References
Alkhalifah, T., Song, C., Waheed, U. bin, & Hao, Q. (2022). Machine
learning for data-driven geophysics. Surveys in Geophysics,
43, 191–218. https://doi.org/10.1007/s10712-021-09681-9
An, P., & Moon, W. M. (2005). Reservoir characterization using
feedforward neural networks. SEG Technical Program Expanded
Abstracts, 258–262. https://doi.org/10.1190/1.1822454
An, P., Moon, W. M., & Kalantzis, F. (2001). Reservoir
characterization using seismic waveform and feedforword neural networks.
Geophysics, 66(5). https://doi.org/10.1190/1.1487090
Azizzadenesheli, K., Kovachki, N., Li, Z., Liu-Schiaffini, M., Kossaifi,
J., & Anandkumar, A. (2024). Neural operators for accelerating
scientific simulations and design. Nature Reviews Physics,
6, 320–328. https://doi.org/10.1038/s42254-024-00712-5
Benaouda, D., Wadge, G., Whitmarsh, R. B., Rothwell, R. G., &
MacLeod, C. (1999). Inferring the lithology of borehole rocks by
applying neural network classifiers to downhole logs: An example from
the ocean drilling program. Geophysical Journal International,
136(2), 477–491. https://doi.org/10.1046/j.1365-246X.1999.00746.x
Bergen, K. J., Johnson, P. A., Hoop, M. V. de, & Beroza, G. C.
(2019). Machine learning for data-driven discovery in solid earth
geoscience. Science, 363(6433). https://doi.org/10.1126/science.aau0323
Bezanson, J., Edelman, A., Karpinski, S., & Shah, V. B. (2017).
Julia: A fresh approach to numerical computing. SIAM Review,
59(1), 65–98. https://doi.org/10.1137/141000671
Bi, K., Xie, L., Zhang, H., Chen, X., Gu, X., & Tian, Q. (2023).
Accurate medium-range global weather forecasting with 3D neural
networks. Nature, 619, 533–538. https://doi.org/10.1038/s41586-023-06185-3
Calderón-Macı́as, C., Sen, M. K., & Stoffa, P. L. (1998). Automatic
NMO correction and velocity estimation by a feedforward
neural network. Geophysics, 63(5). https://doi.org/10.1190/1.1444465
Chen, R. T. Q., Rubanova, Y., Bettencourt, J., & Duvenaud, D.
(2018). Neural ordinary differential equations. Advances in Neural
Information Processing Systems, 31.
Chen, T., & Chen, H. (1995). Universal approximation to nonlinear
operators by neural networks with arbitrary activation functions and its
application to dynamical systems. IEEE Transactions on Neural
Networks, 6(4), 911–917. https://doi.org/10.1109/72.392253
Cho, K., Merriënboer, B. van, Gulcehre, C., Bahdanau, D., Bougares, F.,
Schwenk, H., & Bengio, Y. (2014). Learning phrase representations
using RNN encoder-decoder for statistical machine translation.
Proceedings of the 2014 Conference on Empirical Methods in Natural
Language Processing (EMNLP), 1724–1734. https://doi.org/10.3115/v1/D14-1179
Cybenko, G. (1989). Approximation by superpositions of a sigmoidal
function. Mathematics of Control, Signals and Systems,
2(4), 303–314. https://doi.org/10.1007/BF02551274
Devlin, J., Chang, M.-W., Lee, K., & Toutanova, K. (2019). BERT:
Pre-training of deep bidirectional transformers for language
understanding. Proceedings of NAACL-HLT, 4171–4186.
Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X.,
Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S.,
Uszkoreit, J., & Houlsby, N. (2021). An image is worth 16x16 words:
Transformers for image recognition at scale. Proceedings of the
International Conference on Learning Representations (ICLR).
Dramsch, J. S. (2020). 70 years of machine learning in geoscience in
review. Advances in Geophysics, 61, 1–55. https://doi.org/10.1016/bs.agph.2020.08.002
Elman, J. L. (1990). Finding structure in time. Cognitive
Science, 14(2), 179–211. https://doi.org/10.1207/s15516709cog1402_1
Gilmer, J., Schoenholz, S. S., Riley, P. F., Vinyals, O., & Dahl, G.
E. (2017). Neural message passing for quantum chemistry. Proceedings
of the 34th International Conference on Machine Learning (ICML),
1263–1272.
Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D.,
Ozair, S., Courville, A., & Bengio, Y. (2014). Generative
adversarial nets. Advances in Neural Information Processing
Systems, 27.
Goswami, S., Yin, M., Yu, Y., & Karniadakis, G. E. (2023).
