×

zbMATH — the first resource for mathematics

U-net generative adversarial network for subsurface facies modeling. (English) Zbl 1453.86047
Summary: Subsurface models are central pieces of information in different earth-related disciplines such as groundwater management and hydrocarbon reservoir characterization. These models are normally obtained using geostatistical simulation methods. Recently, methods based on deep learning algorithms have been applied as subsurface model generators. However, there are still challenges on how to include conditioning data and ensure model variability within a set of realizations. We illustrate the potential of Generative Adversarial Networks (GANs) to create unconditional and conditional facies models. Based on a synthetic facies dataset, we first train a Deep Convolution GAN (DCGAN) to produce unconditional facies models. Then, we show how image-to-image translation based on a U-Net GAN framework, including noise-layers, content loss function and diversity loss function, is used to model conditioning geological facies. Results show that GANs are powerful models to capture complex geological facies patterns and to generate facies realizations indistinguishable from the ones comprising the training dataset. The U-Net GAN framework performs well in providing variable models while honoring conditioning data in several scenarios. The results shown herein are expected to spark a new generation of methods for subsurface geological facies with fragmentary measurements.
MSC:
86A32 Geostatistics
68T05 Learning and adaptive systems in artificial intelligence
Software:
CycleGAN; GSLIB; pix2pix
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Arjovsky, M., Bottou, L.: Towards principled methods for training generative adversarial networks. arXiv preprint arXiv:1701.04862 (2017)
[2] Arjovsky, M., Chintala, S., Bottou, L.: Wasserstein gan. arXiv preprint arXiv:1701.07875 (2017)
[3] Arpat, GB; Caers, J., Conditional simulation with patterns, Math. Geol., 39, 2, 177-203 (2007)
[4] Audebert, N., Le Saux, B., Lefèvre, S.: Generative adversarial networks for realistic synthesis of hyperspectral samples. In: IGARSS 2018-2018 IEEE International Geoscience and Remote Sensing Symposium 2018, pp. 4359-4362. IEEE
[5] Azevedo, L.; Nunes, R.; Correia, P.; Soares, A.; Guerreiro, L.; Neto, GS, Multidimensional scaling for the evaluation of a geostatistical seismic elastic inversion methodology, Geophysics, 79, 1, M1-M10 (2014)
[6] Azevedo, L.; Paneiro, G.; Santos, A.; Soares, A., Generative adversarial network as a stochastic subsurface model reconstruction, Comput. Geosci., 24, 4, 1673-1692 (2020)
[7] Caterini, A., Chang, D.E.: A Novel Representation of Neural Networks. arXiv e-prints (2016)
[8] Caterini, A.L., Chang, D.E.: A geometric framework for convolutional neural networks. arXiv preprint arXiv:1608.04374 (2016)
[9] Chan, S.; Elsheikh, AH, Parametric generation of conditional geological realizations using generative neural networks, Comput. Geosci., 23, 5, 925-952 (2019) · Zbl 1425.86018
[10] Cox, T.F., Cox, M.A.A.: Multidimensional scaling. Chapman & Hall/CRC, Boca Raton (2001) · Zbl 1004.91067
[11] Creswell, A.; White, T.; Dumoulin, V.; Arulkumaran, K.; Sengupta, B.; Bharath, AA, Generative adversarial networks: an overview, IEEE Signal Process. Mag., 35, 1, 53-65 (2018)
[12] Daly, C., Caers, J.: Multi-point geostatistics-an introductory overview. First Break 28(9), 39-47 (2010)
[13] Deutsch, C.V., Journel, A.G.: Geostatistical software library and user’s guide. New York 119(147) (1992)
