A0860
Title: Physics-informed priors with application to boundary layer velocity
Authors: Luca Menicali - University of Notre Dame (United States) [presenting]
Stefano Castruccio - University of Notre Dame (United States)
David Richter - University of Notre Dame (United States)
Abstract: One of the most popular recent areas of machine learning predicates the use of neural networks augmented by information about the underlying process in the form of partial differential equations (PDEs). These physics-informed neural networks are obtained by penalizing the inference with a PDE and have been cast as a minimization problem, which currently lacks a formal approach to quantifying uncertainty. A novel model-based framework is proposed, which regards the PDE as prior information of a deep Bayesian neural network. The prior is calibrated without data to resemble the PDE solution in the prior mean, while the degree of confidence in the PDE with respect to the data is expressed in terms of the prior variance. The information embedded in the PDE is then propagated to the posterior, yielding physics-informed forecasts with uncertainty quantification. The approach is applied to experimentally obtained turbulent boundary layer velocity in a wind tunnel using an appropriately simplified Navier-Stokes equation. The approach requires very few observations to produce physically consistent forecasts as opposed to non-physical forecasts stemming from non-informed priors, thereby allowing forecasting complex systems where some amount of data, as well as some contextual knowledge, is available.
