Consensus Equilibrium for Subsurface Delineation. Issue 10 (20th October 2021)

• Record Type: Journal Article
• Authors: Yang, Hyung Jun; Lin, Youzuo; Wohlberg, Brendt; Tartakovsky, Daniel M.
• Is Part Of: Water resources research. Volume 57:Issue 10(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-10-20
• Subjects: Subsurface -- data‐driven -- inverse modeling -- aquifer; Hydrology -- Periodicals; 333.91
• DOI: 10.1029/2021WR030151
• Languages: English
• ISSNs: 0043-1397

Abstract

Abstract: Heterogeneity and insufficient site characterization limit our knowledge of the subsurface. Inversion techniques, which minimize the mismatch between observations and model predictions, have become an essential tool of subsurface characterization. Most optimization‐based approaches fail to incorporate various implicit priors and capture the geological complexity. We overcome these limitations by deploying the plug‐and‐play and consensus equilibrium (CE) strategies, which provide a flexible framework for image reconstruction. Our CE methodology for spatial delineation of geologic formations consists of an image denoiser and a variational auto‐encoder (deep learning‐based emulator). The former ameliorates the reconstruction noise, yielding well‐defined geological structures; its mathematical equivalence with the proximal operator allows the deployment of advanced denoisers (e.g., CNN‐based denoiser) that do not correspond to a regularization objective. The latter defines a geology prior that imposes a geological constraint, for example, continuity and shape of geological features, onto the reconstructed image. We conduct a series of numerical experiments dealing with transient two‐dimensional flow driven by a pumping well and natural hydraulic head gradient. They demonstrate the CE framework's ability to delineate, both probabilistically and deterministically, complex subsurface environments with sufficient quality. Key Points: We developed consensus equilibrium framework to reconstruct the subsurface from sparse data Our framework integrates conventional optimization methods with machine learning‐based methods The method accurately reconstructs geologically complex models and efficiently reduces and quantifies the posterior uncertainty