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].

翻译：我们提议利用物理-知情神经网络来解决球体上的浅水方程式问题。物理-知情神经网络经过培训,与规定的初始和边界数据一起满足差异方程式,因此可以被视为一种替代方法,用以解决差异方程式,而不同于诸如有限差异、有限体积或光谱方法等传统数字方法。我们讨论了物理-知情神经网络在解决球体上的浅水方程式方面的培训困难,并提出了处理相对较长间隔的测试案例的简单多模式方法。我们通过解决Williamson等人提出的最突出测试案例,[J.Compuut.Phys.102,211-224,1992]来说明这种方法的能力。