  Deep learning (DL) is a numerical method that approximates functions.
Recently, its use has become attractive for the simulation and inversion of
multiple problems in computational mechanics, including the inversion of
borehole logging measurements for oil and gas applications. In this context, DL
methods exhibit two key attractive features: a) once trained, they enable to
solve an inverse problem in a fraction of a second, which is convenient for
borehole geosteering operations as well as in other real-time inversion
applications. b) DL methods exhibit a superior capability for approximating
highly-complex functions across different areas of knowledge. Nevertheless, as
it occurs with most numerical methods, DL also relies on expert design
decisions that are problem specific to achieve reliable and robust results.
Herein, we investigate two key aspects of deep neural networks (DNNs) when
applied to the inversion of borehole resistivity measurements: error control
and adequate selection of the loss function. As we illustrate via theoretical
considerations and extensive numerical experiments, these interrelated aspects
are critical to recover accurate inversion results.
