Using self-adaptive physics-informed learning to estimate orographic gravity waves

Despite the continuing increase of computing power, the multi-scale nature of geophysical fluid dynamics implies that many important physical processes are still represented using physical parameterization. This traditional approach exhibits persistent and systematic shortcomings due to an inadequate representation of unresolved processes and remains impractical to employ when the boundary and/or initial conditions are not well-defined. In this context, deep learning models are considered an attractive alternative approach as they offer the potential of generalizing the solution while still being able to respect physical constraints. The starting point of the present work is to use Physics-Informed Neural Networks (PINNs) to estimate orographic gravity wave parameters. A fixed budget online adaptive learning strategy is proposed to improve the performance of PINNs by correcting adaptively the distribution of unsupervised training points during the training process. This strategy is shown to accurately capture important couplings between meteorological variables, especially in the vicinity of the mountain. The numerical results also demonstrate the capability of PINNs for solving inverse problems, i.e. estimating dimensionless parameters related to the flow (Richardson and Reynolds numbers) or the shape of the mountain from a downsampled gravity wave field.