan, J. Choi, J. Neumann, A. Roy-Chowdhury, L. Davis, Learning temporal regularity in video sequences, Proc. IEEE Conf. on Computer Vision and Pattern Recognition (2016)
2016
Later among the works it cites.
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A. Krizhevsky, G. Hinton, Using very deep autoencoders for content based image retrieval, Proc. 19th European Symp. on Artificial Neural Networks (2011)
2011
Cited alongside, same era.
doi:10.1002/nme.4371
D. Amsallem, M. J. Zahr, C. Farhat, Nonlinear model order reduction based on local reduced-order bases, International Journal for Numerical Methods in Engineering 92 (10) (2012) 891–916 · 2012
Cited alongside, same era.
M. P. Mignolet, A. Przekop, S. A. Rizzi, S. M. Spottswood, A review of indirect/non-intrusive reduced order modeling of nonlinear geometric structures, Journal of Sound and Vibration 332 (10) (2013) 2437 – 2460
2013
Cited alongside, same era.
J. P. M. de Almeida, A basis for bounding the errors of proper generalised decomposition solutions in solid mechanics, International Journal for Numerical Methods in Engineering 94 (10) (2013) 961–984
2013
Cited alongside, same era.
doi:10.2514/1.C032062
K. H. Park, S. O. Jun, S. M. Baek, M. H. Cho, K. J. Yee, D. H. Lee, Reduced-order model with an artificial neural network for aerostructural design optimization, Journal of Aircraft 50 (4) (2013) 1106–1116 · 2013
Cited alongside, same era.
doi:https://doi.org/10.1016/j.cam.2014.09.011
Q. Ye, W. Zhi, Discrete hessian eigenmaps method for dimensionality reduction, Journal of Computational and Applied Mathematics 278 (2015) 197 – 212 · 2014
Cited alongside, same era.
D. Kingma, J. Ba, Adam: A method for stochastic optimization, International Conference on Learning Representations (12 2014)
2014
Cited alongside, same era.
doi:10.1002/nme.4820
C. Farhat, T. Chapman, P. Avery, Structure-preserving, stability, and accuracy properties of the energy-conserving sampling and weighting method for the hyper reduction of nonlinear finite element dynamic models, International Journal for Numerical Methods in Engineering 102 (5) (2015) 1077–1110 · 2015
Cited alongside, same era.
J. 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.
doi:https://doi.org/10.1016/j.cma.2018.07.017
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.
2018
Later among the works it cites.
A. Baydin, B. Pearlmutter, A. Radul, J. Siskind, Automatic differentiation in machine learning: A survey, Journal of Machine Learning Research 18 (2018) 1–43
2018
Later among the works it cites.
C. Nwankpa, W. Ijomah, A. Gachagan, S. Marshall, Activation functions: Comparison of trends in practice and research for deep learning (11 2018)
2018
Later among the works it cites.
doi:10.1109/CVPR.2019.00463
N. Kolotouros, G. Pavlakos, K. Daniilidis, Convolutional mesh regression for single-image human shape reconstruction, 2019, pp. 4496–4505 · 2019
Later among the works it cites.
doi:10.1109/CAC48633.2019.8996842
X. Zhao, X. Han, W. Su, Z. Yan, Time series prediction method based on convolutional autoencoder and lstm, 2019, pp. 5790–5793 · 2019
Later among the works it cites.
doi:https://doi.org/10.1016/j.compstruc.2019.05.015
G. Noh, K.-J. Bathe, For direct time integrations: A comparison of the newmark and ρ i n f t y \rho^{infty} -bathe schemes, Computers & Structures 225 (2019) 106079 · 2019
Later among the works it cites.
doi:https://doi.org/10.1016/j.compstruc.2020.106358
T. Zhou, Y. Peng, Kernel principal component analysis-based gaussian process regression modelling for high-dimensional reliability analysis, Computers & Structures 241 (2020) 106358 · 2020
Later among the works it cites.
doi:10.1002/nme.6236
I. Kalogeris, V. Papadopoulos, Diffusion maps-based surrogate modeling: An alternative machine learning approach, International Journal for Numerical Methods in Engineering 121 (4) (2020) 602–620 · 2020
Later among the works it cites.
doi:https://doi.org/10.1016/B978-0-12-815739-8.00011-0
W. H. Lopez Pinaya, S. Vieira, R. Garcia-Dias, A. Mechelli, Chapter 11 - autoencoders, in: A. Mechelli, S. Vieira (Eds.), Machine Learning, Academic Press, 2020, pp. 193 – 208 · 2020
Later among the works it cites.
doi:https://doi.org/10.1016/j.cma.2020.113379
J. Xu, K. Duraisamy, Multi-level convolutional autoencoder networks for parametric prediction of spatio-temporal dynamics , Computer Methods in Applied Mechanics and Engineering 372 (2020) 113379 · 2020
Later among the works it cites.
doi:https://doi.org/10.3182/20130904-3-FR-2041.00155
B. Lombard, D. Matignon, Y. Le Gorrec, A fractional burgers equation arising in nonlinear acoustics: theory and numerics, IFAC Proceedings Volumes 46 (23) (2013) 406 – 411, 9th IFAC Symposium on Nonlinear Control Systems · 2041
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