  A novel approach is presented for the solution of instantaneous chemical
equilibrium problems. The chemical equilibrium can be considered, due to its
intrinsically local character, as a mapping of the three-dimensional parameter
space spanned by the temperature, hydrogen density and electron density into
many one-dimensional spaces representing the number density of each species. We
take advantage of the ability of artificial neural networks to approximate
non-linear functions and construct neural networks for the fast and efficient
solution of the chemical equilibrium problem in typical stellar atmosphere
physical conditions. The neural network approach has the advantage of providing
an analytic function, which can be rapidly evaluated. The networks are trained
with a learning set (that covers the entire parameter space) until a relative
error below 1% is reached. It has been verified that the networks are not
overtrained by using an additional verification set. The networks are then
applied to a snapshot of realistic three-dimensional convection simulations of
the solar atmosphere showing good generalization properties.
