  Discovering governing equations of a physical system, represented by partial
differential equations (PDEs), from data is a central challenge in a variety of
areas of science and engineering. Current methods require either some prior
knowledge (e.g., candidate PDE terms) to discover the PDE form, or a large
dataset to learn a surrogate model of the PDE solution operator. Here, we
propose the first learning method that only needs one PDE solution, i.e.,
one-shot learning. We first decompose the entire computational domain into
small domains, where we learn a local solution operator, and then find the
coupled solution via a fixed-point iteration. We demonstrate the effectiveness
of our method on different PDEs, and our method exhibits a strong
generalization property.
