Hamdi Tchelepi | Department Chair, Professor of Energy Resources Engineering
Olga Fuks and Hamdi Tchelepi (Presenter)
ABSTRACTDeep learning techniques have recently been applied to a wide range of computational physics problems. We focus on developing a physics-based approach that enables the neural network to learn the solution of a fluid-flow problem governed by a nonlinear partial differential equation (PDE). Physics Informed Machine Learning (PIML) approaches encode the underlying physical law (i.e., the PDE) into the neural network. We investigate the applicability of a specific PIML approach to the forward problem of immiscible two-phase fluid flow in a one-dimensional porous medium. This problem is governed by a nonlinear first-order hyperbolic PDE subject to initial and boundary data. PIML is used to solve this forward problem without any labeled data in the interior of the domain. Particularly, we are interested in nonconvex flux functions that can lead to saturation profiles with shocks and mixed waves (shocks and rarefactions). We found that such a PIML approach fails to provide reasonable approximations to the solution, especially when shocks emerge from smooth initial data. We investigated several architectures and experimented with wide ranges of neural-network parameters. Our overall finding is that PIML strategies that employ the nonlinear hyperbolic conservation equation in the loss function fail to "learn" the solution. However, we have found that employing a parabolic form of the conservation equation, whereby a small amount of diffusion is added, makes it possible for the neural network to consistently learn accurate approximations of saturation profiles involving shocks and mixed waves.
BIODr. Tchelepi is interested in numerical simulation of flow and transport processes in natural porous media. Application areas include reservoir simulation and subsurface CO2 sequestration. Current research activities include (1) modeling unstable miscible and immiscible flow in heterogeneous formations, (2) developing multiscale formulations and scalable solution algorithms for multiphase flow in large-scale subsurface systems, and (3) developing stochastic formulations for quantification of the uncertainty associated with predictions of flow and transport in large subsurface formations.
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