Surrogate‐Model Assisted Plausibility‐Check, Calibration, and Posterior‐Distribution Evaluation of Subsurface‐Flow Models

Abstract

AbstractModern physics‐based subsurface‐flow models often require many parameters and computationally costly simulations. This prohibits traditional ensemble‐based conditioning. We expedite the calibration of such models by using surrogate/proxy models based on Gaussian Process Regression (GPR). In an iterative procedure, we use the proxy models to (a) estimate the direction of steepest descent, (b) propose only parameter combinations for full‐model runs that are likely to lead to plausible results, and (c) preselect proposed parameter combinations by their predicted performance. This method yields an ensemble of full‐model runs covering the full plausible parameter space, but at higher resolution close to the optimum. This is the basis for Markov‐Chain Monte Carlo (MCMC) simulations using GPR to estimate the posterior parameter distribution. We tested several variants of the scheme on a 3‐D variably‐saturated steady‐state subsurface‐flow model and compared it to a Neural Posterior Estimation (NPE) scheme, which requires samples of the prior distribution only. While the estimated posterior distributions of the two approaches were similar, the GPR‐based MCMC approach reproduced the data better than samples from the NPE‐based posterior distributions.