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

Teeratorn Kadeethum

doi:10.1038/s43588-021-00171-3

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

2021-12-20

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DOI：10.1038/s43588-021-00171-3

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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.

Keywords:

INFORMED NEURAL-NETWORKS

DEEP LEARNING FRAMEWORK

MONTE-CARLO

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

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