Effective Characterization of Fractured Media With PEDL: A Deep Learning‐Based Data Assimilation Approach

Abstract Geological formations with fractures are frequently encountered in various research fields. Accurately characterizing these fractured media is of paramount importance when it comes to tasks that demand precise predictions of liquid flow and solute transport within them. Since directly measuring fractured media poses inherent challenges, data assimilation (DA) techniques are typically employed to derive inverse estimates of media properties using observable state variables. Nonetheless, the considerable difficulties arising from the strong heterogeneity and non‐Gaussian nature of fractured media have diminished the effectiveness of existing DA methods. In this study, we formulate a novel DA approach known as parameter estimator with deep learning (PEDL) that harnesses the capabilities of DL to capture nonlinear relationships and extract non‐Gaussian features. To evaluate PEDL's performance, we conduct three case studies, comprising two numerical cases and one real‐world case. In these cases, we systematically compare PEDL with three widely used DA methods: ensemble smoother with multiple DA (ESMDA), iterative local updating ES (ILUES), and ES with DL‐based update (ESDL). Notably, in the problems characterized by highly non‐Gaussian features, ESMDA and ILUES produce significantly divergent results. Conversely, employing the DL‐based update, ESDL demonstrates improved performance. However, its estimation uncertainty remains high, potentially attributable to ESDL's updating mechanism. Comprehensive analyses confirm PEDL's validity and adaptability across various ensemble sizes and DL model architectures. Moreover, even in scenarios where structural difference exists between the accurate reference model and the simplified forecast model, PEDL adeptly identifies the primary characteristics of fracture networks.