Combining dimensional and statistical analysis for efficient data driven modelling of complex systems

Dimensional analysis is a well-known approach to model building in engineering, because it can contribute to identifying more parsimonious and meaningful equations for describing complex phenomena. Unfortunately, it is not always exploited to the full, because it is typically applied prior to any form of statistical evaluation, often resulting in poor choices of the dimensionless quantities and consequently in suboptimal models. A completely general and data driven technique is proposed, which integrates dimensional and statistical analysis with the help of genetic programming supported symbolic regression and neural computing. The methodology exploits the potential of various machine-learning techniques and allows extracting mathematical models in terms of dimensionless quantities directly from the dimensional databases available. A battery of numerical tests and examples from fluid dynamics and thermonuclear fusion illustrate the unquestionable advantages of the approach for statistical inference and for the interpretation of the large amounts of data produced by modern physics experiments and engineering studies.