Physics-informed DeepONets for modeling fracture mechanics. Computer
Methods in Applied Mechanics and Engineering, 406, 115852.
https://doi.org/10.1016/j.cma.2023.115852
Goutorbe, B., Lucazeau, F., & Bonneville, A. (2006). Using neural
networks to predict thermal conductivity from geophysical well logs.
Geophysical Journal International, 166(1), 115–125. https://doi.org/10.1111/j.1365-246X.2006.02924.x
Grathwohl, W., Chen, R. T. Q., Bettencourt, J., Sutskever, I., &
Duvenaud, D. (2019). FFJORD: Free-form continuous dynamics
for scalable reversible generative models. Proceedings of the
International Conference on Learning Representations (ICLR).
Ham, Y.-G., Kim, J.-H., & Luo, J.-J. (2019). Deep learning for
multi-year ENSO forecasts. Nature, 573, 568–572. https://doi.org/10.1038/s41586-019-1559-7
He, K., Zhang, X., Ren, S., & Sun, J. (2016). Deep residual learning
for image recognition. Proceedings of the IEEE Conference on
Computer Vision and Pattern Recognition (CVPR), 770–778. https://doi.org/10.1109/CVPR.2016.90
He, Q., Barajas-Solano, D., Tartakovsky, G., & Tartakovsky, A. M.
(2020). Physics-informed neural networks for multiphysics data
assimilation with application to subsurface transport. Advances in
Water Resources, 141, 103610. https://doi.org/10.1016/j.advwatres.2020.103610
Hinton, G. E., & Salakhutdinov, R. R. (2006). Reducing the
dimensionality of data with neural networks. Science,
313(5786), 504–507. https://doi.org/10.1126/science.1127647
Ho, J., Jain, A., & Abbeel, P. (2020). Denoising diffusion
probabilistic models. Advances in Neural Information Processing
Systems, 33, 6840–6851.
Hochreiter, S., & Schmidhuber, J. (1997). Long short-term memory.
Neural Computation, 9(8), 1735–1780. https://doi.org/10.1162/neco.1997.9.8.1735
Hornik, K., Stinchcombe, M., & White, H. (1989). Multilayer
feedforward networks are universal approximators. Neural
Networks, 2(5), 359–366. https://doi.org/10.1016/0893-6080(89)90020-8
Huang, Z., Shimeld, J., Williamson, M., & Katsube, J. (1996).
Permeability prediction with artificial neural network modeling in the
venture gas field, offshore eastern canada. Geophysics,
61(2), 422–436. https://doi.org/10.1190/1.1443970
Huang, Z., & Williamson, M. A. (1997). Determination of porosity and
permeability in reservoir intervals by artificial neural network
modelling, offshore eastern canada. Petroleum Geoscience,
3(3), 245–254. https://doi.org/10.1144/petgeo.3.3.245
Ioffe, S., & Szegedy, C. (2015). Batch normalization: Accelerating
deep network training by reducing internal covariate shift.
Proceedings of the 32nd International Conference on Machine Learning
(ICML), 448–456.
Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S.,
& Yang, L. (2021). Physics-informed machine learning. Nature
Reviews Physics, 3, 422–440. https://doi.org/10.1038/s42254-021-00314-5
Kashinath, K., Mustafa, M., Albert, A., Wu, J., Jiang, C., Esmaeilzadeh,
S., Azizzadenesheli, K., Wang, R., Chattopadhyay, A., Singh, A., et al.
(2021). Physics-informed machine learning: Case studies for weather and
climate modelling. Philosophical Transactions of the Royal Society
A, 379(2194), 20200093. https://doi.org/10.1098/rsta.2020.0093
Kingma, D. P., & Ba, J. (2015). Adam: A method for stochastic
optimization. Proceedings of the 3rd International Conference on
Learning Representations (ICLR). https://arxiv.org/abs/1412.6980
Kingma, D. P., & Welling, M. (2014). Auto-encoding variational
bayes. Proceedings of the 2nd International Conference on Learning
Representations (ICLR). https://arxiv.org/abs/1312.6114
Kipf, T. N., & Welling, M. (2017). Semi-supervised classification
with graph convolutional networks. Proceedings of the 5th
International Conference on Learning Representations (ICLR). https://arxiv.org/abs/1609.02907
Kovachki, N., Li, Z., Liu, B., Azizzadenesheli, K., Bhatt, K., Stuart,
A., & Anandkumar, A. (2023). Neural operator: Learning maps between
function spaces with applications to PDEs. Journal of Machine
Learning Research, 24(89), 1–97.
