Symbolic regression via genetic programming to derive empirical models and scaling laws as monomial or polynomial expansions

Many processes in plasma physics are inherently complex and highly nonlinear. Typically their behaviour is difficult to interpret with theoretical models based on first principles. To perform high-quality inferences, these processes have to be modelled starting directly from the experimental data. In this contribution we study and analyse the capabilities of Symbolic Regression via Genetic Programming as a tool for advanced data mining in Nuclear Fusion to derive Empirical Models. Whereas traditional linear and non-linear regression techniques simply try to find the best parameters of predefined model by fitting the available data, Symbolic Regression via Genetic Programming searches for the Best Unconstrained Empirical Model Structure. This implies deriving the significant variables, the functional form of the model and its parameters. A set of synthetic problems are used to assess some important capabilities of SR tools: over-fitting avoidance, extrapolation properties, identification of model constants, scalability to higher-dimensional problems and capacity to handle noisy data. As an example of application to Nuclear Fusion research, the method has been applied to the ITPA database of the energy confinement time of Tokamak plasmas in H mode.