Inscrição na biblioteca: Guest
Journal of Machine Learning for Modeling and Computing

Publicou 4 edições por ano

ISSN Imprimir: 2689-3967

ISSN On-line: 2689-3975

Indexed in

USING PHYSICS-INFORMED NEURAL NETWORKS TO SOLVE FOR PERMEABILITY FIELD UNDER TWO-PHASE FLOW IN HETEROGENEOUS POROUS MEDIA

Volume 4, Edição 1, 2023, pp. 1-19
DOI: 10.1615/JMachLearnModelComput.2023046921
Get accessDownload

RESUMO

Physics-informed neural networks (PINNs) have recently been applied to a wide range of computational physical problems. In this paper, we use PINNs to solve an inverse two-phase flow problem in heterogeneous porous media where only sparse direct and indirect measurements are available. The forward two-phase flow problem is governed by a coupled system of partial differential equations (PDEs) with initial and boundary conditions. As for inverse problems, the solutions are assumed to be known at scattered locations but some coefficients or variable functions in the PDEs are missing or incomplete. The idea is to train multiple neural networks representing the solutions and the unknown variable function at the same time such that both the underlying physical laws and the measurements can be honored. The numerical results show that our proposed method is able to recover the incomplete permeability field in different scenarios. Moreover, we show that the method can be used to forecast the future dynamics with the same format of loss function formulation. In addition, we employ a neural network structure inspired by the deep operator networks (DeepONets) to represent the solutions which can potentially shorten the time of the training process.

Referências
  1. Alnaes, M., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., and Wells, G.N., The FEniCS Project Version 1.5, Arch. Numer. Software, 2015. DOI: 10.11588/ans.2015.100.20553.

  2. Berg, J. and Nystrom, K., A Unified Deep Artificial Neural Network Approach to Partial Differential Equations in Complex Geometries, Neurocomput., vol. 317, pp. 28-41, 2018.

  3. Fraces, C.G., Papaioannou, A., and Tchelepi, H., Physics Informed Deep Learning for Transport in Porous Media. Buckley Leverett Problem, arXiv: 2001.05172, 2020.

  4. Goswami, S., Anitescu, C., Chakraborty, S., and Rabczuk, T., Transfer Learning Enhanced Physics Informed Neural Network for Phase-Field Modeling of Fracture, Theor. Appl. Fracture Mech., vol. 106, p. 102447, 2020.

  5. Haghighat, E., Raissi, M.,Moure, A., Gomez, H., and Juanes, R., A Deep Learning Framework for Solution and Discovery in Solid Mechanics, arXiv: 2003.02751, 2020.

  6. He, Q., Barajas-Solano, D., Tartakovsky, G., and Tartakovsky, A.M., Physics-Informed Neural Networks forMultiphysics Data Assimilation with Application to Subsurface Transport, Adv. Water Res., vol. 141, no. 2, p. 103610, 2020.

  7. Kharazmi, E., Zhang, Z., and Karniadakis, G.E., hp-VPINNs: Variational Physics-Informed Neural Networks with Domain Decomposition, arXiv: 2003.05385, 2020.

  8. Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., and Lerer, A., Automatic Differentiation in PyTorch, in 31st Conf. on Neural Information Processing Systems (NIPS 2017), Long Beach, CA, USA, December 4-9, 2017.

  9. Raissi, M., Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations, J. Mach. Learn. Res., vol. 19, no. 1, pp. 932-955, 2018.

  10. Song, D.H. and Tartakovsky, D.M., Transfer Learning on Multifidelity Data, J. Mach. Learn. Model. Comput., vol. 3, no. 1, pp. 31-47, 2022.

  11. Tartakovsky, A.M., Marrero, C.O., Perdikaris, P., Tartakovsky, G.D., and Barajas-Solano, D., Learning Parameters and Constitutive Relationship with Physics Informed Deep Neural Networks, arXiv: 1808.03398, 2018.

  12. Tchelepi, H.A. and Fuks, O., Limitations of Physics InformedMachine Learning for Nonlinear Two-Phase Transport in Porous Media, J. Machine Learn. Model. Comput., vol. 1, no. 1, pp. 19-37, 2020.

  13. Wang, N., Chang, H., and Zhang, D., Theory-Guided Auto-Encoder for Surrogate Construction and Inverse Modeling, Comput. Methods Appl. Mech. Eng., vol. 385, p. 114037, 2021a.

  14. Wang, N., Chang, H., Zhang, D., Xue, L., and Chen, Y., Efficient Well Placement Optimization Based on Theory-Guided Convolutional Neural Network, J. Petrol. Sci. Eng., vol. 208, p. 109545, 2022.

  15. Wang, S. and Perdikaris, P., Long-Time Integration of Parametric Evolution Equations with Physics-Informed Deeponets, arXiv: 2106.05384, 2021.

  16. Wang, S., Wang, H., and Perdikaris, P., Learning the Solution Operator of Parametric Partial Differential Equations with Physics-Informed DeepONets, Sci. Adv., vol. 7, no. 40, p. eabi8605, 2021b.

  17. Wang, Y. and Lin, G., Efficient Deep Learning Techniques for Multiphase Flow Simulation in Heterogeneous Porousc Media, J. Comput. Phys., vol. 401, p. 108968, 2020.

  18. Yang, L., Zhang, D., and Karniadakis, G.E., Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations, arXiv: 1811.02033, 2018.

  19. Yang, M. and Foster, J.T., hp-Variational Physics-Informed Neural Networks for Nonlinear Two-Phase Transport in Porous Media, J. Mach. Learn. Model. Comput., vol. 2, no. 2, pp. 15-32, 2021.

  20. Zhou, Z., Zabaras, N., and Tartakovsky, D.M., Deep Learning for Simultaneous Inference of Hydraulic and Transport Properties, Water Res. Res., vol. 58, no. 10, p. e2021WR031438, 2022.

  21. Zhu, Y., Zabaras, N., Koutsourelakis, P.S., and Perdikaris, P., Physics-ConstrainedDeep Learning for High-Dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data, J. Comput. Phys., vol. 394, pp. 56-81, 2019.

Portal Digital Begell Biblioteca digital da Begell eBooks Diários Referências e Anais Coleções de pesquisa Políticas de preços e assinaturas Begell House Contato Language English 中文 Русский Português German French Spain