Built on

VIV Model Test of a Catenary Riser, Tech. Rep. 512345.00.01, Norwegian Marine Technology Research Institute (2001)
2001
Earlier work this paper cites.
C. E. Rasmussen, Gaussian processes in Machine Learning, in: Summer school on machine learning, Springer, 2003, pp. 63–71
2003
Earlier work this paper cites.
R. M. Neal, Bayesian learning for neural networks, Vol. 118, Springer Science & Business Media, 2012
2012
Earlier work this paper cites.
M. M. Meerschaert, M. Dogan, R. L. Van Dam, D. W. Hyndman, D. A. Benson, Hydraulic conductivity fields: Gaussian or not?, Water Resources Research 49 (8) (2013) 4730–4737
2013
Earlier work this paper cites.
T. Chen, E. Fox, C. Guestrin, Stochastic gradient Hamiltonian Monte Carlo, in: International conference on machine learning, PMLR, 2014, pp. 1683–1691
2014
Earlier work this paper cites.
M. D. Hoffman, A. Gelman, The No-U-Turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo, Journal of Machine Learning Research 15 (1) (2014) 1593–1623
2014
Earlier work this paper cites.
I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, Y. Bengio, Generative adversarial networks, arXiv preprint arXiv:1406.2661 (2014)
Original
2014
Earlier work this paper cites.
Y. LeCun, Y. Bengio, G. Hinton, Deep learning, Nature 521 (7553) (2015) 436–444
2015
Earlier work this paper cites.
C. Blundell, J. Cornebise, K. Kavukcuoglu, D. Wierstra, Weight uncertainty in neural network, in: International Conference on Machine Learning, PMLR, 2015, pp. 1613–1622
2015
Earlier work this paper cites.
I. Goodfellow, Y. Bengio, A. Courville, Y. Bengio, Deep learning, Vol. 1, MIT press Cambridge, 2016
2016
Earlier work this paper cites.
A. Kendall, Y. Gal, What uncertainties do we need in Bayesian deep learning for computer vision?, arXiv preprint arXiv:1703.04977 (2017)
Original
2017
Earlier work this paper cites.

Similar

M. Raissi, P. Perdikaris, G. E. Karniadakis, Machine learning of linear differential equations using Gaussian processes, Journal of Computational Physics 348 (2017) 683–693
2017
Cited alongside, same era.
J. Lee, Y. Bahri, R. Novak, S. S. Schoenholz, J. Pennington, J. Sohl-Dickstein, Deep neural networks as Gaussian processes, arXiv preprint arXiv:1711.00165 (2017)
Original
2017
Cited alongside, same era.
D. Flam-Shepherd, J. Requeima, D. Duvenaud, Mapping Gaussian process priors to Bayesian neural networks, in: NIPS Bayesian deep learning workshop, 2017
2017
Cited alongside, same era.
C. Finn, P. Abbeel, S. Levine, Model-agnostic meta-learning for fast adaptation of deep networks, in: International Conference on Machine Learning, PMLR, 2017, pp. 1126–1135
2017
Cited alongside, same era.
I. Gulrajani, F. Ahmed, M. Arjovsky, V. Dumoulin, A. Courville, Improved training of Wasserstein GANs, arXiv preprint arXiv:1704.00028 (2017)

Then

B.-H. Tran, S. Rossi, D. Milios, M. Filippone, All you need is a good functional prior for Bayesian deep learning, arXiv preprint arXiv:2011.12829 (2020)
Original
2020
Later among the works it cites.
L. Yang, D. Zhang, G. E. Karniadakis, Physics-informed generative adversarial networks for stochastic differential equations, SIAM Journal on Scientific Computing 42 (1) (2020) A292–A317
2020
Later among the works it cites.
D. V. Patel, A. A. Oberai, GAN-based priors for quantifying uncertainty, arXiv preprint arXiv:2003.12597 (2020)
Original
2020
Later among the works it cites.
Q. Zheng, L. Zeng, G. E. Karniadakis, Physics-informed semantic inpainting: Application to geostatistical modeling, Journal of Computational Physics 419 (2020) 109676
2020
Later among the works it cites.
T. Hospedales, A. Antoniou, P. Micaelli, A. Storkey, Meta-learning in neural networks: A survey, arXiv preprint arXiv:2004.05439 (2020)

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2021

Learning Functional Priors and Posteriors from Data and Physics

Meng, Xuhui, Yang, Liu, Mao, Zhiping et al.

