  Fragments productions in spallation reactions are key infrastructure data for
various applications. Based on the empirical parameterizations {\sc spacs}, a
Bayesian-neural-network (BNN) approach is established to predict the fragment
cross sections in the proton induced spallation reactions. A systematic
investigation have been performed for the measured proton induced spallation
reactions of systems ranging from the intermediate to the heavy nuclei and the
incident energy ranging from 168 MeV/u to 1500 MeV/u. By learning the residuals
between the experimental measurements and the {\sc spacs} predictions, the BNN
predicted results are in good agreement with the measured results. The
established method is suggested to benefit the related researches in the
nuclear astrophysics, nuclear radioactive beam source, accelerator driven
systems, and proton therapy, etc.
