标题： 一种用于发现物理现象背后理论的迭代式科学机器学习方法 显示英文标题

标题： An Iterative Scientific Machine Learning Approach for Discovery of Theories Underlying Physical Phenomena

摘要： 从纯粹的数学观点来看，可以定义表示不同物理现象的常见函数形式。 例如，化学反应速率、扩散和热传递都由指数型表达式所支配。 如果将机器学习用于物理问题，根据领域知识推断出的原始特征可以以一种方式转换，使得最终的表达式与底层物理高度一致且相关。 这应该在迭代次数、架构和所需数据点数量方面显著减少训练工作量。 我们通过从中立的位置入手来扩展这一方法，并提出了一种系统且迭代的方法来发现物理现象背后的理论。 首先，使用理论表达式的常见观测函数形式来转换原始特征，然后进行相关性分析以输出结果。 使用高度相关表达式的随机组合，进行神经网络（NN）的训练。 通过比较训练中的收敛速度或平均误差，可以发现描述底层物理问题的表达式，从而提取显式的解析方程。 这种方法被用于三个针对不同物理现象的盲测演示中。 显示英文摘要

摘要： Form a pure mathematical point of view, common functional forms representing different physical phenomena can be defined. For example, rates of chemical reactions, diffusion and heat transfer are all governed by exponential-type expressions. If machine learning is used for physical problems, inferred from domain knowledge, original features can be transformed in such a way that the end expressions are highly aligned and correlated with the underlying physics. This should significantly reduce the training effort in terms of iterations, architecture and the number of required data points. We extend this by approaching a problem from an agnostic position and propose a systematic and iterative methodology to discover theories underlying physical phenomena. At first, commonly observed functional forms of theoretical expressions are used to transform original features before conducting correlation analysis to output. Using random combinations of highly correlated expressions, training of Neural Networks (NN) are performed. By comparing the rates of convergence or mean error in training, expressions describing the underlying physical problems can be discovered, leading to extracting explicit analytic equations. This approach was used in three blind demonstrations for different physical phenomena.