Groundwater Contaminant Transport Solved by Monte Carlo Methods Accelerated by Deep Learning Meta-Model

Abstract

Groundwater contaminant transport modeling is a vitally important topic. Since modeled processes include uncertainties, Monte Carlo methods are adopted to obtain some statistics. However, accurate models have a substantial computational cost. This drawback can be overcome by employing the multilevel Monte Carlo method (MLMC) or approximating the original model using a meta-model. We combined both of these approaches. A stochastic model is substituted with a deep learning meta-model that consists of a graph convolutional neural network and a feed-forward neural network. This meta-model can approximate models solved on unstructured meshes. The meta-model within the standard Monte Carlo method can bring significant computational cost savings. Nevertheless, the meta-model must be highly accurate to obtain similar errors as when using the original model. Proposed MLMC with the new lowest-accurate level of meta-models can reduce total computational costs, and the accuracy of the meta-model does not have to be so high. The size of the computational cost savings depends on the cost distribution across MLMC levels. Our approach is especially efficacious when the dominant computational cost is on the lowest-accuracy MLMC level. Depending on the number of estimated moments, we can reduce computational costs by up to ca. 25% while maintaining the accuracy of estimates.