[14] Donahue, C., McAuley, J., Puckette, M.: Synthesizing audio with generative adversarial networks. arXiv preprint arXiv:1802.04208 1 (2018)
[15] Drozdzal, M., Vorontsov, E., Chartrand, G., Kadoury, S., Pal, C.: The importance of skip connections in biomedical image segmentation. In: Carneiro G, et al. (eds.) Deep Learning and Data Labeling for Medical Applications. DLMIA 2016, LABELS 2016. Lecture Notes in Computer Science, vol 10008. Springer, Cham (2016). doi:10.1007/978-3-319-46976-8_19
[16] Dupont, E., Zhang, T., Tilke, P., Liang, L., Bailey, W.: Generating realistic geology conditioned on physical measurements with generative adversarial networks. arXiv preprint arXiv:1802.03065 (2018)
[17] Goodfellow, I.: NIPS 2016 tutorial: Generative adversarial networks. arXiv preprint arXiv:1701.00160 (2016)
[18] Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., Bengio, Y.: Generative adversarial nets. In: Advances in neural information processing systems 2014, pp. 2672-2680
[19] Hong, Y.; Hwang, U.; Yoo, J.; Yoon, S., How generative adversarial networks and their variants work: an overview, ACM Comput. Surv. (CSUR), 52, 1, 1-43 (2019)
[20] Hore, A., Ziou, D.: Image quality metrics: PSNR vs. SSIM. In: 2010 20th international conference on pattern recognition 2010, pp. 2366-2369. IEEE
[21] Isola, P., Zhu, J.-Y., Zhou, T., Efros, A.A.: Image-to-Image Translation with Conditional Adversarial Networks. In: Proceedings of the IEEE conference on computer vision and pattern recognition 2017, pp. 1125-1134
[22] Jetchev, N., Bergmann, U., Vollgraf, R.: Texture synthesis with spatial generative adversarial networks. arXiv preprint arXiv:1611.08207 (2016)
[23] Karras, T., Laine, S., Aila, T.: A Style-Based Generator Architecture for Generative Adversarial Networks. In: Proceedings of the IEEE conference on computer vision and pattern recognition 2019, pp. 4401-4410
[24] Laloy, E.; Hérault, R.; Jacques, D.; Linde, N., Training-image based geostatistical inversion using a spatial generative adversarial neural network, Water Resour. Res., 54, 1, 381-406 (2018)
[25] Laloy, E.; Linde, N.; Ruffino, C.; Hérault, R.; Gasso, G.; Jacques, D., Gradient-based deterministic inversion of geophysical data with generative adversarial networks: is it feasible?, Comput. Geosci., 133, 104333 (2019)
[26] Ledig, C., Theis, L., Huszár, F., Caballero, J., Cunningham, A., Acosta, A., Aitken, A., Tejani, A., Totz, J., Wang, Z.: Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network. In: Proceedings of the IEEE conference on computer vision and pattern recognition 2017, pp. 4681-4690
[27] Mao, Q., Lee, H.-Y., Tseng, H.-Y., Ma, S., Yang, M.-H.: Mode Seeking Generative Adversarial Networks for Diverse Image Synthesis. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition 2019, pp. 1429-1437
[28] Mariethoz, G.; Caers, J., Multiple-Point Geostatistics: Stochastic Modeling with Training Images (2014), Hoboken: John Wiley & Sons, Hoboken
[29] Mariethoz, G., Renard, P., Straubhaar, J.: The direct sampling method to perform multiple-point geostatistical simulations. Water Resources Research 46(11) (2010)
[30] Matheron, G., Beucher, H., De Fouquet, C., Galli, A., Guerillot, D., Ravenne, C.: Conditional simulation of the geometry of fluvio-deltaic reservoirs. In: Spe annual technical conference and exhibition 1987. Society of Petroleum Engineers
[31] Metz, L., Poole, B., Pfau, D., Sohl-Dickstein, J.: Unrolled generative adversarial networks. arXiv preprint arXiv:1611.02163 (2016)
