A new framework for experimental design using Bayesian Evidential Learning: The case of wellhead protection area

Comparing Well and Geophysical Data for Temperature Monitoring Within a Bayesian Experimental Design Framework

“…Thibaut et al. (2021), for example, demonstrated how this can be easily accomplished using multivariate Gaussian inference, provided that the CVs' bivariate distributions are both Gaussian and linear. Kernel Density Estimation (KDE) is another method for approximating the bivariate distribution for each CCA dimension without requiring such assumptions to be verified (e.g., Hermans et al., 2019; Michel et al., 2020).…”

“…Previous BEL applications have demonstrated that making accurate predictions with a data set of this size is possible (Athens & Caers, 2019; Hermans et al., 2016, 2018, 2019; J. Park & Caers, 2020; Michel et al., 2020; Yin et al., 2020; Thibaut et al., 2021). While a small training set size is inevitable due to the time‐consuming nature of the simulations, it is sufficient because the prediction is a temperature distribution that varies smoothly in both time and space and results from advection, diffusion, and dispersion processes.…”

“…Thibaut et al. (2021) provide an overview of these two simplifications. Iterative approaches requiring multiple forward problem runs, such as McMC methods, are commonly used to solve the problem (Laloy & Vrugt, 2012; Ryan et al., 2016; Vrugt, 2016).…”

“…This paper presents a methodology for improving the design of field experiments using well and geophysical data by utilizing Bayesian Evidential Learning (BEL). BEL is a technique that combines Monte Carlo simulations and machine learning that can be used to improve estimation of predictions uncertainty (Hermans et al., 2016, 2018; Michel et al., 2020; Thibaut et al., 2021). It performs the Bayesian inference (usually within a low‐dimensional latent space) using a direct relationship between predictor (data) and target (prediction) learned from a training set sampled from the prior distribution.…”

“…Thibaut et al. (2021) demonstrated, for instance, how BEL can be used to predict the wellhead protection area (WHPA) surrounding pumping wells. The WHPA (target) was predicted using a small number of tracing experiments (predictors).…”