Towards solving inverse problems with deep vector-to-image domain transfer networks

Abstract:

We present vec2pix, a deep neural network designed to infer categorical or continuous 2D subsurface property fields from one-dimensional measurement data (e.g., time series), thereby providing a new way to solve hydrogeological and hydrogeophysical inverse problems. The performance of the approach is demonstrated using two types of synthetic inverse problems: (a) a crosshole ground penetrating radar (GPR) tomography experiment with GPR travel times being used to predict a 2D velocity field, and (2) a multi-well pumping experiment within an unconfined aquifer with time series of transient hydraulic heads being used to recover a 2D hydraulic conductivity field. For each type of problem, both a multi-Gaussian and a binary channelized subsurface domain with long-range connectivity are considered. Using a training set of 20,000 examples, the approach is found to retrieve a 2D model that is in much closer agreement with the true model than the closest training model in the forward-simulated data space. Further testing with smaller training sample sizes shows that despite a moderate reduction in performance, this remains the case when using 5000 training examples only. Even if the models inferred by vec2pix are close to the true ones in the model space, the data misfits associated with their forward responses are generally larger than the noise level used to contaminate the true data. Uncertainty of the inverse solution is estimated using deep ensembles, in which the network is trained repeatedly with random initialization. Overall, our findings open up a promising research avenue on how to use deep learning to infer 2D and 3D subsurface models from indirect 1D measurement data.