Krizhevsky, A., Sutskever, I., & Hinton, G. E. (2012). ImageNet
classification with deep convolutional neural networks. Advances in
Neural Information Processing Systems, 25.
Lagaris, I. E., Likas, A., & Fotiadis, D. I. (1998). Artificial
neural networks for solving ordinary and partial differential equations.
IEEE Transactions on Neural Networks, 9(5), 987–1000.
https://doi.org/10.1109/72.712178
Laloy, E., Hérault, R., Jacques, D., & Linde, N. (2018).
Training-image based geostatistical inversion using a spatial generative
adversarial neural network. Water Resources Research,
54(1), 381–406. https://doi.org/10.1002/2017WR022148
Lam, R., Sanchez-Gonzalez, A., Willson, M., Wirnsberger, P., Fortunato,
M., Alet, F., Ravuri, S., Ewalds, T., Eaton-Rosen, Z., Hu, W., et al.
(2023). Learning skillful medium-range global weather forecasting.
Science, 382(6677), 1416–1421. https://doi.org/10.1126/science.adi2336
LeCun, Y., Bengio, Y., & Hinton, G. (2015). Deep learning.
Nature, 521, 436–444. https://doi.org/10.1038/nature14539
LeCun, Y., Boser, B., Denker, J. S., Henderson, D., Howard, R. E.,
Hubbard, W., & Jackel, L. D. (1989). Backpropagation applied to
handwritten zip code recognition. Neural Computation,
1(4), 541–551. https://doi.org/10.1162/neco.1989.1.4.541
Li, Z., Huang, D. Z., Liu, B., & Anandkumar, A. (2023). Fourier
neural operator with learned deformations for PDEs on general
geometries. Journal of Machine Learning Research,
24(388), 1–26.
Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhatt, K., Stuart,
A., & Anandkumar, A. (2021). Fourier neural operator for parametric
partial differential equations. Proceedings of the International
Conference on Learning Representations (ICLR). https://arxiv.org/abs/2010.08895
Lipman, Y., Chen, R. T. Q., Ben-Hamu, H., Nickel, M., & Le, M.
(2023). Flow matching for generative modeling. Proceedings of the
International Conference on Learning Representations (ICLR).
Lopez-Alvis, J., Hermans, T., Nguyen, F., Caterina, D., & Haugerud,
A. J. (2019). Deep-learning-based inverse modeling approaches: A
subsurface transport example. Water Resources Research,
55(8), 6305–6327. https://doi.org/10.1029/2018WR024638
Lu, L., Jin, P., Pang, G., Zhang, Z., & Karniadakis, G. E. (2021).
Learning nonlinear operators via DeepONet based on the universal
approximation theorem of operators. Nature Machine
Intelligence, 3, 218–229. https://doi.org/10.1038/s42256-021-00302-5
Lu, L., Meng, X., Mao, Z., & Karniadakis, G. E. (2021). DeepXDE: A
deep learning library for solving differential equations. SIAM
Review, 63(1), 208–228. https://doi.org/10.1137/19M1274067
McClenny, L. D., & Braga-Neto, U. M. (2023). Self-adaptive
physics-informed neural networks. Journal of Computational
Physics, 474, 111722. https://doi.org/10.1016/j.jcp.2022.111722
McCormack, M. D., Zaucha, D. E., & Dushek, D. W. (1993). First-break
refraction event picking and seismic data trace editing using neural
networks. Geophysics, 58(1). https://doi.org/10.1190/1.1443352
Mildenhall, B., Srinivasan, P. P., Tancik, M., Barron, J. T.,
Ramamoorthi, R., & Ng, R. (2022). NeRF: Representing scenes as
neural radiance fields for view synthesis. Communications of the
ACM, 65(1), 99–106. https://doi.org/10.1145/3503250
Moseley, B., Markham, A., & Nissen-Meyer, T. (2020). Deep learning
for fast simulation of seismic waves in complex media. Solid
Earth, 11, 1527–1549. https://doi.org/10.5194/se-11-1527-2020
Mosser, L., Dubrule, O., & Blunt, M. J. (2017). Reconstruction of
three-dimensional porous media using generative adversarial neural
networks. Physical Review E, 96(4), 043309. https://doi.org/10.1103/PhysRevE.96.043309
Mosser, L., Dubrule, O., & Blunt, M. J. (2020). Stochastic seismic
waveform inversion using generative adversarial networks as a geological
prior. Mathematical Geosciences, 52, 53–79. https://doi.org/10.1007/s11004-019-09832-6
Mousavi, S. M., Ellsworth, W. L., Zhu, W., Chuber, L. Y., & Beroza,
G. C. (2020). Earthquake transformer – an attentive deep-learning model
for simultaneous earthquake detection and phase picking. Nature
Communications, 11(3952). https://doi.org/10.1038/s41467-020-17591-w
Nair, V., & Hinton, G. E. (2010). Rectified linear units improve
restricted boltzmann machines. Proceedings of the 27th International
Conference on Machine Learning (ICML), 807–814.
