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

本文运用Rao-Blackwellization的概念，通过物理信息来提高人工神经网络的预测能力。利用基于物理条件的充分信息，将误差范数和改进的证明从原始统计概念转化为确定性概念。该策略应用于材料建模，并通过识别屈服函数、弹塑性钢模拟、寻找准脆性损伤驱动力和橡胶实验的例子进行了说明。充分的物理信息被应用，例如不变量、最小化问题的参数、尺寸分析、同性和可微性。证明了如果信息足够丰富，直观的信息积累可以带来改进，但是不足或多余的信息可能会导致损害。文章探讨了在训练数据集、网络结构和输出过滤器方面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，即使是粗略的初始预测也可以显著改进。

The paper aims to improve the prediction accuracy of artificial neural networks by incorporating physical information. It applies this strategy to material modeling and simulations, as well as the identification of driving forces for quasi-brittle damage and rubber experiments.

The key idea of the paper is to employ physical information in the form of invariants, parameters of a minimization problem, dimensional analysis, isotropy, and differentiability to improve the prediction accuracy of artificial neural networks. The paper also explores opportunities for improvement in terms of the training data set, network structure, and output filters.

The paper presents examples of the application of the proposed strategy to material modeling and simulations, as well as the identification of driving forces for quasi-brittle damage and rubber experiments. It shows how even crude initial predictions can be remarkably improved by reducing noise, overfitting, and data requirements. The paper also discusses the limitations of the proposed strategy and the potential for future research.

Related work in this field includes the use of physical constraints in machine learning, such as the incorporation of physical laws into neural networks and the use of physics-informed neural networks. Some relevant papers include 'Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations' by Raissi et al. and 'Incorporating physical constraints in machine learning for image segmentation' by Wang et al.