Application of physics-informed neural networks for self-similar and transient solutions of spontaneous imbibition

Deng, Lichi; Pan, Yuewei

doi:10.1016/j.petrol.2021.108644

Cited by 17 publications

(3 citation statements)

References 31 publications

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“…We will show their results in the following pages. Deng et al (Deng and Pan, 2021) adopted the concept and workflow of the deep physics-informed neural networks to solve Spontaneous imbibition (as shown in Figure 2). This is because the traditional method is very complicated to solve the spontaneous imbibition governing equation, whether it is a self-similar solution controlled by an ordinary differential equation or a transient solution.…”

Section: Methods Used Referencementioning

confidence: 99%

“…Previous studies (Papaliangas et al, 1993;Sklavounos and Sakellariou, 1995;Indraratna et al, 1999;Wang et al, 2000;Jin et al, 2006;Vardakos. et al, 2007;Tiryaki, 2008;Zorlu et al, 2008;Ceryan et al, 2012;Samani and Bafghi, 2012;Yagiz et al, 2012;Rajesh Kumar et al, 2013;Zheng et al, 2013;Gu et al, 2015;Liu et al, 2015;Song et al, 2015;Wang et al, 2015;Raissi et al, 2018;Matos et al, 2019;Almajid and Abu-Alsaud, 2021;Dantas Neto et al, 2021;Deng and Pan, 2021;Haghighat et al, 2021;Hasanipanah et al, 2021;Fathipour-Azar, 2022;Garg et al, 2022;Li and Chen, 2022;Mahmoodzadeh et al, 2022) have shown that machine learning methods can provide new ideas for rock mechanics problems, and this issue is no exception (Ghaboussi and Sidarta, 1998;Jaksa. and Maier., 2009).…”

Section: Determining Constitutive Behaviorsmentioning

confidence: 99%

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Machine learning for rock mechanics problems; an insight

Taleghani

Balushi

et al. 2022

Front. Mech. Eng.

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Due to inherent heterogeneity of geomaterials, rock mechanics involved with extensive lab experiments and empirical correlations that often lack enough accuracy needed for many engineering problems. Machine learning has several characters that makes it an attractive choice to reduce number of required experiments or develop more effective correlations. The timeliness of this effort is supported by several recent technological advances. Machine learning, data analytics, and data management have expanded rapidly in many commercial sectors, providing an array of resources that can be leveraged for subsurface applications. In the last 15 years, deep learning in the form of deep neural networks, has been used very effectively in diverse applications, such as computer vision, seismic inversion, and natural language processing. Despite the remarkable success in these and related areas, deep learning has not yet been widely used in the field of scientific computing specially when it comes to subsurface applications due to the lack of large amount of data to train algorithms. In this paper, we review such efforts and try to envision future game-changing advances that may impact this field.

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Section: Methods Used Referencementioning

confidence: 99%

Section: Determining Constitutive Behaviorsmentioning

confidence: 99%

Machine learning for rock mechanics problems; an insight

Taleghani

Balushi

et al. 2022

Front. Mech. Eng.

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“…A key challenge was capturing the shock front behavior. Deng and Pan 22 applied PINN to study 1D spontaneous imbibition using a Lagrangian formulation. They investigated ET flow for self-similar counter-and cocurrent flow and also considered more general boundary conditions during co-current SI where the ET flow would not be self-similar due to countercurrent production at the inlet.…”

Section: Usedmentioning

confidence: 99%

Simulation and Prediction of Countercurrent Spontaneous Imbibition at Early and Late Time Using Physics-Informed Neural Networks

Abbasi,

Andersen

2023

Energy Fuels

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The application of physics-informed neural networks (PINNs) is investigated for the first time in solving the onedimensional 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 = T 0.5 ; and the third as a sole function of Z = X/T 0.5 (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 nonlinearity 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.

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Physics-informed deep learning for three-dimensional transient heat transfer analysis of functionally graded materials

et al. 2023

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We present a physics-informed deep learning model for the transient heat transfer analysis of three-dimensional functionally graded materials (FGMs) employing a Runge–Kutta discrete time scheme. Firstly, the governing equation, associated boundary conditions and the initial condition for transient heat transfer analysis of FGMs with exponential material variations are presented. Then, the deep collocation method with the Runge–Kutta integration scheme for transient analysis is introduced. The prior physics that helps to generalize the physics-informed deep learning model is introduced by constraining the temperature variable with discrete time schemes and initial/boundary conditions. Further the fitted activation functions suitable for dynamic analysis are presented. Finally, we validate our approach through several numerical examples on FGMs with irregular shapes and a variety of boundary conditions. From numerical experiments, the predicted results with PIDL demonstrate well agreement with analytical solutions and other numerical methods in predicting of both temperature and flux distributions and can be adaptive to transient analysis of FGMs with different shapes, which can be the promising surrogate model in transient dynamic analysis.

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Application of physics-informed neural networks for self-similar and transient solutions of spontaneous imbibition

Cited by 17 publications

References 31 publications

Machine learning for rock mechanics problems; an insight

Machine learning for rock mechanics problems; an insight

Simulation and Prediction of Countercurrent Spontaneous Imbibition at Early and Late Time Using Physics-Informed Neural Networks

Physics-informed deep learning for three-dimensional transient heat transfer analysis of functionally graded materials

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