Pathak, J., Subramanian, S., Harrington, P., Raja, S., Chattopadhyay,
A., Mardani, M., Kurth, T., Hall, D., Li, Z., Azizzadenesheli, K.,
Hassanzadeh, P., Kashinath, K., & Anandkumar, A. (2022).
FourCastNet: A global data-driven high-resolution weather forecasting
model using adaptive fourier neural operators. arXiv Preprint
arXiv:2202.11214.
Perol, T., Gharbi, M., & Denolle, M. (2018). Convolutional neural
network for earthquake detection and location. Science
Advances, 4(2), e1700578. https://doi.org/10.1126/sciadv.1700578
Rackauckas, C., Ma, Y., Martensen, J., Warner, C., Zubov, K., Supekar,
R., Skinner, D., Ramadhan, A., & Edelman, A. (2020). Universal
differential equations for scientific machine learning. arXiv
Preprint arXiv:2001.04385.
Radford, A., Metz, L., & Chintala, S. (2016). Unsupervised
representation learning with deep convolutional generative adversarial
networks. Proceedings of the International Conference on Learning
Representations (ICLR). https://arxiv.org/abs/1511.06434
Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019).
Physics-informed neural networks: A deep learning framework for solving
forward and inverse problems involving nonlinear partial differential
equations. Journal of Computational Physics, 378,
686–707. https://doi.org/10.1016/j.jcp.2018.10.045
Rasht-Behesht, M., Huber, C., Shukla, K., & Karniadakis, G. E.
(2022). Physics-informed neural networks (PINNs) for wave propagation
and full waveform inversions. Journal of Geophysical Research: Solid
Earth, 127(5), e2021JB023120. https://doi.org/10.1029/2021JB023120
Reichstein, M., Camps-Valls, G., Stevens, B., Jung, M., Denzler, J.,
Carvalhais, N., & Prabhat. (2019). Deep learning and process
understanding for data-driven earth system science. Nature,
566, 195–204. https://doi.org/10.1038/s41586-019-0912-1
Ronneberger, O., Fischer, P., & Brox, T. (2015). U-net:
Convolutional networks for biomedical image segmentation. Medical
Image Computing and Computer-Assisted Intervention (MICCAI),
234–241. https://doi.org/10.1007/978-3-319-24574-4_28
Rosenblatt, F. (1958). The perceptron: A probabilistic model for
information storage and organization in the brain. Psychological
Review, 65(6), 386–408. https://doi.org/10.1037/h0042519
Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986). Learning
representations by back-propagating errors. Nature,
323, 533–536. https://doi.org/10.1038/323533a0
Scarselli, F., Gori, M., Tsoi, A. C., Hagenbuchner, M., &
Monfardini, G. (2009). The graph neural network model. IEEE
Transactions on Neural Networks, 20(1), 61–80. https://doi.org/10.1109/TNN.2008.2005605
Shi, X., Chen, Z., Wang, H., Yeung, D.-Y., Wong, W., & Woo, W.
(2015). Convolutional LSTM network: A machine learning approach for
precipitation nowcasting. Advances in Neural Information Processing
Systems, 28.
Sitzmann, V., Martel, J. N. P., Bergman, A. W., Lindell, D. B., &
Wetzstein, G. (2020). Implicit neural representations with periodic
activation functions. Advances in Neural Information Processing
Systems, 33, 7462–7473.
Smith, J. D., Azizzadenesheli, K., & Ross, Z. E. (2021). EikoNet:
Solving the eikonal equation with deep neural networks. IEEE
Transactions on Geoscience and Remote Sensing, 59(12),
10685–10696. https://doi.org/10.1109/TGRS.2020.3039165
Sohl-Dickstein, J., Weiss, E. A., Maheswaranathan, N., & Ganguli, S.
(2015). Deep unsupervised learning using nonequilibrium thermodynamics.
Proceedings of the 32nd International Conference on Machine Learning
(ICML), 2256–2265.
Song, C., & Alkhalifah, T. (2023). Simulating seismic multifrequency
wavefields with the fourier feature physics-informed neural network.
