. .. Introduction, Introduction, Introduction, 2020.

. .. , Handling the Likelihood Term

. .. , Surface chemical analysis. Handling of specimens prior to analysis

. .. , Putting Everything Together, The Empowered Investor

. .. Stochastic-variation,

. .. Temporal-variation, Figure 6: Temporal variation of carbon capture.

. .. Datasets,

D. .. Results,

. .. Stochastic-results, Figure 1.2. Stochastic simulation results

. .. Baselines,

E. Young, Our Favourite English Word, We are Better than This, pp.65-66, 2015.

. As-for-newson, Figure 12. Regulatory map of neurotransmitter specification.

J. Aach and G. M. Church, Aligning gene expression time series with time warping algorithms, Bioinformatics, vol.17, issue.6, pp.495-508, 2001.

A. Almahairi, S. Rajeswar, A. Sordoni, P. Bachman, and A. Courville, Preprint repository arXiv achieves milestone million uploads, Physics Today, 2014.

M. A. Alvarez, D. Luengo, and N. D. Lawrence, Linear Latent Force Models Using Gaussian Processes, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.35, issue.11, pp.2693-2705, 2013.

A. Azcarate, A. Aïda, M. Barth, J. Rixen, and . Beckers, Reconstruction of incomplete oceanographic data sets using empirical orthogonal functions: application to the Adriatic Sea surface temperature, 2005.

M. Asim, F. Shamshad, and A. Ahmed, Blind Image Deconvolution Using Deep Generative Priors, IEEE Transactions on Computational Imaging, vol.6, pp.1493-1506, 2020.

I. Ayed, E. D. Bezenac, A. Pajot, and P. Gallinari, Learning the Spatio-Temporal Dynamics of Physical Processes from Partial Observations, ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2020.

C. Ballester, M. Bertalmio, V. Caselles, G. Sapiro, and J. Verdera, Filling-in by joint interpolation of vector fields and gray levels, IEEE Transactions on Image Processing, vol.10, issue.8, pp.1200-1211, 2001.

C. Barnes, E. Shechtman, A. Finkelstein, and D. B. Goldman, PatchMatch, ACM Transactions on Graphics, vol.28, issue.3, pp.1-11, 2009.

D. Béréziat and I. Herlin, Coupling Dynamic Equations and Satellite Images for Modelling Ocean Surface Circulation, Communications in Computer and Information Science, pp.191-205, 2015.

R. L. Bernstein, Sea surface temperature estimation using the NOAA 6 satellite advanced very high resolution radiometer, Journal of Geophysical Research, vol.87, issue.C12, p.9455, 1982.

M. Bertalmio, G. Sapiro, V. Caselles, and C. Ballester, Image inpainting, Proceedings of the 27th annual conference on Computer graphics and interactive techniques - SIGGRAPH '00, p.24, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00522652

E. D. Bezenac, A. Pajot, and P. Gallinari, Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02418362

M. Bocquet, Parameter-field estimation for atmospheric dispersion: application to the Chernobyl accident using 4D-Var, Quarterly Journal of the Royal Meteorological Society, vol.138, issue.664, pp.664-681, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00705045

A. Bora, A. Jalal, E. Price, and A. G. Dimakis, Compressed Sensing using Generative Models, vol.90, p.67, 2017.

A. Bora, E. Price, and A. G. Dimakis, AmbientGAN: Generative models from lossy measurements, International Conference on Learning Representations. url: https : / / openreview . net / forum ? id = Hy7fDog0b, 2018.

A. K. Boyat and B. K. Joshi, A Review Paper : Noise Models in Digital Image Processing, Signal & Image Processing : An International Journal, vol.6, issue.2, pp.63-75, 2015.

E. J. Candès, J. K. Romberg, and T. Tao, Stable signal recovery from incomplete and inaccurate measurements, Communications on Pure and Applied Mathematics, vol.59, issue.8, pp.1207-1223, 2006.