[32] Mirza, M., Osindero, S.: Conditional generative adversarial nets. arXiv preprint arXiv:1411.1784 (2014)
[33] Mosser, L.; Dubrule, O.; Blunt, MJ, Reconstruction of three-dimensional porous media using generative adversarial neural networks, Phys. Rev. E, 96, 4 (2017)
[34] Mosser, L.; Dubrule, O.; Blunt, MJ, Stochastic reconstruction of an oolitic limestone by generative adversarial networks, Transp. Porous Media, 125, 1, 81-103 (2018)
[35] Mosser, L., Dubrule, O., Blunt, M.J.: Conditioning of three-dimensional generative adversarial networks for pore and reservoir-scale models. arXiv preprint arXiv:1802.05622 (2018) · Zbl 1428.86022
[36] Pyrcz, MJ; Deutsch, CV, Geostatistical reservoir modeling (2014), Oxford: Oxford university press, Oxford
[37] Radford, A., Metz, L., Chintala, S.: Unsupervised representation learning with deep convolutional generative adversarial networks. arXiv preprint arXiv:1511.06434 (2015)
[38] Ronneberger, O., Fischer, P., Brox, T.: U-net: convolutional networks for biomedical image segmentation. In: International Conference on Medical image computing and computer-assisted intervention 2015, pp. 234-241. Springer
[39] Sarkar, BC; Sikdar, PK, Geostatistics in groundwater Modelling, Groundwater Development and Management: Issues and Challenges in South Asia, 147-169 (2019), Cham: Springer International Publishing, Cham
[40] Song, S., Mukerji, T., Hou, J.: GANSim: Conditional Facies Simulation Using an Improved Progressive Growing of Generative Adversarial Networks (GANs). EarthArXiv. doi:10.31223/osf.io/fm24b (2020)
[41] Strebelle, S., Conditional simulation of complex geological structures using multiple-point statistics, Math. Geol., 34, 1, 1-21 (2002) · Zbl 1036.86013
[42] Sun, AY, Discovering state-parameter mappings in subsurface models using generative adversarial networks, Geophys. Res. Lett., 45, 20, 11,137-111,146 (2018)
[43] Wackernagel, H.: Multivariate Geostatistics: an Introduction with Applications. Springer Science & Business Media (2013) · Zbl 0871.62105
[44] Wang, Z.; Bovik, AC; Sheikh, HR; Simoncelli, EP, Image quality assessment: from error visibility to structural similarity, IEEE Trans. Image Process., 13, 4, 600-612 (2004)
[45] Yang, D., Hong, S., Jang, Y., Zhao, T., Lee, H.: Diversity-sensitive conditional generative adversarial networks. arXiv preprint arXiv:1901.09024 (2019)
[46] Yeh, R.A., Chen, C., Yian Lim, T., Schwing, A.G., Hasegawa-Johnson, M., Do, M.N.: Semantic Image Inpainting with Deep Generative Models. In: Proceedings of the IEEE conference on computer vision and pattern recognition 2017, pp. 5485-5493
[47] Zhang, T-F; Tilke, P.; Dupont, E.; Zhu, L-C; Liang, L.; Bailey, W., Generating geologically realistic 3D reservoir facies models using deep learning of sedimentary architecture with generative adversarial networks, Pet. Sci., 16, 3, 541-549 (2019)
[48] Zhong, Z.; Sun, AY; Jeong, H., Predicting co2 plume migration in heterogeneous formations using conditional deep convolutional generative adversarial network, Water Resour. Res., 55, 7, 5830-5851 (2019)
[49] Zhu, J-Y; Park, T.; Isola, P.; Efros, AA, Unpaired Image-to-Image Translation Using Cycle-Consistent Adversarial Networks (2017), In: Proceedings of the IEEE international conference on computer vision, In
[50] Zhu, L.; Chen, Y.; Ghamisi, P.; Benediktsson, JA, Generative adversarial networks for hyperspectral image classification, IEEE Trans. Geosci. Remote Sens., 56, 9, 5046-5063 (2018)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.