  The concept of Rao-Blackwellization is employed to improve predictions of
artificial neural networks by physical information. The error norm and the
proof of improvement are transferred from the original statistical concept to a
deterministic one, using sufficient information on physics-based conditions.
The proposed strategy is applied to material modeling and illustrated by
examples of the identification of a yield function, elasto-plastic steel
simulations, the identification of driving forces for quasi-brittle damage and
rubber experiments. Sufficient physical information is employed, e.g., in the
form of invariants, parameters of a minimization problem, dimensional analysis,
isotropy and differentiability. It is proven how intuitive accretion of
information can yield improvement if it is physically sufficient, but also how
insufficient or superfluous information can cause impairment. Opportunities for
the improvement of artificial neural networks are explored in terms of the
training data set, the networks' structure and output filters. Even crude
initial predictions are remarkably improved by reducing noise, overfitting and
data requirements.