A. Carrassi, M. Bocquet, L. Bertino, and G. Evensen, Data assimilation in the geosciences: An overview of methods, issues, and perspectives, Wiley Interdisciplinary Reviews: Climate Change, vol.9, issue.5, p.e535, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02905891

A. Chambolle, An Algorithm for Total Variation Minimization and Applications, Journal of Mathematical Imaging and Vision, vol.20, p.92, 2004.

T. Chen, Y. Qi, J. Rubanova, D. Bettencourt, and . Duvenaud, Neural Ordinary Differential Equations, 2018.

K. Cho, B. Van-merrienboer, C. Gulcehre, D. Bahdanau, F. Bougares et al., Learning Phrase Representations using RNN Encoder?Decoder for Statistical Machine Translation, Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP), pp.1724-1734, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01433235

C. Chu, A. Zhmoginov, and M. Sandler, Preprint repository arXiv achieves milestone million uploads, Physics Today, p.79, 2014.

J. T. Connor, R. D. Martin, and L. E. Atlas, Recurrent neural networks and robust time series prediction, IEEE Transactions on Neural Networks, vol.5, issue.2, pp.240-254, 1994.

N. Cressie and C. K. Wikle, Statistics for Spatio-Temporal Data, vol.13, p.9, 2015.

J. P. Crutchfield and B. S. Mcnamara, Equations of motion from a data series, Complex Systems, p.18, 1987.

S. B. Damelin and N. S. Hoang, On Surface Completion and Image Inpainting by Biharmonic Functions: Numerical Aspects, International Journal of Mathematics and Mathematical Sciences, vol.2018, pp.1-8, 2018.

U. Demir and G. Unal, Patch-Based Image Inpainting with Generative Adversarial Networks, p.70, 2018.

R. Dey and F. M. Salem, Gate-variants of Gated Recurrent Unit (GRU) neural networks, 2017 IEEE 60th International Midwest Symposium on Circuits and Systems (MWSCAS), p.10, 2017.

L. Dinh, J. Sohl-dickstein, and S. Bengio, Density estimation using Real NVP, p.67, 2016.

A. Dosovitskiy, P. Fischer, E. Ilg, P. Hausser, C. Hazirbas et al., FlowNet: Learning Optical Flow with Convolutional Networks, 2015 IEEE International Conference on Computer Vision (ICCV), pp.2758-2766, 2015.

F. Ebert, C. Finn, A. X. Lee, and S. Levine, 10.3726/978-3-653-05268-8/5, Inactive DOIs, p.86
URL : https://hal.archives-ouvertes.fr/hal-00819689

R. Fablet, S. Ouala, and C. Herzet, Bilinear Residual Neural Network for the Identification and Forecasting of Geophysical Dynamics, 2018 26th European Signal Processing Conference (EUSIPCO), p.18, 2018.

C. Finn, I. J. Goodfellow, and S. Levine, Unsupervised Learning for Physical Interaction through Video Prediction, vol.34, p.12, 2016.

I. J. Goodfellow, J. Pouget-abadie, M. Mirza, B. Xu, D. Warde-farley et al., Generative adversarial networks, Communications of the ACM, vol.63, issue.11, pp.139-144, 2020.

. Grathwohl, R. T. Will, J. Chen, I. Bettencourt, D. Sutskever et al., 2e révision de la LAMal: une loi mesquine, pointilleuse, et illusoire, Bulletin des Médecins Suisses, vol.84, issue.26, pp.01367-01367, 2003.

A. Graves, A. Mohamed, and G. Hinton, Speech recognition with deep recurrent neural networks, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, pp.6645-6649, 2013.

J. Hays and A. A. Efros, Scene completion using millions of photographs, ACM Transactions on Graphics, vol.26, issue.3, p.4, 2007.

K. He, X. Zhang, S. Ren, and J. Sun, Deep Residual Learning for Image Recognition, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016.

