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.

通过物理信息利用 Rao-Blackwellization 的概念来改善人工神经网络的预测，提出的策略应用于材料建模，并通过识别屈服函数、弹塑性钢模拟、脆性破坏驱动力识别和橡胶实验的示例进行了说明。通过使用足够的物理信息，例如不变量、最小化问题的参数、尺度分析、各向同性和可微性，证明了直观增加信息如何在物理上具有足够的改善作用，但不充分或多余的信息如何导致损害。还探讨了通过训练数据集、网络结构和输出过滤器改善人工神经网络的机会。通过减少噪声、过拟合和数据要求，即使是粗糙的初步预测也可以显著提高。