Fast and accurate methods are required to predict stresses in the vicinity of open and closed holes in composite structures, especially in a global-local modelling context as applied during the design of airframe structures. Fast analytical solutions for infinite-width anisotropic plates with open holes do not consider finite-width effects. Heuristic methods and semi-analytical solutions can be used to towards addressing such effects. To improve the accuracy and speed of these respective methods, we use machine learning (ML) methods trained on high-fidelity finite element analyses (FEA) to make finite-width corrections. However, such methods require large amounts of training data to reduce errors to satisfactory levels. Therefore, in this study, the fusion of analytical solutions with machine learning is performed. We develop an analytical solution-informed ML model that is as fast as an analytical solution and superior in accuracy to analytical solutions with heuristic finite-width scaling. Our informed ML model offers accuracies equal to analytical solutions for the infinite-width case, and it is capable for use in a global-local modelling context, under uniaxial and biaxial loading. Our informed ML model outperforms prediction accuracy across all cases compared to uninformed ML models and requires a significantly lower size training dataset size.