  Modern adaptive optics (AO) systems for large telescopes require tomographic
techniques to reconstruct the phase aberrations induced by the turbulent
atmosphere along a line of sight to a target which is angularly separated from
the guide sources that are used to sample the atmosphere. Multi-object adaptive
optics (MOAO) is one such technique. Here, we present a method which uses an
artificial neural network (ANN) to reconstruct the target phase given off-axis
references sources. We compare our ANN method with a standard least squares
type matrix multiplication method and to the learn and apply method developed
for the CANARY MOAO instrument. The ANN is trained with a large range of
possible turbulent layer positions and therefore does not require any input of
the optical turbulence profile. It is therefore less susceptible to changing
conditions than some existing methods. We also exploit the non-linear response
of the ANN to make it more robust to noisy centroid measurements than other
linear techniques.