M. Heusel, H. Ramsauer, T. Unterthiner, B. Nessler, G. Klambauer et al., GANs Trained by a Two Time-Scale Update Rule Converge to a Nash Equilibrium, p.89, 2017.

S. Hochreiter and J. Schmidhuber, Long Short-Term Memory, Neural Computation, vol.9, issue.8, pp.1735-1780, 1997.

S. Iizuka, E. Simo-serra, and H. Ishikawa, Globally and locally consistent image completion, ACM Transactions on Graphics, vol.36, issue.4, pp.1-14, 2017.

E. Ilg, N. Mayer, T. Saikia, M. Keuper, A. Dosovitskiy et al., FlowNet 2.0: Evolution of Optical Flow Estimation with Deep Networks, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), p.11, 2017.

P. Isola, J. Zhu, T. Zhou, and A. A. Efros, Image-to-Image Translation with Conditional Adversarial Networks, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017.

M. Jaderberg, K. Simonyan, A. Zisserman, and K. Kavukcuoglu, Disziplinarverfahren wegen Aufdeckung eines Titelbetrugs, Schweizerische Ärztezeitung, vol.82, issue.38, pp.02025-02025, 2001.

N. Kalchbrenner, A. Van-den-oord, K. Simonyan, I. Danihelka, O. Vinyals et al., Video Pixel Networks, p.12, 2016.

D. P. Kingma and J. Ba, Preprint repository arXiv achieves milestone million uploads, Physics Today, p.85, 2014.

D. P. Kingma and M. Welling, Preprint repository arXiv achieves milestone million uploads, Physics Today, p.67, 2014.

L. Ladický, S. Jeong, B. Solenthaler, M. Pollefeys, and M. Gross, Data-driven fluid simulations using regression forests, ACM Transactions on Graphics, vol.34, issue.6, pp.1-9, 2015.

H. Guo, F. Jiang, S. Liu, and D. Zhao, Natural images scale invariance and high-fidelity image restoration, 2013 Visual Communications and Image Processing (VCIP), p.21, 2013.

Y. Lecun, G. Touresky, T. Hinton, and . Sejnowski, A theoretical framework for back-propagation, Proceedings of the 1988 connectionist models summer school, vol.1, p.53, 1988.

C. Ledig, L. Theis, F. Huszar, J. Caballero, A. Cunningham et al., Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017.

J. Lehtinen, J. Munkberg, J. Hasselgren, S. Laine, T. Karras et al., Noise2Noise: Learning Image Restoration without Clean Data, p.23, 2018.

S. Li, B. Cheng-xian, B. Jiang, and . Marlin, MisGAN: Learning from Incomplete Data with Generative Adversarial Networks, vol.93, p.24, 2018.

J. Ling, A. Kurzawski, and J. Templeton, Reynolds averaged turbulence modelling using deep neural networks with embedded invariance, Journal of Fluid Mechanics, vol.807, pp.155-166, 2016.

G. Liu, F. A. Reda, K. J. Shih, T. Wang, A. Tao et al., Image Inpainting for Irregular Holes Using Partial Convolutions, Computer Vision ? ECCV 2018, pp.89-105, 2018.

Z. Liu, P. Luo, X. Wang, and X. Tang, Deep Learning Face Attributes in the Wild, 2015 IEEE International Conference on Computer Vision (ICCV), vol.85, p.67, 2015.

Z. Long, Y. Lu, and B. Dong, PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network, Journal of Computational Physics, vol.399, p.108925, 2019.

G. Madec, Laplace, Pierre Simon De, vol.27, p.35

X. Mao, Q. Li, H. Xie, R. Y. Lau, Z. Wang et al., Least Squares Generative Adversarial Networks, 2017 IEEE International Conference on Computer Vision (ICCV), p.20, 2017.

M. Mardani, E. Gong, J. Y. Cheng, S. S. Vasanawala, G. Zaharchuk et al., Deep Generative Adversarial Neural Networks for Compressive Sensing MRI, IEEE Transactions on Medical Imaging, vol.38, issue.1, pp.167-179, 2019.

