Error-aware surrogate modelling with input dimension reduction for groundwater modelling in heterogenous media

Machine learning approaches have gained high notoriety to approximate computationally-expensive models in the geosciences. Surrogate models are trained using input-output pairs to emulate the numerics of full complexity models. These fast models then assist in forward and inverse uncertainty quantification for various applied problems. However, large input dimensions, typically found in groundwater modelling for very heterogeneous environments, present a challenge for surrogate models. Input dimension reduction (IDR) methods, such as the Karhunen-Loéve expansion (KLE), are known to reduce the number of input parameters used to train surrogate models, while also generating stochastic realizations of the input random fields for groundwater modelling applications. Traditionally, KLE truncates the input parameters such that 90% of the input variance is considered. However, in some applied cases, this dimension remains too large for reliable surrogate model training. Specifically, using a smaller number of input parameters (considering a smaller percentage of the input variance) may introduce IDR-associated errors in the surrogate output. These errors are often overlooked when assessing uncertainty in surrogate model outputs and could be particularly significant in Bayesian inverse modelling. We are offering a surrogate modelling framework tailored for high-dimensional problems that accounts for IDR-induced errors in the context of Bayesian inverse modelling. Our framework allows for more informed decision-making when using surrogate models as approximators and to widen the scope in which surrogates can be used in heterogeneous media applications. We demonstrate the introduced approach using a groundwater flow and transport model with a heterogeneous hydraulic conductivity field to estimate contaminant concentrations and pressure head values.