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

• URL: http://arxiv.org/abs/2104.00615v1
• Date: Thu, 1 Apr 2021 16:47:40 GMT
• Title: Physics-informed neural networks for the shallow-water equations on the sphere
• Authors: Alex Bihlo and Roman O. Popovych
• Abstract summary: Physics-informed neural networks are trained to satisfy the differential equations along with the prescribed initial and boundary data. We propose a simple multi-model approach to tackle test cases of comparatively long time intervals.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose the use of physics-informed neural networks for solving the shallow-water equations on the sphere. Physics-informed neural networks are trained to satisfy the differential equations along with the prescribed initial and boundary data, and thus can be seen as an alternative approach to solving differential equations compared to traditional numerical approaches such as finite difference, finite volume or spectral methods. We discuss the training difficulties of physics-informed neural networks for the shallow-water equations on the sphere and propose a simple multi-model approach to tackle test cases of comparatively long time intervals. We illustrate the abilities of the method by solving the most prominent test cases proposed by Williamson et al. [J. Comput. Phys. 102, 211-224, 1992].

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