  Bias due to imperfect shear calibration is the biggest obstacle when
constraints on cosmological parameters are to be extracted from large area weak
lensing surveys such as Pan-STARRS-3pi, DES or future satellite missions like
Euclid. We demonstrate that bias present in existing shear measurement
pipelines (e.g. KSB) can be almost entirely removed by means of neural
networks. In this way, bias correction can depend on the properties of the
individual galaxy instead on being a single global value. We present a
procedure to train neural networks for shear estimation and apply this to
subsets of simulated GREAT08 RealNoise data. We also show that circularization
of the PSF before measuring the shear reduces the scatter related to the PSF
anisotropy correction and thus leads to improved measurements, particularly on
low and medium signal-to-noise data. Our results are competitive with the best
performers in the GREAT08 competition, especially for the medium and higher
signal-to-noise sets. Expressed in terms of the quality parameter defined by
GREAT08 we achieve a Q = 40, 140 and 1300 without and 50, 200 and 1300 with
circularization for low, medium and high signal-to-noise data sets,
respectively.
