A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks.

Autor: Kadeethum T; Sibley School of Mechanical and Aerospace, EngineeringCornell University, Ithaca, NY, USA., O'Malley D; Computational Earth Science, Los Alamos National Laboratory, Los Alamos, NM, USA., Fuhg JN; Sibley School of Mechanical and Aerospace, EngineeringCornell University, Ithaca, NY, USA., Choi Y; Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA, USA., Lee J; Civil & Environmental Engineering/Water Resources Research Center, University of Hawai'i at Manoa, Honolulu, HI, USA., Viswanathan HS; Computational Earth Science, Los Alamos National Laboratory, Los Alamos, NM, USA., Bouklas N; Sibley School of Mechanical and Aerospace, EngineeringCornell University, Ithaca, NY, USA. nbouklas@cornell.edu.; Center for Applied Mathematics, Cornell University, Ithaca, NY, USA. nbouklas@cornell.edu.
Jazyk: angličtina
Zdroj: Nature computational science [Nat Comput Sci] 2021 Dec; Vol. 1 (12), pp. 819-829. Date of Electronic Publication: 2021 Dec 20.
DOI: 10.1038/s43588-021-00171-3
Abstrakt: Here 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.
(© 2021. The Author(s), under exclusive licence to Springer Nature America, Inc.)
Databáze: MEDLINE
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