Porous-DeepONet: Learning the Solution Operators of Parametric Reactive Transport Equations in Porous Media

Pan Huang, Yifei Leng, Cheng Lian, Honglai Liu

Engineering ›› 2024, Vol. 39 ›› Issue (8) : 94-103.

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Engineering ›› 2024, Vol. 39 ›› Issue (8) : 94-103. DOI: 10.1016/j.eng.2024.07.002
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Porous-DeepONet: Learning the Solution Operators of Parametric Reactive Transport Equations in Porous Media

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Abstract

Reactive transport equations in porous media are critical in various scientific and engineering disciplines, but solving these equations can be computationally expensive when exploring different scenarios, such as varying porous structures and initial or boundary conditions. The deep operator network (DeepONet) has emerged as a popular deep learning framework for solving parametric partial differential equations. However, applying the DeepONet to porous media presents significant challenges due to its limited capability to extract representative features from intricate structures. To address this issue, we propose the Porous-DeepONet, a simple yet highly effective extension of the DeepONet framework that leverages convolutional neural networks (CNNs) to learn the solution operators of parametric reactive transport equations in porous media. By incorporating CNNs, we can effectively capture the intricate features of porous media, enabling accurate and efficient learning of the solution operators. We demonstrate the effectiveness of the Porous-DeepONet in accurately and rapidly learning the solution operators of parametric reactive transport equations with various boundary conditions, multiple phases, and multi-physical fields through five examples. This approach offers significant computational savings, potentially reducing the computation time by 50-1000 times compared with the finite-element method. Our work may provide a robust alternative for solving parametric reactive transport equations in porous media, paving the way for exploring complex phenomena in porous media.

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Porous media / Reactive transport / Solution operator / DeepONet / Neural network

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Pan Huang, Yifei Leng, Cheng Lian, Honglai Liu. Porous-DeepONet: Learning the Solution Operators of Parametric Reactive Transport Equations in Porous Media. Engineering, 2024, 39(8): 94‒103 https://doi.org/10.1016/j.eng.2024.07.002

