  Deep operator networks (DeepONets), a class of neural operators that learn
mappings between function spaces, have recently been developed as surrogate
models for parametric partial differential equations (PDEs). In this work we
propose a derivative-enhanced deep operator network (DE-DeepONet), which
leverages the derivative information to enhance the prediction accuracy, and
provide a more accurate approximation of the derivatives, especially when the
training data are limited. DE-DeepONet incorporates dimension reduction of
input into DeepONet and includes two types of derivative labels in the loss
function for training, that is, the directional derivatives of the output
function with respect to the input function and the gradient of the output
function with respect to the physical domain variables. We test DE-DeepONet on
three different equations with increasing complexity to demonstrate its
effectiveness compared to the vanilla DeepONet.
