Abstract

Widely used in hydraulics, the Colebrook equation for flow friction relates implicitly to the input parameters; the Reynolds number, Re and the relative roughness of an inner pipe surface, ε/D with an unknown output parameter; the flow friction factor, λ; λ = f (λ, Re, ε/D). In this paper, a few explicit approximations to the Colebrook equation; λ≈f (Re, ε/D), are generated using the ability of artificial intelligence to make inner patterns to connect input and output parameters in an explicit way not knowing their nature or the physical law that connects them, but only knowing raw numbers, {Re, ε/D}→{λ}. The fact that the used genetic programming tool does not know the structure of the Colebrook equation, which is based on computationally expensive logarithmic law, is used to obtain a better structure of the approximations, which is less demanding for calculation but also enough accurate. All generated approximations have low computational cost because they contain a limited number of logarithmic forms used for normalization of input parameters or for acceleration, but they are also sufficiently accurate. The relative error regarding the friction factor λ, in in the best case is up to 0.13% with only two logarithmic forms used. As the second logarithm can be accurately approximated by the Padé approximation, practically the same error is obtained also using only one logarithm.

Abstract

As data science becomes increasingly mainstream, there will be an ever-growing demand for data science tools that are more accessible, flexible, and scalable. In response to this demand, automated machine learning (AutoML) researchers have begun building systems that automate the process of designing and optimizing machine learning pipelines. In this chapter we present TPOT v0.3, an open source genetic programming-based AutoML system that optimizes a series of feature preprocessors and machine learning models with the goal of maximizing classification accuracy on a supervised classification task. We benchmark TPOT on a series of 150 supervised classification tasks and find that it significantly outperforms a basic machine learning analysis in 21 of them, while experiencing minimal degradation in accuracy on 4 of the benchmarks—all without any domain knowledge nor human input. As such, genetic programming-based AutoML systems show considerable promise in the AutoML domain. Document type: Part of book or chapter of book