J. Marin, A. Biswas, F. Ofli, N. Hynes, A. Salvador et al., Recipe1M: A Dataset for Learning Cross-Modal Embeddings for Cooking Recipes and Food Images, vol.86, p.67, 2018.

M. Mathieu, C. Couprie, and Y. Lecun, Kündigung des Chefarztes einer katholischen Klinik wegen Wiederverheiratung, Medizinrecht, vol.33, issue.5, pp.339-342, 2015.

T. Miyato and M. Koyama, Generative Adversarial Network (GAN), Computer Vision, pp.1-6, 2020.

J. F. Mota, N. Deligiannis, and M. R. Rodrigues, Compressed Sensing With Prior Information: Strategies, Geometry, and Bounds, IEEE Transactions on Information Theory, vol.63, issue.7, pp.4472-4496, 2017.

A. Newson, A. Almansa, M. Fradet, Y. Gousseau, and P. Pérez, Video Inpainting of Complex Scenes, SIAM Journal on Imaging Sciences, vol.7, issue.4, pp.1993-2019, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00937795

A. Pajot, E. De-bezenac, and P. Gallinari, Unsupervised Adversarial Image Reconstruction, 2018.

A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang et al., Broome, Adam Edward, (born 11 Nov. 1968), Director, Adam Broome Ltd, since 2014, 2012.

D. Pathak, P. Krahenbuhl, J. Donahue, T. Darrell, and A. A. Efros, Context Encoders: Feature Learning by Inpainting, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), p.24, 2016.

. Patraucean, A. Viorica, R. Handa, and . Cipolla, 10.3726/978-3-653-06309-7/6, Inactive DOIs, vol.34, p.12

K. G. Pressel, C. M. Kaul, T. Schneider, Z. Tan, and S. Mishra, Large-eddy simulation in an anelastic framework with closed water and entropy balances, Journal of Advances in Modeling Earth Systems, vol.7, issue.3, pp.1425-1456, 2015.

M. Raissi, Linear, degenerate backward stochastic partial differential equations, Lecture Notes in Mathematics, pp.103-136

M. Raissi, P. Perdikaris, and G. E. Karniadakis, Machine learning of linear differential equations using Gaussian processes, Journal of Computational Physics, vol.348, pp.683-693, 2017.

O. Ronneberger, P. Fischer, and T. Brox, U-Net: Convolutional Networks for Biomedical Image Segmentation, Lecture Notes in Computer Science, pp.234-241, 2015.

A. Rossler, D. Cozzolino, L. Verdoliva, C. Riess, J. Thies et al., FaceForensics++: Learning to Detect Manipulated Facial Images, 2019 IEEE/CVF International Conference on Computer Vision (ICCV), p.86, 2019.

S. H. Rudy, S. L. Brunton, J. L. Proctor, and J. N. Kutz, Data-driven discovery of partial differential equations, Science Advances, vol.3, issue.4, p.e1602614, 2017.

C. Schuldt, I. Laptev, and B. Caputo, Recognizing human actions: a local SVM approach, Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004., vol.3, pp.32-36, 2004.

W. Shi, J. Caballero, F. Huszar, J. Totz, A. P. Aitken et al., Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), p.23, 2016.

X. Shi, Z. Chen, H. Wang, D. Yeung, W. Wong et al., Convolutional LSTM network: A machine learning approach for precipitation nowcasting, Advances in Neural Information Processing Systems, vol.28, pp.802-810, 2015.

D. Simakov, Y. Caspi, E. Shechtman, and M. Irani, Summarizing visual data using bidirectional similarity, 2008 IEEE Conference on Computer Vision and Pattern Recognition, p.24, 2008.

Z. Sirkes and E. Tziperman, Finite Difference of Adjoint or Adjoint of Finite Difference?, Monthly Weather Review, vol.125, issue.12, pp.3373-3378, 1997.