References

[1]
G. Cai, P. Yan, L. Zhang, H.C. Zhou, H.L. Jiang. Metal-organic framework-based hierarchically porous materials: synthesis and applications. Chem Rev, 121 (20) (2021), pp. 12278-12326.
[2]
M.H. Sun, S.Z. Huang, L.H. Chen, Y. Li, X.Y. Yang, Z.Y. Yuan, et al. Applications of hierarchically structured porous materials from energy storage and conversion, catalysis, photocatalysis, adsorption, separation, and sensing to biomedicine. Chem Soc Rev, 45 (12) (2016), pp. 3479-3563.
[3]
J. Zhou, B. Wang. Emerging crystalline porous materials as a multifunctional platform for electrochemical energy storage. Chem Soc Rev, 46 (22) (2017), pp. 6927-6945.
[4]
C. Perego, R. Millini. Porous materials in catalysis: challenges for mesoporous materials. Chem Soc Rev, 42 (9) (2013), pp. 3956-3976.
[5]
X. Wang, L. Chen, S.Y. Chong, M.A. Little, Y. Wu, W.H. Zhu, et al. Sulfone-containing covalent organic frameworks for photocatalytic hydrogen evolution from water. Nat Chem, 10 (12) (2018), pp. 1180-1189.
[6]
H. Yuk, T. Zhang, S. Lin, G.A. Parada, X. Zhao. Tough bonding of hydrogels to diverse non-porous surfaces. Nat Mater, 15 (2) (2016), pp. 190-196.
[7]
H. Pan, Y. Shao, P. Yan, Y. Cheng, K.S. Han, Z. Nie, et al. Reversible aqueous zinc/manganese oxide energy storage from conversion reactions. Nat Energy, 1 (5) (2016), p. 16039.
[8]
S. Tian, B. Wang, W. Gong, Z. He, Q. Xu, W. Chen, et al. Dual-atom Pt heterogeneous catalyst with excellent catalytic performances for the selective hydrogenation and epoxidation. Nat Commun, 12 (1) (2021), p. 3181.
[9]
C. Lian, M. Janssen, H. Liu, R. van Roij. Blessing and curse: how a supercapacitor’s large capacitance causes its slow charging. Phys Rev Lett, 124 (7) (2020), Article 076001.
[10]
H. Tao, C. Lian, H. Liu. Multiscale modeling of electrolytes in porous electrode: from equilibrium structure to non-equilibrium transport. Green Energy Environ, 5 (3) (2020), pp. 303-321.
[11]
S. Wang, H. Wang, P. Perdikaris. Learning the solution operator of parametric partial differential equations with physics-informed DeepONets. Sci Adv, 7 (40) (2021), Article eabi8605.
[12]
L. Lu, X. Meng, Z. Mao, G.E. Karniadakis. DeepXDE: a deep learning library for solving differential equations. SIAM Rev, 63 (1) (2021), pp. 208-228.
[13]
R. Bostanabad, Y. Zhang, X. Li, T. Kearney, L.C. Brinson, D.W. Apley, et al. Computational microstructure characterization and reconstruction: review of the state-of-the-art techniques. Prog Mater Sci, 95 (2018), pp. 1-41.
[14]
A. Quarteroni, G. Rozza, A. Manzoni. Certified reduced basis approximation for parametrized partial differential equations and applications. J Math Ind, 1 (1) (2011), p. 3.
[15]
R.B. Yunus, S.A. Abdul Karim, A. Shafie, M. Izzatullah, A. Kherd, M.K. Hasan, et al. An overview on deep learning techniques in solving partial differential equations. S.A. Abdul Karim (Ed.), Intelligent systems modeling and simulation II:machine learning, neural networks, efficient numerical algorithm and statistical methods, Springer International Publishing, Cham (2022), pp. 37-47.
[16]
G.E. Karniadakis, I.G. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, L. Yang. Physics-informed machine learning. Nat Rev Phys, 3 (6) (2021), pp. 422-440.
[17]
P. Ren, C. Rao, Y. Liu, J.X. Wang, H. Sun. PhyCRNet: physics-informed convolutional-recurrent network for solving spatiotemporal PDEs. Comput Methods Appl Mech Eng, 389 (2022), Article 114399.
[18]
N. Winovich, K. Ramani, G. Lin. ConvPDE-UQ: convolutional neural networks with quantified uncertainty for heterogeneous elliptic partial differential equations on varied domains. J Comput Phys, 394 (2019), pp. 263-279.
[19]
L. Ruthotto, E. Haber. Deep neural networks motivated by partial differential equations. J Math Imaging Vis, 62 (3) (2020), pp. 352-364.
[20]
H. Gao, L. Sun, J.X. Wang. PhyGeoNet: physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain. J Comput Phys, 428 (2021), Article 110079.
[21]
C. Beck, M. Hutzenthaler, A. Jentzen, B. Kuckuck. An overview on deep learning-based approximation methods for partial differential equations. Discrete Contin Dyn Syst B, 28 (6) (2023), pp. 3697-3746.
[22]
T. Chen, H. Chen. Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems. IEEE Trans Neural Netw, 6 (4) (1995), pp. 911-917.
[23]
L. Lu, P. Jin, G. Pang, Z. Zhang, G.E. Karniadakis. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nat Mach Intell, 3 (3) (2021), pp. 218-229.
[24]
