Deep Convolutional Encoder‐Decoder Networks for Uncertainty Quantification of Dynamic Multiphase Flow in Heterogeneous Media

Abstract

Surrogate strategies are used widely for uncertainty quantification of groundwater models in order to improve computational efficiency. However, their application to dynamic multiphase flow problems is hindered by the curse of dimensionality, the saturation discontinuity due to capillarity effects, and the time dependence of the multi‐output responses. In this paper, we propose a deep convolutional encoder‐decoder neural network methodology to tackle these issues. The surrogate modeling task is transformed to an image‐to‐image regression strategy. This approach extracts high‐level coarse features from the high‐dimensional input permeability images using an encoder and then refines the coarse features to provide the output pressure/saturation images through a decoder. A training strategy combining a regression loss and a segmentation loss is proposed in order to better approximate the discontinuous saturation field. To characterize the high‐dimensional time‐dependent outputs of the dynamic system, time is treated as an additional input to the network that is trained using pairs of input realizations and of the corresponding system outputs at a limited number of time instances. The proposed method is evaluated using a geological carbon storage process‐based multiphase flow model with a 2,500‐dimensional stochastic permeability field. With a relatively small number of training data, the surrogate model is capable of accurately characterizing the spatiotemporal evolution of the pressure and discontinuous CO2 saturation fields and can be used efficiently to compute the statistics of the system responses.

Integration of Adversarial Autoencoders With Residual Dense Convolutional Networks for Estimation of Non‐Gaussian Hydraulic Conductivities

“…To illustrate the superior performance of the proposed DRDCN network architecture against the DDCN network architecture employed in our previous studies (Mo, Zabaras et al,, Mo, Zhu et al ; Zhu & Zabaras, ; Zhu et al, ) for surrogate modeling of systems with highly complex input‐output mappings, the DDCN network is also trained using the same training sets as those used in DRDCN. The DDCN network architecture is introduced in Appendix .…”

“…The two factors together make the commonly used surrogate methods, such as Gaussian processes (Rasmussen & Williams, ) and polynomial chaos expansion (Xiu & Karniadakis, ), difficult to work. Deep neural networks have already exhibited a promising and impressive performance for surrogate modeling of forward models with high‐dimensional input and output fields (Kani & Elsheikh, ; Mo, Zabaras, et al, ; Mo, Zhu, et al ; Sun, ; Tripathy & Bilionis, ; Zhong et al, ; Zhu & Zabaras, ; Zhu et al, ). For example, in Tripathy and Bilionis () a deep neural network was proposed to build a surrogate model for a single‐phase flow forward model.…”

Managing uncertainty in data-derived densities to accelerate density functional theory

“…Evaluating an error or measure of confidence in a data-driven prediction like n(x) is a well studied problem [15,16]. Applications of uncertainty quantification have recently begun appearing in materials science, with some even in DFT, such as the linear model exchange correlation functional of Aldegunde et al [17][18][19][20][21]. In this work, we show that useful applications of a predictive uncertainty in n(x) can be realised for just one of many possible approaches.…”

How can Big Data and machine learning benefit environment and water management: a survey of methods, applications, and future directions

“…Zhu and Zabaras [181] developed an endto-end FCN model to capture the complex forward mapping between the high-dimensional input-output fields in a stochastic partial differential equation. Mo et al [182] developed a similar FCN model to learn the high-dimensional input-output relationship in a subsurface multiphase flow model by using paired permeability realizations and the corresponding system outputs for training. In Sun [183], a state-parameter identification GAN is formed to learn not only the forward mapping, but also the reverse mapping between high-dimensional model inputs and outputs.…”