Reproduce “Physics-informed neural networks for the shallow-water equations on the sphere” on OpenResearch

About this paper

Alex Bihlo, Roman O. Popovych

This research from Memorial University of Newfoundland and the University of Vienna demonstrates the application of physics-informed neural networks (PINNs) to solve the shallow-water equations on a sphere. The study introduces a sequential multi-model approach and hard-constrained boundary conditions, enabling accurate long-time integrations and effectively addressing coordinate singularities at the poles in benchmark geophysical fluid dynamics problems.

Key insights

• The sequential multi-model approach with warm-starting is crucial for extending PINN applicability to long-duration simulations in GFD, overcoming the limitations of single-model training.
• Hard-coding boundary conditions directly into the neural network architecture via a coordinate transformation provides an elegant and effective solution to numerical issues arising from spherical coordinate singularities.
• PINNs, when appropriately configured, can accurately capture complex geophysical phenomena like wave propagation and steady-state flows while maintaining reasonable conservation properties.

Summary by alphaXiv.