Geophysical Journal International, 232(3), 1503–1514.
https://doi.org/10.1093/gji/ggac399
Song, C., Alkhalifah, T., & Waheed, U. bin. (2021). Solving the
frequency-domain acoustic VTI wave equation using physics-informed
neural networks. Geophysical Journal International,
225(2), 846–859. https://doi.org/10.1093/gji/ggab010
Song, Y., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Ermon, S., &
Poole, B. (2021). Score-based generative modeling through stochastic
differential equations. Proceedings of the International Conference
on Learning Representations (ICLR).
Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I., &
Salakhutdinov, R. (2014). Dropout: A simple way to prevent neural
networks from overfitting. Journal of Machine Learning
Research, 15(1), 1929–1958.
Stanev, E. V., Schulz-Stellenfleth, J., & Grayek, S. (2021).
Hydrological coherence of remotely sensed water level data products with
graph neural networks. Journal of Hydrology, 603,
126923. https://doi.org/10.1016/j.jhydrol.2021.126923
Sun, Q., Burghardt, J., & Bhatt, D. (2023). Physics-informed neural
networks for geothermal reservoir simulation. Geothermics,
109, 102644. https://doi.org/10.1016/j.geothermics.2023.102644
Tancik, M., Srinivasan, P. P., Mildenhall, B., Fridovich-Keil, S.,
Raghavan, N., Singhal, U., Ramamoorthi, R., Barron, J. T., & Ng, R.
(2020). Fourier features let networks learn high frequency functions in
low dimensional domains. Advances in Neural Information Processing
Systems, 33, 7537–7547.
Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez,
A. N., Kaiser, Ł., & Polosukhin, I. (2017). Attention is all you
need. Advances in Neural Information Processing Systems,
30.
Waheed, U. bin, Haghighat, E., Alkhalifah, T., Song, C., & Hao, Q.
(2021). PINNeik: Eikonal solution using physics-informed neural
networks. Computers & Geosciences, 155, 104833. https://doi.org/10.1016/j.cageo.2021.104833
Wang, M., Wang, S., & Perdikaris, P. (2023). Reliable extrapolation
of deep neural operators informed by physics or sparse observations.
Computer Methods in Applied Mechanics and Engineering,
412, 116064. https://doi.org/10.1016/j.cma.2023.116064
Wang, S., Teng, Y., & Perdikaris, P. (2021). Understanding and
mitigating gradient flow pathologies in physics-informed neural
networks. SIAM Journal on Scientific Computing, 43(5),
A3055–A3081. https://doi.org/10.1137/20M1318043
Wang, S., Wang, H., & Perdikaris, P. (2021). Learning the solution
operator of parametric partial differential equations with
physics-informed DeepONets. Science Advances,
7(40), eabi8605. https://doi.org/10.1126/sciadv.abi8605
Wen, G., Li, Z., Azizzadenesheli, K., Anandkumar, A., & Benson, S.
M. (2022). U-FNO – an enhanced fourier neural operator-based
deep-learning model for multiphase flow. Advances in Water
Resources, 163, 104180. https://doi.org/10.1016/j.advwatres.2022.104180
Wu, X., Liang, L., Shi, Y., & Fomel, S. (2019). FaultSeg3D: Using
synthetic data sets to train an end-to-end convolutional neural network
for 3D seismic fault segmentation. Geophysics, 84(3),
IM35–IM45. https://doi.org/10.1190/geo2018-0646.1
Yang, F., & Ma, J. (2019). Deep-learning inversion: A
next-generation seismic velocity model building method.
Geophysics, 84(4), R583–R599. https://doi.org/10.1190/geo2018-0249.1
Yin, Z., Orozco, R., Louboutin, M., & Herrmann, F. J. (2023).
Solving multiphysics-based inverse problems with learned surrogates and
constraints. Advanced Modeling and Simulation in Engineering
Sciences, 10, 14. https://doi.org/10.1186/s40323-023-00252-0
Yuan, S., Liu, J., Wang, S., Wang, T., & Shi, P. (2020). Seismic
waveform classification and first-break picking using convolution neural
networks. IEEE Geoscience and Remote Sensing Letters,
17(8), 1408–1412. https://doi.org/10.1109/LGRS.2019.2948601
Zhu, W., & Beroza, G. C. (2019). PhaseNet: A
deep-neural-network-based seismic arrival-time picking method.
Geophysical Journal International, 216(1), 261–273. https://doi.org/10.1093/gji/ggy423
Zhu, Y., Zabaras, N., Koutsourelakis, P.-S., & Perdikaris, P.
(2019). Physics-constrained deep learning for high-dimensional surrogate
modeling and uncertainty quantification without labeled data.
Journal of Computational Physics, 394, 56–81. https://doi.org/10.1016/j.jcp.2019.05.024