Understand

We develop a new Bayesian framework based on deep neural networks to be able to extrapolate in space-time using historical data and to quantify uncertainties arising from both noisy and gappy data in physical problems.

Specifically, the proposed approach has two stages: (1) prior learning and (2) posterior estimation.
At the first stage, we employ the physics-informed Generative Adversarial Networks (PI-GAN) to learn a functional prior either from a prescribed function distribution, e.g., Gaussian process, or from historical data and physics.
At the second stage, we employ the Hamiltonian Monte Carlo (HMC) method to estimate the posterior in the latent space of PI-GANs.

Built on

VIV Model Test of a Catenary Riser, Tech. Rep. 512345.00.01, Norwegian Marine Technology Research Institute (2001)
2001
Earlier work this paper cites.
C. E. Rasmussen, Gaussian processes in Machine Learning, in: Summer school on machine learning, Springer, 2003, pp. 63–71
2003
Earlier work this paper cites.
R. M. Neal, Bayesian learning for neural networks, Vol. 118, Springer Science & Business Media, 2012
2012
Earlier work this paper cites.
M. M. Meerschaert, M. Dogan, R. L. Van Dam, D. W. Hyndman, D. A. Benson, Hydraulic conductivity fields: Gaussian or not?, Water Resources Research 49 (8) (2013) 4730–4737
2013
Earlier work this paper cites.
T. Chen, E. Fox, C. Guestrin, Stochastic gradient Hamiltonian Monte Carlo, in: International conference on machine learning, PMLR, 2014, pp. 1683–1691
2014
Earlier work this paper cites.
M. D. Hoffman, A. Gelman, The No-U-Turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo, Journal of Machine Learning Research 15 (1) (2014) 1593–1623
2014
Earlier work this paper cites.
I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, Y. Bengio, Generative adversarial networks, arXiv preprint arXiv:1406.2661 (2014)
Original
2014
Earlier work this paper cites.
Y. LeCun, Y. Bengio, G. Hinton, Deep learning, Nature 521 (7553) (2015) 436–444
2015
Earlier work this paper cites.
C. Blundell, J. Cornebise, K. Kavukcuoglu, D. Wierstra, Weight uncertainty in neural network, in: International Conference on Machine Learning, PMLR, 2015, pp. 1613–1622
2015
Earlier work this paper cites.
I. Goodfellow, Y. Bengio, A. Courville, Y. Bengio, Deep learning, Vol. 1, MIT press Cambridge, 2016
2016
Earlier work this paper cites.
A. Kendall, Y. Gal, What uncertainties do we need in Bayesian deep learning for computer vision?, arXiv preprint arXiv:1703.04977 (2017)
Original
2017
Earlier work this paper cites.

Similar

M. Raissi, P. Perdikaris, G. E. Karniadakis, Machine learning of linear differential equations using Gaussian processes, Journal of Computational Physics 348 (2017) 683–693
2017
Cited alongside, same era.
J. Lee, Y. Bahri, R. Novak, S. S. Schoenholz, J. Pennington, J. Sohl-Dickstein, Deep neural networks as Gaussian processes, arXiv preprint arXiv:1711.00165 (2017)
Original
2017
Cited alongside, same era.
D. Flam-Shepherd, J. Requeima, D. Duvenaud, Mapping Gaussian process priors to Bayesian neural networks, in: NIPS Bayesian deep learning workshop, 2017
2017
Cited alongside, same era.
C. Finn, P. Abbeel, S. Levine, Model-agnostic meta-learning for fast adaptation of deep networks, in: International Conference on Machine Learning, PMLR, 2017, pp. 1126–1135
2017
Cited alongside, same era.
I. Gulrajani, F. Ahmed, M. Arjovsky, V. Dumoulin, A. Courville, Improved training of Wasserstein GANs, arXiv preprint arXiv:1704.00028 (2017)

