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

Incorporating sufficient physical information into artificial neural networks: a guaranteed improvement via physics-based Rao-Blackwellization