52 research outputs found
Learning Generic Solutions for Multiphase Transport in Porous Media via the Flux Functions Operator
Traditional numerical schemes for simulating fluid flow and transport in
porous media can be computationally expensive. Advances in machine learning for
scientific computing have the potential to help speed up the simulation time in
many scientific and engineering fields. DeepONet has recently emerged as a
powerful tool for accelerating the solution of partial differential equations
(PDEs) by learning operators (mapping between function spaces) of PDEs. In this
work, we learn the mapping between the space of flux functions of the
Buckley-Leverett PDE and the space of solutions (saturations). We use
Physics-Informed DeepONets (PI-DeepONets) to achieve this mapping without any
paired input-output observations, except for a set of given initial or boundary
conditions; ergo, eliminating the expensive data generation process. By
leveraging the underlying physical laws via soft penalty constraints during
model training, in a manner similar to Physics-Informed Neural Networks
(PINNs), and a unique deep neural network architecture, the proposed
PI-DeepONet model can predict the solution accurately given any type of flux
function (concave, convex, or non-convex) while achieving up to four orders of
magnitude improvements in speed over traditional numerical solvers. Moreover,
the trained PI-DeepONet model demonstrates excellent generalization qualities,
rendering it a promising tool for accelerating the solution of transport
problems in porous media.Comment: 23 pages, 11 figure
Physics-informed machine learning for solving partial differential equations in porous media
Physical phenomenon in nature is generally simulated by partial differential equations. Among different sorts of partial differential equations, the problem of two-phase flow in porous media has been paid intense attention. As a promising direction, physics-informed neural networks shed new light on the solution of partial differential equations. However, current physics-informed neural networks’ ability to learn partial differential equations relies on adding artificial diffusion or using prior knowledge to increase the number of training points along the shock trajectory, or adaptive activation functions. To address these issues, this study proposes a physics-informed neural network with long short-term memory and attention mechanism, an ingenious method to solve the Buckley-Leverett partial differential equations representing two-phase flow in porous media. The designed network structure overcomes the dependency on artificial diffusion terms and enhances the importance of shallow features. The experimental results show that the proposed method is in good agreement with analytical solutions. Accurate approximations are shown even when encountering shock points in saturated fields of porous media. Furthermore, experiments show our innovative method outperforms existing traditional physics-informed machine learning approaches.Cited as: Shan, L., Liu, C., Liu, Y., Tu, Y., Dong, L., Hei, X. Physics-informed machine learning for solving partial differential equations in porous media. Advances in Geo-Energy Research, 2023, 8(1): 37-44. https://doi.org/10.46690/ager.2023.04.0
Simulation and Prediction of Countercurrent Spontaneous Imbibition at Early and Late Time Using Physics-Informed Neural Networks
The application of physics-informed neural networks (PINNs) is investigated for the first time in solving the one-dimensional countercurrent spontaneous imbibition (COUCSI) problem at both early and late time (i.e., before and after the imbibition front meets the no-flow boundary). We introduce the utilization of Change-of-Variables as a technique for improving the performance of PINNs. We formulated the COUCSI problem in three equivalent forms by changing the independent variables. The first describes saturation as a function of normalized position X and time T; the second as a function of X and Y = T0.5; and the third as a sole function of Z = X/T0.5 (valid only at early time). The PINN model was generated using a feed-forward neural network and trained based on minimizing a weighted loss function, including the physics-informed loss term and terms corresponding to the initial and boundary conditions. All three formulations could closely approximate the correct solutions, with water saturation mean absolute errors around 0.019 and 0.009 for XT and XY formulations and 0.012 for the Z formulation at early time. The Z formulation perfectly captured the self-similarity of the system at early time. This was less captured by XT and XY formulations. The total variation of saturation was preserved in the Z formulation, and it was better preserved with XY- than XT formulation. Redefining the problem based on the physics-inspired variables reduced the non-linearity of the problem and allowed higher solution accuracies, a higher degree of loss-landscape convexity, a lower number of required collocation points, smaller network sizes, and more computationally efficient solutions.publishedVersio
Inverse modeling of nonisothermal multiphase poromechanics using physics-informed neural networks
We propose a solution strategy for parameter identification in multiphase
thermo-hydro-mechanical (THM) processes in porous media using physics-informed
neural networks (PINNs). We employ a dimensionless form of the THM governing
equations that is particularly well suited for the inverse problem, and we
leverage the sequential multiphysics PINN solver we developed in previous work.
We validate the proposed inverse-modeling approach on multiple benchmark
problems, including Terzaghi's isothermal consolidation problem, Barry-Mercer's
isothermal injection-production problem, and nonisothermal consolidation of an
unsaturated soil layer. We report the excellent performance of the proposed
sequential PINN-THM inverse solver, thus paving the way for the application of
PINNs to inverse modeling of complex nonlinear multiphysics problems
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