Attempts to use machine learning to discover hidden physical rules are in their infancy, and such attempts confront more challenges when experiments involve multifaceted measurements over three-dimensional objects. Here we propose a framework that can infuse scientists’ basic knowledge into a glass-box rule learner to extract hidden physical rules behind complex physics phenomena. A “convolved information index” is proposed to handle physical measurements over three-dimensional nano-scale specimens, and the multi-layered convolutions are “externalized” over multiple depths at the information level, not in the opaque networks. A transparent, flexible link function is proposed as a mathematical expression generator, thereby pursuing “glass-box” prediction. Consistent evolution is realized by integrating a Bayesian update and evolutionary algorithms. The framework is applied to nano-scale contact electrification phenomena, and results show promising performances in unraveling transparent expressions of a hidden physical rule. The proposed approach will catalyze a synergistic machine learning-physics partnership.

尝试使用机器学习发现隐藏的物理规则尚处于初期阶段，当实验涉及对三维对象的多方面测量时，此类尝试面临更多挑战。在这里，我们提出了一个框架，该框架可以将科学家的基础知识注入到玻璃盒规则学习器中，以提取复杂物理现象背后的隐藏物理规则。提出了“卷积信息索引”来处理三维纳米尺度样本的物理测量，并且多层卷积在信息级别的多个深度上被“外部化”，而不是在不透明的网络中。提出了一种透明，灵活的链接函数作为数学表达式生成器，从而追求“玻璃盒”预测。通过集成贝叶斯更新和进化算法来实现一致的进化。该框架被应用于纳米级接触带电现象，结果表明在揭示隐藏的物理规则的透明表达方面有希望的表现。拟议的方法将促进机器学习与物理之间的协同合作。