We employ and adapt the image-to-image translation concept based on conditional generative adversarial networks (cGAN) for learning a forward and an inverse solution operator of partial differential equations (PDEs). We focus on steady-state solutions of coupled hydromechanical processes in heterogeneous porous media and present the parameterization of the spatially heterogeneous coefficients, which is exceedingly difficult using standard reduced-order modeling techniques. We show that our framework provides a speed-up of at least 2,000 times compared to a finite-element solver and achieves a relative root-mean-square error (r.m.s.e.) of less than 2% for forward modeling. For inverse modeling, the framework estimates the heterogeneous coefficients, given an input of pressure and/or displacement fields, with a relative r.m.s.e. of less than 7%, even for cases where the input data are incomplete and contaminated by noise. The framework also provides a speed-up of 120,000 times compared to a Gaussian prior-based inverse modeling approach while also delivering more accurate results.
Kadeethum, Teeratorn, et al. "A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks." Nature Computational Science, vol. 1, no. 12, Dec. 2021. https://doi.org/10.1038/s43588-021-00171-3
Kadeethum, Teeratorn, O’Malley, Daniel, Fuhg, Jan Niklas, et al., "A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks," Nature Computational Science 1, no. 12 (2021), https://doi.org/10.1038/s43588-021-00171-3
@article{osti_1843114,
author = {Kadeethum, Teeratorn and O’Malley, Daniel and Fuhg, Jan Niklas and Choi, Youngsoo and Lee, Jonghyun and Viswanathan, Hari S. and Bouklas, Nikolaos},
title = {A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks},
annote = {We employ and adapt the image-to-image translation concept based on conditional generative adversarial networks (cGAN) for learning a forward and an inverse solution operator of partial differential equations (PDEs). We focus on steady-state solutions of coupled hydromechanical processes in heterogeneous porous media and present the parameterization of the spatially heterogeneous coefficients, which is exceedingly difficult using standard reduced-order modeling techniques. We show that our framework provides a speed-up of at least 2,000 times compared to a finite-element solver and achieves a relative root-mean-square error (r.m.s.e.) of less than 2% for forward modeling. For inverse modeling, the framework estimates the heterogeneous coefficients, given an input of pressure and/or displacement fields, with a relative r.m.s.e. of less than 7%, even for cases where the input data are incomplete and contaminated by noise. The framework also provides a speed-up of 120,000 times compared to a Gaussian prior-based inverse modeling approach while also delivering more accurate results.},
doi = {10.1038/s43588-021-00171-3},
url = {https://www.osti.gov/biblio/1843114},
journal = {Nature Computational Science},
issn = {ISSN 2662-8457},
number = {12},
volume = {1},
place = {United States},
publisher = {Springer Nature},
year = {2021},
month = {12}}
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)
Medical Image Computing and Computer-Assisted Intervention – MICCAI 2015: 18th International Conference, Munich, Germany, October 5-9, 2015, Proceedings, Part IIIhttps://doi.org/10.1007/978-3-319-24574-4_28