  Neural networks, especially the recent proposed neural operator models, are
increasingly being used to find the solution operator of differential
equations. Compared to traditional numerical solvers, they are much faster and
more efficient in practical applications. However, one critical issue is that
training neural operator models require large amount of ground truth data,
which usually comes from the slow numerical solvers. In this paper, we propose
a physics-guided data augmentation (PGDA) method to improve the accuracy and
generalization of neural operator models. Training data is augmented naturally
through the physical properties of differential equations such as linearity and
translation. We demonstrate the advantage of PGDA on a variety of linear
differential equations, showing that PGDA can improve the sample complexity and
is robust to distributional shift.
