论文标题
贝叶斯机器科学家比较Nikuradse数据集的数据崩溃
Bayesian machine scientist to compare data collapses for the Nikuradse dataset
论文作者
论文摘要
自Nikuradse在1933年进行湍流摩擦的实验以来，就已经进行了理论上的尝试来描述他的测量方法，通过将数据崩溃成单变量的函数。但是，这种方法在物理和其他领域的其他领域很常见，受到缺乏比较替代数据崩溃的严格定量方法的限制。在这里，我们通过使用无监督的方法来解决此限制，以找到最佳描述Nikuradse数据集的每个数据崩溃的分析功能。通过降低这些分析功能，我们表明，缩放数据的分散性较低并不能保证数据崩溃是对原始数据的良好描述。实际上，我们发现，在所有提出的数据崩溃中，Prandtl和Nikuradse在80年前提出的原始数据提供了迄今为止数据的最佳描述，并且如果允许某些模型参数可以在各种实验之间变化，则它也与最近的实验数据相吻合。
Ever since Nikuradse's experiments on turbulent friction in 1933, there have been theoretical attempts to describe his measurements by collapsing the data into single-variable functions. However, this approach, which is common in other areas of physics and in other fields, is limited by the lack of rigorous quantitative methods to compare alternative data collapses. Here, we address this limitation by using an unsupervised method to find analytic functions that optimally describe each of the data collapses for the Nikuradse dataset. By descaling these analytic functions, we show that a low dispersion of the scaled data does not guarantee that a data collapse is a good description of the original data. In fact, we find that, out of all the proposed data collapses, the original one proposed by Prandtl and Nikuradse over 80 years ago provides the best description of the data so far, and that it also agrees well with recent experimental data, provided that some model parameters are allowed to vary across experiments.
