Massive finite element computations for deep learning inversion

Abstract

We focus on the inversion of borehole resistivity measurements in real time. To perform this task, we propose the use of Deep Learning methods. One critical task on this en- deavor is to produce a large database that can be used to train Deep Neural Networks. In this work, we explore different venues to obtain such database conforming the ground truth data via massive finite element computer simulations of the so-called forward prob- lem. This consists of solving multiple Boundary Value Problems governed by a Partial Differential Equation with different material coefficients. After describing the Finite Ele- ment Method, we investigate a venue to achieve high performance for performing a large amount of simulations using a Fourier approximation based Finite Element Method. The idea is to exploit the orthogonality of Fourier basis functions under reasonable assumptions often satisfied in our geophysics applications to reduce the computational cost of building the corresponding systems of linear equations. Solving such systems requires the use of advanced iterative solvers, which will be analyzed during the Ph.D. studies of Carlos Uri- arte.