Empirical uncertainty quantification in deep learning: Applications to fluid dynamics

Deep learning is becoming increasingly pervasive within the fluid mechanics community. However, it continues to face resistance due to the difficulty of predicting its generalization behavior. This challenge can be partially addressed by training models that know when they are wrong—that is, models capable of providing meaningful estimates of uncertainty alongside their predictions. Although uncertainty quantification is a well-established area in the deep learning literature, it has yet to gain widespread adoption in fluid mechanics, particularly for neural network-based models. This paper reviews recent advances in uncertainty-aware deep learning, focusing on methods that are grounded in rigorous mathematical frameworks while requiring minimal modifications to standard architectures or training procedures. Four approaches — Deep Ensembles, Monte Carlo Dropout, Stochastic Gradient Langevin Dynamics, and ZigZag — are evaluated on two fluid mechanics datasets of increasing complexity to illustrate their respective strengths and limitations. The importance of recalibration is also stressed.