Contaminant Source Identification via Transfer Learning on Multifidelity-Data.

Reconstruction of contaminant release history is crucial for subsurface remediation actions. This task amounts to a high-dimensional inverse problem, whose solution requires multiple forward solves of contaminant transport equations. It also must cope with both sparse observations of solute concentration and subsurface heterogeneity. The computational burden of solving this inverse problem can be reduced by deploying a surrogate model, e.g., neural networks (NNs), which provides a low-cost approximation of its expensive physics-based counterpart. However, to construct such NNs, a large amount of high-fidelity forward runs may be required to provide training data, and these computations might be as cost-prohibitive as the solution of the inverse problem. To address this issue, we generate multi-fidelity data by running simulations of the forward transport model on fine and coarse meshes. The resulting high- and low-fidelity temporal snapshots of solute concentration are subsequently used, with a Transfer Learning technique, to train a Convolutional NN to identify the initial contaminant source location. The training is divided into three phases. In the initial phase, the training exclusively employs low-fidelity data. In the subsequent two steps, the learning phase for the network is finalized with only a relatively small number of high-fidelity data. The obtained results demonstrate that the transfer-learning-based surrogate model is a promising tool to reduce the computational cost as well as to obtain accurate solutions of high dimensional inverse problems.