Correlating the Internal Encoding of Boundary-Layer Profiles: Insights in Neural Networks Used for Boundary-Layer Stability Prediction

Abstract

Linear stability theory is an established method for the prediction of boundary-layer transition. Practical application of this method often involves surrogate-models, which in this work are artificial neural networks. This paper focuses on partially gaining insights into such black-box models trained for two different modes, namely two-dimensional Tollmien-Schlichting and stationary crossflow instabilities. By design of its topology, the network is forced to encode the information of the relevant wall-normal boundary-layer profile in the output of a single neuron at an intermediate stage. Employing symbolic regression for this task, this latent feature is then correlated with known boundary-layer parameters, in order to investigate whether the neural networks learn to derive known physical parameters.