A physics-informed and hierarchically regularized data-driven model for predicting fluid flow through porous media

Wang, Kun; Chen, Yu; Mehana, Mohamed; Lubbers, Nicholas; Bennett, Kane C.; Kang, Qinjun; Viswanathan, Hari; Germann, Timothy C.

doi:10.1016/j.jcp.2021.110526

Cited by 37 publications

(5 citation statements)

References 56 publications

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“…At the mesoscopic scale, the physical and mechanical properties of an assembly can be trained into prediction models, for instance, by training constitutive response as a surrogate model to replace conventional constitutive models in continuum-based numerical methods 193 . Although there has been recent progress in applying data-driven 194 and physics-informed 195 techniques to obtain improved learning performance, ML approaches still need ground-truth data that are most often synthesized by DNS. A more promising direction for ML is to solve partial differential equations directly for large-scale simulations without having to use DNS.…”

Section: Technical Reviewmentioning

confidence: 99%

The role of particle shape in computational modelling of granular matter

Zhao,

Luding

2023

Nat Rev Phys

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Granular matter is ubiquitous in nature and is present in diverse forms in important engineering, industrial and natural processes. Particle-based computational modelling has become indispensable to understand and predict the complex behaviour of granular matter in these processes. The success of modern computational models requires realistic and efficient consideration of particle shape. Realistic particle shapes in naturally occurring and engineered materials offer diverse challenges owing to their multiscale nature in both length and time. Furthermore, the complex interactions with other materials, such as interstitial fluids, are highly nonlinear and commonly involve multiphysics coupling. This Technical Review presents a comprehensive appraisal of state-of-the-art computational models for granular particles of either naturally occurring shapes or engineered geometries. It focuses on particle shape characterization, representation and implementation, as well as its important effects. In addition, the particles may be hard, highly deformable, crushable or phase transformable; they might change their behaviour in the presence of interstitial fluids and are sensitive to density, confining stress and flow state. We describe generic methodologies that capture the universal features of granular matter and some unique approaches developed for special but important applications. Sections• Consideration of shape effects in coupled simulations of granular particles and environmental fluids requires revamped theories and methods to faithfully reflect their underpinning multiphase, multiphysics nature.• Incorporating realistic particle shapes in granular matter modelling must harness the latest advances in parallel computing and machine learning for effective large-scale computations.Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

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Section: Technical Reviewmentioning

confidence: 99%

The role of particle shape in computational modelling of granular matter

Zhao,

Luding

2023

Nat Rev Phys

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“…Physics-informed neural networks (PINNs) [29] and their extensions [30,31,32] have shown promising applications in computational science and engineering [33,34,35,36]. The physics-informed learning is usually implemented using artificial neural networks (ANNs) [37,38], thus requiring separate training if any new parameters or coefficients change [23]. Similar to traditional numerical simulations, physics-informed learning for solving geologic carbon storage problems can be computationally inefficient.…”

Section: Introductionmentioning

confidence: 99%

Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration

Jiang¹,

Zhu²,

Li³

et al. 2023

Preprint

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Geologic Carbon Storage (GCS) is an important technology that aims to reduce the amount of carbon dioxide in the atmosphere. Multiphase flow in porous media is essential to understand CO 2 migration and pressure fields in the subsurface associated with GCS. However, numerical simulation for such problems in 4D is computationally challenging and expensive, due to the multiphysics and multiscale nature of the highly nonlinear governing partial differential equations (PDEs). It prevents us from considering multiple subsurface scenarios and conducting real-time optimization. Here, we develop a Fourier-enhanced multiple-input neural operator (Fourier-MIONet) to learn the solution operator of the problem of multiphase flow in porous media. Fourier-MIONet utilizes the recently developed framework of the multiple-input deep neural operators (MIONet) and incorporates the Fourier neural operator (FNO) in the network architecture. Once Fourier-MIONet is trained, it can predict the evolution of saturation and pressure of the multiphase flow under various reservoir conditions, such as permeability and porosity heterogeneity, anisotropy, injection configurations, and multiphase flow properties. Compared to the enhanced FNO (U-FNO), the proposed Fourier-MIONet has 90% fewer unknown parameters, and it can be trained in significantly less time (about 3.5 times faster) with much lower CPU memory (< 15%) and GPU memory (< 35%) requirements, to achieve similar prediction accuracy. In addition to the lower computational cost, Fourier-MIONet can be trained with only 6 snapshots of time to predict the PDE solutions for 30 years. The excellent generalizability of Fourier-MIONet is enabled by its adherence to the physical principle that the solution to a PDE is continuous over time. Moreover, the developed Fourier-MIONet makes it possible to solve the long-time evolution of geological carbon sequestration in a large-scale three-dimensional space accurately and efficiently.

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“…In addition, some PDE models have successfully solved practical application problems. For instance, Physics-informed neural networks [16,17] are used to predict the fluid flow in porous media [18] and simulate heat transfer [19]. Although these methods have successfully solved various problems, they are time-consuming, laborious, and not universal.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Method for Solving Two-Dimensional Partial Differential Equations with the Deep Operator Network

Zhang,

Wang,

Peng

et al. 2023

Axioms

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Partial differential equations (PDEs) usually apply for modeling complex physical phenomena in the real world, and the corresponding solution is the key to interpreting these problems. Generally, traditional solving methods suffer from inefficiency and time consumption. At the same time, the current rise in machine learning algorithms, represented by the Deep Operator Network (DeepONet), could compensate for these shortcomings and effectively predict the solutions of PDEs by learning the operators from the data. The current deep learning-based methods focus on solving one-dimensional PDEs, but the research on higher-dimensional problems is still in development. Therefore, this paper proposes an efficient scheme to predict the solution of two-dimensional PDEs with improved DeepONet. In order to construct the data needed for training, the functions are sampled from a classical function space and produce the corresponding two-dimensional data. The difference method is used to obtain the numerical solutions of the PDEs and form a point-value data set. For training the network, the matrix representing two-dimensional functions is processed to form vectors and adapt the DeepONet model perfectly. In addition, we theoretically prove that the discrete point division of the data ensures that the model loss is guaranteed to be in a small range. This method is verified for predicting the two-dimensional Poisson equation and heat conduction equation solutions through experiments. Compared with other methods, the proposed scheme is simple and effective.

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A physics-informed and hierarchically regularized data-driven model for predicting fluid flow through porous media

Cited by 37 publications

References 56 publications

The role of particle shape in computational modelling of granular matter

The role of particle shape in computational modelling of granular matter

Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration

An Efficient Method for Solving Two-Dimensional Partial Differential Equations with the Deep Operator Network

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