Mollified-sharp decomposition: a probabilistic regularization of parametric POD for shock-bearing flows

This paper presents the mollified-sharp decomposition method for probabilistic regularization of moving shocks in parametric reduced-order models. Each detected shock location is modeled as a random variable with a prescribed probability density function, where averaging over this artificial distribution replaces localized pressure changes with smooth transitions. Each snapshot is decomposed exactly into regular and sharp components, enabling accurate handling of shock dynamics in fluid mechanics simulations.