Continuous conditional generative adversarial networks for data-driven solutions of poroelasticity with heterogeneous material properties

Kadeethum, T.; O'Malley, D.; Choi, Y.; Viswanathan, H. S.; Bouklas, N.; Yoon, H.

doi:10.48550/arxiv.2111.14984

Cited by 4 publications

(9 citation statements)

References 38 publications

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“…The proposed model utilizes continuous conditional generative adversarial networks [21,22] referred to as CCGAN in this paper, to predict the saturation distribution using the input data from the injection well and the two adjacent monitoring wells in a forward setting, with the aim of substantially reducing the computational cost, and allowing the set-up of a real-time monitoring tool.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…To achieve this, we employ continuous conditional generative adversarial networks (CCGAN) [21,22] to efficiently parametrize the physical spatial heterogeneous properties and the operation conditions and measurements. Previous works have successfully shown the application of GANs [23] for predicting the solution of PDEs [22,24,25]. First, we carry multiple numerical simulations of two-phase flow for immiscible CO2/brine in highly heterogeneous porous media with Petrel [26] and Eclipse 100 [27].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Predicting the CO2 propagation in geological formations from sparsely available well data

Ferreira¹,

Stępień²,

Hosseinzadehsadati³

et al. 2022

SSRN Journal

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Predicting the CO2 propagation in geological formations from sparsely available well data

Ferreira¹,

Stępień²,

Hosseinzadehsadati³

et al. 2022

SSRN Journal

View full text Add to dashboard Cite

“…Among them, neural networks have been the most popular framework because of their rich representation capability supported by the universal approximation theorem. Such surrogate models have been applied to various physical simulations, including, but not limited to, particle simulation [30], nanophotonic particle design [31], porous media flow [32][33][34][35], storm prediction [36], fluid dynamics [37], hydrology [38,39], bioinformatics [40], highenergy physics [41], turbulence modeling [42][43][44][45], uncertainty propagation in a stochastic elliptic partial differential equation [46], bioreactor with unknown reaction rate [47], barotropic climate models [48], and deep Koopman dynamical models [49]. However, these methods lack the interpretability due to the black-box nature caused by its complex underlying structure of interpolators, e.g., neural networks.…”

Section: Introductionmentioning

confidence: 99%

LaSDI: Parametric Latent Space Dynamics Identification

William¹,

He²,

Choi³

2022

Preprint

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Enabling fast and accurate physical simulations with data has become an important area of computational physics to aid in inverse problems, design-optimization, uncertainty quantification, and other various decision-making applications. This paper presents a data-driven framework for parametric latent space dynamics identification procedure that enables fast and accurate simulations. The parametric model is achieved by building a set of local latent space model and designing an interaction among them. An individual local latent space dynamics model achieves accurate solution in a trust region. By letting the set of trust region to cover the whole parameter space, our model shows an increase in accuracy with an increase in training data. We introduce two different types of interaction mechanisms, i.e., point-wise and regionbased approach. Both linear and nonlinear data compression techniques are used. We illustrate the framework of Latent Space Dynamics Identification (LaSDI) enable a fast and accurate solution process on various partial differential equations, i.e., Burgers' equations, radial advection problem, and nonlinear heat conduction problem, achieving O(100)x speed-up and O(1)% relative error with respect to the corresponding full order models.

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“…Among various interpolation techniques, such as Gaussian processes [41,42], radial basis functions [43,44], Kriging [45,46], neural networks (NNs) have been most popular due to their strong flexibility and capability supported by the universal approximation theorem [47]. NN-based surrogates have been applied to various physical simulations, such as fluid dynamics [48], particle simulations [49], bioinformatics [50], deep Koopman dynamical models [51], porous media flow [52,53,54,55], etc. However, pure black-box NN-based surrogates lack interpretability and suffer from unstable and inaccurate generalization performance.…”

Section: Introductionmentioning

confidence: 99%

gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identification

He¹,

Choi²,

William³

et al. 2022

Preprint

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A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust datadriven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the proposed gLaSDI framework, an autoencoder discovers intrinsic nonlinear latent representations of high-dimensional data, while dynamics identification (DI) models capture local latent-space dynamics. An interactive training algorithm is adopted for the autoencoder and local DI models, which enables identification of simple latent-space dynamics and enhances accuracy and efficiency of data-driven reduced-order modeling. To maximize and accelerate the exploration of the parameter space for the optimal model performance, an adaptive greedy sampling algorithm integrated with a physics-informed residualbased error indicator and random-subset evaluation is introduced to search for the optimal training samples on-the-fly. Further, to exploit local latent-space dynamics captured by the local DI models for an improved modeling accuracy with a minimum number of local DI models in the parameter space, an efficient k-nearest neighbor convex interpolation scheme is employed. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including Burgers equations, nonlinear heat conduction, and radial advection. The proposed adaptive greedy sampling outperforms the conventional predefined uniform sampling in terms of accuracy. Compared with the high-fidelity models, gLaSDI achieves 66 to 4,417× speed-up with 1 to 5% relative errors.

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Continuous conditional generative adversarial networks for data-driven solutions of poroelasticity with heterogeneous material properties

Cited by 4 publications

References 38 publications

Predicting the CO2 propagation in geological formations from sparsely available well data

Predicting the CO2 propagation in geological formations from sparsely available well data

LaSDI: Parametric Latent Space Dynamics Identification

gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identification

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