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Numerical simulations on fluid dynamics problems primarily rely on spatially or/and temporally discretization of the governing equation into the finite-dimensional algebraic system solved by computers.
1901
Earlier work this paper cites.
1901
Earlier work this paper cites.
1901
Earlier work this paper cites.
1902
Earlier work this paper cites.
1903
Earlier work this paper cites.
1906
Earlier work this paper cites.
H. Lee, I. S. Kang, Neural algorithm for solving differential equations, Journal of Computational Physics 91 (1) (1990) 110–131
1990
Earlier work this paper cites.
J. D. Anderson, J. Wendt, Computational fluid dynamics, Vol. 206, Springer, 1995
1995
Earlier work this paper cites.
F. Scarselli, A. C. Tsoi, Universal approximation using feedforward neural networks: A survey of some existing methods, and some new results, Neural networks 11 (1) (1998) 15–37
1998
Earlier work this paper cites.
I. E. Lagaris, A. Likas, D. I. Fotiadis, Artificial neural networks for solving ordinary and partial differential equations, IEEE Transactions on Nneural Networks 9 (5) (1998) 987–1000
1998
Earlier work this paper cites.
M. C. Kennedy, A. O’Hagan, Predicting the output from a complex computer code when fast approximations are available, Biometrika 87 (1) (2000) 1–13
2000
Earlier work this paper cites.
I. E. Lagaris, A. C. Likas, D. G. Papageorgiou, Neural-network methods for boundary value problems with irregular boundaries, IEEE Transactions on Neural Networks 11 (5) (2000) 1041–1049
2000
Earlier work this paper cites.
S. Berger, L.-D. Jou, Flows in stenotic vessels, Annual review of fluid mechanics 32 (1) (2000) 347–382
2000
Earlier work this paper cites.
D. Xiu, G. E. Karniadakis, The wiener–askey polynomial chaos for stochastic differential equations, SIAM Journal on Scientific Computing 24 (2) (2002) 619–644
2002
Earlier work this paper cites.
J. L. Brisman, J. K. Song, D. W. Newell, Cerebral aneurysms, New England journal of medicine 355 (9) (2006) 928–939
2006
Earlier work this paper cites.
R. G. Regis, C. A. Shoemaker, A stochastic radial basis function method for the global optimization of expensive functions, INFORMS Journal on Computing 19 (4) (2007) 497–509
2007
Earlier work this paper cites.
H. Jasak, A. Jemcov, U. Kingdom, OpenFOAM: A C++ library for complex physics simulations, in: International Workshop on Coupled Methods in Numerical Dynamics, IUC, 2007, pp. 1–20
2007
Earlier work this paper cites.
H. N. Najm, Uncertainty quantification and polynomial chaos techniques in computational fluid dynamics, Annual Review of Fluid Mechanics 41 (2009) 35–52
2009
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
Earlier work this paper cites.
W.-X. Ren, H.-B. Chen, Finite element model updating in structural dynamics by using the response surface method, Engineering Structures 32 (8) (2010) 2455–2465
2010
Cited alongside, same era.
O. Le Maître, O. M. Knio, Spectral methods for uncertainty quantification: with applications to computational fluid dynamics, Springer Science & Business Media, 2010
2010
Cited alongside, same era.
X. Glorot, Y. Bengio, Understanding the difficulty of training deep feedforward neural networks, in: In Proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS’10). Society for Artificial Intelligence and Statistics, 2010
2010
Cited alongside, same era.
J. R. Cebral, F. Mut, J. Weir, C. M. Putman, Association of hemodynamic characteristics and cerebral aneurysm rupture, American Journal of Neuroradiology 32 (2) (2011) 264–270
2011
Cited alongside, same era.
C. Beck, E. Weinan, A. Jentzen, Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations, Journal of Nonlinear Science (2017) 1–57
2017
Later among the works it cites.
A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga, A. Lerer, Automatic differentiation in PyTorch, in: NIPS Autodiff Workshop, 2017
2017
Later among the works it cites.
C. Huang, K. Duraisamy, C. Merkle, Challenges in reduced order modeling of reacting flows, in: 2018 Joint Propulsion Conference, 2018, p. 4675
2018
Later among the works it cites.
J.-X. Wang, C. J. Roy, H. Xiao, Propagation of input uncertainty in presence of model-form uncertainty: a multifidelity approach for computational fluid dynamics applications, ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering 4 (1) (2018) 011002
2018
Later among the works it cites.