M. Sharma Priyadarshini, S. Venturi, I. Zanardi, M. Panesi. Efficient quasi-classical trajectory calculations by means of neural operator architectures. Phys Chem Chem Phys, 25 (20) (2023), pp. 13902-13912.
[25]
C. Lin, M. Maxey, Z. Li, G.E. Karniadakis. A seamless multiscale operator neural network for inferring bubble dynamics. J Fluid Mech, 929 (2021), p. A18.
[26]
C. Lin, Z. Li, L. Lu, S. Cai, M. Maxey, G.E. Karniadakis. Operator learning for predicting multiscale bubble growth dynamics. J Chem Phys, 154 (10) (2021), Article 104118.
[27]
Q. Zheng, X. Yin, D. Zhang. Inferring electrochemical performance and parameters of Li-ion batteries based on deep operator networks. J Energy Storage, 65 (2023), Article 107176.
[28]
C. Moya, S. Zhang, G. Lin, M. Yue. DeepONet-grid-UQ: a trustworthy deep operator framework for predicting the power grid’s post-fault trajectories. Neurocomputing, 535 (2023), pp. 166-182.
[29]
M. Yin, E. Ban, B.V. Rego, E. Zhang, C. Cavinato, J.D. Humphrey, et al. Simulating progressive intramural damage leading to aortic dissection using DeepONet: an operator-regression neural network. J R Soc Interface, 19 (187) (2022), Article 20210670.
[30]
E. Pickering, S. Guth, G.E. Karniadakis, T.P. Sapsis. Discovering and forecasting extreme events via active learning in neural operators. Nat Comput Sci, 2 (12) (2022), pp. 823-833.
[31]
S. Cai, Z. Wang, L. Lu, T.A. Zaki, G.E. Karniadakis. DeepM&Mnet: inferring the electroconvection multiphysics fields based on operator approximation by neural networks. J Comput Phys, 436 (2021), Article 110296.
[32]
M. Yin, E. Zhang, Y. Yu, G.E. Karniadakis. Interfacing finite elements with deep neural operators for fast multiscale modeling of mechanics problems. Comput Methods Appl Mech Eng, 402 (2022), Article 115027.
[33]
L. Lu, R. Pestourie, S.G. Johnson, G. Romano. Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport. Phys Rev Res, 4 (2) (2022), Article 023210.
[34]
L. Lu, X. Meng, S. Cai, Z. Mao, S. Goswami, Z. Zhang, et al. A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data. Comput Methods Appl Mech Eng, 393 (2022), Article 114778.
[35]
W. Li, M.Z. Bazant, J. Zhu. Phase-field DeepONet: physics-informed deep operator neural network for fast simulations of pattern formation governed by gradient flows of free-energy functionals. Comput Methods Appl Mech Eng, 416 (2023), Article 116299.
[36]
S. Goswami, K. Kontolati, M.D. Shields, G.E. Karniadakis. Deep transfer operator learning for partial differential equations under conditional shift. Nat Mach Intell, 4 (12) (2022), pp. 1155-1164.
[37]
S. Goswami, A. Bora, Y. Yu, G.E. Karniadakis. Physics-informed deep neural operator networks. T. Rabczuk, K.J. Bathe (Eds.), Machine learning in modeling and simulation: methods and applications, Springer, Cham (2023), pp. 219-254.
[38]
J. Sun, J. Li, Y. Hao, C. Qi, C. Ma, H. Sun, et al. Boundary-to-solution mapping for groundwater flows in a Toth basin. Adv Water Resour, 176 (2023), Article 104448.
[39]
K.M. Jablonka, D. Ongari, S.M. Moosavi, B. Smit. Big-data science in porous materials: materials genomics and machine learning. Chem Rev, 120 (16) (2020), pp. 8066-8129.
[40]
T. Cawte, A. Bazylak. A 3D convolutional neural network accurately predicts the permeability of gas diffusion layer materials directly from image data. Curr Opin Electrochem, 35 (2022), Article 101101.
[41]
Y. Wang, C.H. Arns, S.S. Rahman, J.Y. Arns. Porous structure reconstruction using convolutional neural networks. Math Geosci, 50 (7) (2018), pp. 781-799.
[42]
K. Kontolati, S. Goswami, M.D. Shields, G.E. Karniadakis. On the influence of over-parameterization in manifold based surrogates and deep neural operators. J Comput Phys, 479 (2023), Article 112008.
[43]
Q. Sun, W.X. Zhou, J. Fan. Adaptive huber regression. J Am Stat Assoc, 115 (529) (2020), pp. 254-265.
[44]
J.T. Gostick, Z.A. Khan, T.G. Tranter, M.D.R. Kok, M. Agnaou, M. Sadeghi, et al. PoreSpy: a Python toolkit for quantitative analysis of porous media images. J Open Source Softw, 4 (37) (2019), p. 1296.
[45]
P. Huang, H. Tao, J. Yang, C. Lian, H. Liu. Four stages of thermal effect coupled with ion-charge transports during the charging process of porous electrodes. AIChE J, 68 (10) (2022), Article e17790.
[46]
P. Huang, H. Tao, H. Liu, C. Lian. Accelerating charging dynamics using self-driven optimizing porous structures. AIChE J, 70 (4) (2024), Article e18313.
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