- Helmholtz-Zentrum Hereon
The shallow water equations (SWEs) are widely employed for governing a large-scale fluid flow system, for example, in the coastal regions, oceans, estuaries, and rivers. These partial differential equations (PDEs) are often solved using semiimplicit schemes that solve a linear system iterativelyat each time step, resulting in high computational costs. Here we use physics constrained deep learning to train a convolutoinal network to solve the SWEs, while training on the discretized PDE directly without any need for numerical simulations as training data data. To improve accuracy and stability over longer integration times, we utilise group equivariant convolutional networks, so that the the learned model respects rotational and translational symmetries in the PDEs as hard constraints at every point in the training process. After training, our networks accurately predict the evolution of SWEs for freely chosen initial conditions and multiple time steps. Overall, we find that symmetry constraints signficantly improve performance compared to standard convolution networks.