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F. Bastien, P. Lamblin, R. Pascanu, J. Bergstra, I. J. Goodfellow, A. Bergeron, N. Bouchard, Y. Bengio, Theano: new features and speed improvements. deep learning and unsupervised feature learning, in: Neural Information Processing Systems Workshop (NIPS), 2012, pp. 1–10
2012
Cited alongside, same era.
N. Chalouhi, B. L. Hoh, D. Hasan, Review of cerebral aneurysm formation, growth, and rupture, Stroke 44 (12) (2013) 3613–3622
2013
Cited alongside, same era.
A. L. Maas, A. Y. Hannun, A. Y. Ng, Rectifier nonlinearities improve neural network acoustic models, in: Proceedings of the 30th Annual International Conference on Machine Learning, Vol. 30, 2013, p. 3
2013
Cited alongside, same era.
T. Lassila, A. Manzoni, A. Quarteroni, G. Rozza, Model order reduction in fluid dynamics: challenges and perspectives, in: Reduced Order Methods for modeling and computational reduction, Springer, 2014, pp. 235–273
2014
Cited alongside, same era.
P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems, SIAM Review 57 (4) (2015) 483–531
2015
Cited alongside, same era.
Y. LeCun, Y. Bengio, G. Hinton, Deep learning, Nature 521 (7553) (2015) 436
2015
Cited alongside, same era.
K. He, X. Zhang, S. Ren, J. Sun, Delving deep into rectifiers: Surpassing human-level performance on imagenet classification, in: Proceedings of the IEEE International Conference on Computer Vision, 2015, pp. 1026–1034
2015
Cited alongside, same era.
J. Ling, R. Jones, J. Templeton, Machine learning strategies for systems with invariance properties, Journal of Computational Physics 318 (2016) 22–35
2016
Cited alongside, same era.
Y. Zhu, N. Zabaras, Bayesian deep convolutional encoder–decoder networks for surrogate modeling and uncertainty quantification, Journal of Computational Physics 366 (2018) 415–447
2018
Later among the works it cites.
R. K. Tripathy, I. Bilionis, Deep uq: Learning deep neural network surrogate models for high dimensional uncertainty quantification, Journal of Computational Physics 375 (2018) 565–588
2018
Later among the works it cites.
S. Lee, N. Baker, Basic research needs for scientific machine learning: Core technologies for artificial intelligence, Tech. rep., USDOE Office of Science (SC)(United States) (2018)
2018
Later among the works it cites.
P. E. Shanahan, D. Trewartha, W. Detmold, Machine learning action parameters in lattice quantum chromodynamics, Physical Review D 97 (9) (2018) 094506
2018
Later among the works it cites.
J. Sirignano, K. Spiliopoulos, Dgm: A deep learning algorithm for solving partial differential equations, Journal of Computational Physics 375 (2018) 1339–1364
2018
Later among the works it cites.
J. Berg, K. Nyström, A unified deep artificial neural network approach to partial differential equations in complex geometries, Neurocomputing 317 (2018) 28–41
2018
Later among the works it cites.
E. Weinan, B. Yu, The deep ritz method: A deep learning-based numerical algorithm for solving variational problems, Communications in Mathematics and Statistics 6 (1) (2018) 1–12
2018
Later among the works it cites.
J. Han, A. Jentzen, E. Weinan, Solving high-dimensional partial differential equations using deep learning, Proceedings of the National Academy of Sciences 115 (34) (2018) 8505–8510
2018
Later among the works it cites.
A. G. Baydin, B. A. Pearlmutter, A. A. Radul, J. M. Siskind, Automatic differentiation in machine learning: a survey, Journal of Machine Learning Research 18 (2018) 1–43
2018
Later among the works it cites.
S. Atkinson, N. Zabaras, Structured bayesian gaussian process latent variable model: Applications to data-driven dimensionality reduction and high-dimensional inversion, Journal of Computational Physics 383 (2019) 166–195
2019
Closest in time.
S. L. Brunton, J. N. Kutz, Data-driven Science and Engineering: Machine Learning, Dynamical Systems, and Control, Cambridge University Press, 2019
2019
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M. Raissi, P. Perdikaris, G. 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
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M. Raissi, Z. Wang, M. S. Triantafyllou, G. E. Karniadakis, Deep learning of vortex-induced vibrations, Journal of Fluid Mechanics 861 (2019) 119–137
2019
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J. R. Holland, J. D. Baeder, K. Duraisamy, Towards integrated field inversion and machine learning with embedded neural networks for rans modeling, in: AIAA Scitech 2019 Forum, 2019, p. 1884
2019
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R. Hamerly, L. Bernstein, A. Sludds, M. Soljačić, D. Englund, Large-scale optical neural networks based on photoelectric multiplication, Physical Review X 9 (2) (2019) 021032
2019
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