  This paper proposes a methodology to estimate stress in the subsurface by a
hybrid method combining finite element modeling and neural networks. This
methodology exploits the idea of obtaining a multi-frequency solution in the
numerical modeling of systems whose behavior involves a wide span of length
scales. One low-frequency solution is obtained via inexpensive finite element
modeling at a coarse scale. The second solution provides the fine-grained
details introduced by the heterogeneity of the free parameters at the fine
scale. This high-frequency solution is estimated via neural networks -trained
with partial solutions obtained in high-resolution finite-element models. When
the coarse finite element solutions are combined with the neural network
estimates, the results are within a 2\% error of the results that would be
computed with high-resolution finite element models. This paper discusses the
benefits and drawbacks of the method and illustrates their applicability via a
worked example.