Then

B.-H. Tran, S. Rossi, D. Milios, M. Filippone, All you need is a good functional prior for Bayesian deep learning, arXiv preprint arXiv:2011.12829 (2020)
Original
2020
Later among the works it cites.
L. Yang, D. Zhang, G. E. Karniadakis, Physics-informed generative adversarial networks for stochastic differential equations, SIAM Journal on Scientific Computing 42 (1) (2020) A292–A317
2020
Later among the works it cites.
D. V. Patel, A. A. Oberai, GAN-based priors for quantifying uncertainty, arXiv preprint arXiv:2003.12597 (2020)
Original
2020
Later among the works it cites.
Q. Zheng, L. Zeng, G. E. Karniadakis, Physics-informed semantic inpainting: Application to geostatistical modeling, Journal of Computational Physics 419 (2020) 109676
2020
Later among the works it cites.
T. Hospedales, A. Antoniou, P. Micaelli, A. Storkey, Meta-learning in neural networks: A survey, arXiv preprint arXiv:2004.05439 (2020)

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2017

Cited alongside, same era.

Z. Mao, G. E. Karniadakis, A spectral method (of exponential convergence) for singular solutions of the diffusion equation with general two-sided fractional derivative, SIAM Journal on Numerical Analysis 56 (1) (2018) 24–49

2018

Cited alongside, same era.

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

Cited alongside, same era.

J. L. Callaham, K. Maeda, S. L. Brunton, Robust flow reconstruction from limited measurements via sparse representation, Physical Review Fluids 4 (10) (2019) 103907

2019

Cited alongside, same era.

X. Kang, X. Shi, A. Revil, Z. Cao, L. Li, T. Lan, J. Wu, Coupled hydrogeophysical inversion to identify non-Gaussian hydraulic conductivity field by jointly assimilating geochemical and time-lapse geophysical data, Journal of Hydrology 578 (2019) 124092

2019

Cited alongside, same era.

X. Meng, G. E. Karniadakis, A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems, Journal of Computational Physics 401 (2020) 109020

2020

Cited alongside, same era.

D. V. Patel, D. Ray, H. Ramaswamy, A. A. Oberai, Bayesian inference in physics-driven problems with adversarial priors

Cited in the paper.

Original

2020

Later among the works it cites.

J. Lao, C. Suter, I. Langmore, C. Chimisov, A. Saxena, P. Sountsov, D. Moore, R. A. Saurous, M. D. Hoffman, J. V. Dillon, tfp. mcmc: Modern Markov Chain Monte Carlo tools built for modern hardware, arXiv preprint arXiv:2002.01184 (2020)

Original

2020

Later among the works it cites.

L. Yang, X. Meng, G. E. Karniadakis, B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data, Journal of Computational Physics 425 (2021) 109913

2021

Closest in time.

X. Meng, H. Babaee, G. E. Karniadakis, Multi-fidelity Bayesian neural networks: Algorithms and Applications, Journal of Computational Physics (2021) 110361

2021

Closest in time.

L. Lu, P. Jin, G. Pang, Z. Zhang, G. E. Karniadakis, Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators, Nature Machine Intelligence 3 (3) (2021) 218–229

2021

Closest in time.

S. Cai, Z. Wang, L. Lu, T. A. Zaki, G. E. Karniadakis, Deepm&mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks, Journal of Computational Physics 436 (2021) 110296

2021

Closest in time.