Graph Networks with Physics-aware Knowledge Informed in Latent Space.

While physics conveys knowledge of nature built from an interplay between observations and theory, it has been considered less important for modeling deep neural networks. Despite the usefulness of physical rules, it is particularly challenging to leverage the knowledge for sparse data since most physics equations are well defined on the continuous and dense space. In addition, it is even harder to inform the equations into a model if the observations are not fully governed by the given physical knowledge. In this work, we present a novel architecture to incorporate physics or domain knowledge given as a form of partial differential equations (PDEs) on sparse observations by utilizing graph structure. Moreover, we leverage the representation power of deep learning by informing the knowledge in latent space. We demonstrate that climate prediction tasks are significantly improved and validate the effectiveness and importance of the proposed model.