Fig. 2: Schematic of the optimization process in IT-π.
Circles represent the information content of the dimensionless input (Π) and output (Πo). The overlapping region denotes their mutual information of order α, Iα(Πo; Π). The area enclosed by the dashed line corresponds to the amount of information in Πo that cannot be inferred from Π, which is related to the irreducible error ϵLB. The optimization is conducted with CMA-ES and proceeds from left to right, evaluating candidate pairs of Π and Πo to minimize ϵLB until the optimal value \({\epsilon }_{LB}^{ * }\) is reached. The candidates are constrained to be dimensionless by the Buckingham-π theorem. The value of α determines the sensitivity of IT-π to different Lp-norms and is learned as part of the optimization process.
