Objective Function Approximation through Machine Learning: Application to a Global Inversion of ERT Data

An inverse problem is usually solved through iterative procedures that are often computationally expensive because of the high number of forward modeling computations. To avoid them reducing the computational effort, we trained a Convolutional Neural Network to approximate the objective function of the inversion. Its inputs are models previously compressed through the Discrete Cosine Transform, whilst the outputs are the corresponding data misfit values. We applied the procedure to the Electrical Resistivity Tomography problem using Genetic Algorithms. Here we show that this approach is feasible and leads to a significant decrease in the computational time required. The implemented method was tested on synthetic data. It produced results similar to the ones obtained with an analogous inversion in which each forward modeling was performed through a Finite Element code. The advantage is that the whole procedure was able to halve the overall computational time. The algorithm can be used to obtain a reliable model in a few minutes after data acquisition. This result can constitute a starting model for a subsequent and more accurate inversion. Further improvements could make the approach useful in other geophysical inversions characterized by more complicated objective functions.