Physics-informed neural networks for the shallow-water equations on the sphere

We propose the use of physics-informed neural networks for solving shallow-water equations on sphere in meteorological context. Physics-informed are trained to satisfy differential along with prescribed initial and boundary data, thus can be seen as an alternative approach compared traditional numerical approaches such finite difference, volume or spectral methods. discuss training difficulties a simple multi-model tackle test cases comparatively long time intervals. Here we train sequence instead single network entire integration interval. also avoid value loss by encoding conditions custom layer. illustrate abilities method most prominent proposed Williamson et al. (1992) [53].