C. Sønderby, J. Kaae, L. Caballero, W. Theis, F. Shi et al., Amortised MAP Inference for Image Super-resolution, p.23, 2016.

Y. Song, C. Yang, Z. Lin, H. Li, Q. Huang et al., Image Inpainting using Multi-Scale Feature Image Translation, p.24, 2017.

A. M. Stuart, Inverse problems: A Bayesian perspective, Acta Numerica, vol.19, pp.451-559, 2010.

D. Sun, S. Roth, J. P. Lewis, and M. J. Black, Learning Optical Flow, Lecture Notes in Computer Science, pp.83-97, 2008.

I. Sutskever and G. Hinton, Temporal-Kernel Recurrent Neural Networks, Neural Networks, vol.23, issue.2, pp.239-243, 2010.

U. Thissen, R. Van-brakel, A. P. De-weijer, W. J. Melssen, and L. M. Buydens, Using support vector machines for time series prediction, Chemometrics and Intelligent Laboratory Systems, vol.69, issue.1-2, pp.35-49, 2003.

J. Tompson, K. Schlachter, P. Sprechmann, and K. Perlin, Accelerating Eulerian Fluid Simulation With Convolutional Networks, Proceedings of Machine Learning Research. International Convention Centre, vol.70, pp.3424-3433, 2017.

, Frechet ChemNet Distance: A Metric for Generative Models for Molecules in Drug Discovery, p.89

Y. Trémolet, Accounting for an imperfect model in 4D-Var, Quarterly Journal of the Royal Meteorological Society, vol.132, issue.621, pp.2483-2504, 2006.

. Tripathi, Z. C. Subarna, T. Q. Lipton, and . Nguyen, Correction by Projection: Denoising Images with Generative Adversarial Networks, vol.67, p.23, 2018.

G. K. Vallis, Atmospheric and Oceanic Fluid Dynamics, p.38, 2017.

. Van-amersfoort, A. Joost, M. Kannan, A. Ranzato, D. Szlam et al., Transformation-Based Models of Video Sequences, p.12, 2017.

. Van-veen, A. David, E. Jalal, S. Price, A. G. Vishwanath et al., Compressed Sensing with Deep Image Prior and Learned Regularization, 2018.

. Wang, M. Ting-chun, J. Liu, G. Zhu, A. Liu et al., Video-to-Video Synthesis, p.94, 2018.

Y. Wang, Z. Gao, M. Long, J. Wang, and P. S. Yu, PredRNN++: Towards A Resolution of the Deep-in-Time Dilemma in Spatiotemporal Predictive Learning, 2018.

C. K. Wikle and M. B. Hooten, A general science-based framework for dynamical spatio-temporal models, TEST, vol.19, issue.3, pp.417-451, 2010.

Y. Yin, A. Pajot, P. Gallinari, and E. De-bézenac, Unsupervised Inpainting for Occluded Sea Surface Temperature Sequences, Climatinformatics Workshop, 2019.

F. Yu, Y. Zhang, S. Song, A. Seff, and J. Xiao, LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop, vol.86, p.67, 2015.

J. J. Yu, A. W. Harley, and K. G. Derpanis, Back to Basics: Unsupervised Learning of Optical Flow via Brightness Constancy and Motion Smoothness, Lecture Notes in Computer Science, pp.3-10, 2016.

J. Yu, Z. Lin, J. Yang, X. Shen, X. Lu et al., Generative Image Inpainting with Contextual Attention, 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, p.24, 2018.

. Zhang, I. J. Han, D. N. Goodfellow, A. Metaxas, and . Odena, Self-Attention Generative Adversarial Networks, vol.85, 2018.

J. Zhu, T. Park, P. Isola, and A. A. Efros, Unpaired Image-to-Image Translation Using Cycle-Consistent Adversarial Networks, 2017 IEEE International Conference on Computer Vision (ICCV), 2017.

J. Zhu, R. Zhang, D. Pathak, T. Darrell, A. A. Efros et al., Toward Multimodal Imageto-Image Translation, 2017.