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We developed a new class of physics-informed generative adversarial networks (PI-GANs) to solve in a unified manner forward, inverse and mixed stochastic problems based on a limited number of scattered measurements.
Artificial neural networks for solving ordinary and partial differential equations,
I. E. Lagaris, A. C. Likas, D. I. Fotiadis, · 1998
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Neural-network methods for boundary value problems with irregular boundaries,
I. E. Lagaris, A. C. Likas, D. G. Papageorgiou, · 2000
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Solving noisy linear operator equations by Gaussian processes: Application to ordinary and partial differential equations,
T. Graepel, · 2003
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Distilling free-form natural laws from experimental data,
M. Schmidt, H. Lipson, · 2009
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Inverse problems: A Bayesian perspective,
A. M. Stuart, · 2010
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Linear operators and stochastic partial differential equations in Gaussian process regression,
S. Särkkä, · 2011
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Generative adversarial nets,
I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, Y. Bengio, · 2014
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Adam: A method for stochastic optimization,
D. P. Kingma, J. Ba, · 2014
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C-RNN-GAN: Continuous recurrent neural networks with adversarial training,
O. Mogren, · 2016
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Discovering governing equations from data by sparse identification of nonlinear dynamical systems,
S. L. Brunton, J. L. Proctor, J. N. Kutz, · 2016
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Probabilistic solvers for partial differential equations,
I. Bilionis, · 2016
Earlier work this paper cites.
BEGAN: Boundary equilibrium generative adversarial networks,
D. Berthelot, T. Schumm, L. Metz, · 2017
Earlier work this paper cites.
Progressive growing of GANs for improved quality, stability, and variation,
T. Karras, T. Aila, S. Laine, J. Lehtinen, · 2017
Cited alongside, same era.
Photo-realistic single image super-resolution using a generative adversarial network,
C. Ledig, L. Theis, F. Huszár, J. Caballero, A. Cunningham, A. Acosta, A. P. Aitken, A. Tejani, J. Totz, Z. Wang, et al., · 2017
Cited alongside, same era.
Unpaired image-to-image translation using cycle-consistent adversarial networks,
J.-Y. Zhu, T. Park, P. Isola, A. A. Efros, · 2017
Cited alongside, same era.
SeqGAN: Sequence generative adversarial nets with policy gradient,
L. Yu, W. Zhang, J. Wang, Y. Yu, · 2017
Cited alongside, same era.
Adversarial feature matching for text generation,
Y. Zhang, Z. Gan, K. Fan, Z. Chen, R. Henao, D. Shen, L. Carin, · 2017
Improved training of Wasserstein GANs,
I. Gulrajani, F. Ahmed, M. Arjovsky, V. Dumoulin, A. C. Courville, · 2017
Later among the works it cites.
Automatic differentiation in machine learning: a survey,
A. G. Baydin, B. A. Pearlmutter, A. A. Radul, J. M. Siskind, · 2017
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R. Flamary, N. Courty, POT Python optimal transport library, (2017)
2017
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MaskGAN: Better text generation via filling in the ______,
W. Fedus, I. Goodfellow, A. M. Dai, · 2018
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Hidden physics models: Machine learning of nonlinear partial differential equations,
M. Raissi, G. E. Karniadakis, · 2018
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Numerical Gaussian processes for time-dependent and nonlinear partial differential equations,
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Cited alongside, same era.
Recurrent topic-transition GAN for visual paragraph generation,
X. Liang, Z. Hu, H. Zhang, C. Gan, E. P. Xing, · 2017
Cited alongside, same era.
Midinet: A convolutional generative adversarial network for symbolic-domain music generation,
L.-C. Yang, S.-Y. Chou, Y.-H. Yang, · 2017
Cited alongside, same era.
Objective-reinforced generative adversarial networks (ORGAN) for sequence generation models,
G. L. Guimaraes, B. Sanchez-Lengeling, C. Outeiral, P. L. C. Farias, A. Aspuru-Guzik, · 2017
Cited alongside, same era.
Solving parametric PDE problems with artificial neural networks,
Y. Khoo, J. Lu, L. Ying, · 2017
Cited alongside, same era.
Machine learning of linear differential equations using Gaussian processes,
M. Raissi, P. Perdikaris, G. E. Karniadakis, · 2017
Cited alongside, same era.
W. E, J. Han, A. Jentzen, · 2017
Cited alongside, same era.
M. Arjovsky, S. Chintala, L. Bottou, · 2017
Cited alongside, same era.
M. Raissi, P. Perdikaris, G. E. Karniadakis, · 2018
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Neural-net-induced Gaussian process regression for function approximation and PDE solution,
G. Pang, L. Yang, G. E. Karniadakis, · 2018
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X. Yang, G. Tartakovsky, A. Tartakovsky, · 2018
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A deep neural network surrogate for high-dimensional random partial differential equations,
M. A. Nabian, H. Meidani, · 2018
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Bayesian deep convolutional encoder-decoder networks for surrogate modeling and uncertainty quantification,
Y. Zhu, N. Zabaras, · 2018
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M. Raissi, · 2018
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D. Zhang, L. Lu, L. Guo, G. E. Karniadakis, · 2018
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