Transition prediction in high-speed boundary layers using Bayesian deep operator networks*

Transition in high-speed boundary layers is sensitive to uncertainty in the oncoming disturbance waves.  Therefore, a transition model that predicts both transition location and its distribution is desirable.  Such model can be learned from direct numerical simulation data.  One approach is to train an ensemble of deep operator networks (DeepONets), and to make an ensemble of predictions for each condition of interest. This strategy provides a measure of the epistemic uncertainty of the network model.  We subsequently introduce a Bayesian approach, where a single Bayesian DeepONet can quantify the uncertainty of predictions.  The loss function in this case is modified to account for the aleatoric uncertainty of transition.  Our results are demonstrated for a flat-plate boundary layer at Mach 4.5, which is forced by a primary planar instability wave that undergoes subharmonic secondary instability and breakdown to turbulence.