Bayesian machine scientist to compare data collapses for the Nikuradse dataset

Abstract

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.

References in corpus (10)

• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Machine learning phases of matter
• Parallel Tempering: Theory, Applications, and New Perspectives
• Learning phase transitions by confusion
• Universal features in the growth dynamics of complex organizations
• A Measure of data-collapse for scaling
• A Bayesian machine scientist to aid in the solution of challenging scientific problems
• Roughness-induced critical phenomena in a turbulent flow
• Reducing Degeneracy in Maximum Entropy Models of Networks
• Sampling motif-constrained ensembles of networks

Cited by in corpus (3)

• Human mobility is well described by closed-form gravity-like models learned automatically from data
• Fundamental limits to learning closed-form mathematical models from data
• The Inefficiency of Genetic Programming for Symbolic Regression