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.

翻译：本文利用Rao-Blackwell化概念，通过物理信息改进人工神经网络的预测性能。将原始统计概念中的误差范数与改进证明转化为确定性框架，基于物理条件的充分信息实现。所提策略应用于材料建模，并通过屈服函数识别、弹塑性钢模拟、准脆性损伤驱动力识别及橡胶实验等实例进行验证。采用充分物理信息，包括不变量形式、最小化问题参数、量纲分析、各向同性及可微性等。研究证明：直觉性的信息累积在物理充分性条件下可带来性能提升，反之，信息不足或冗余则可能导致性能退化。进一步探索了训练数据集、网络结构及输出滤波器对人工神经网络改进的潜力。即使初始预测粗糙，通过降低噪声、过拟合及数据需求，模型性能仍能得到显著改善。