  Current physics-informed (standard or deep operator) neural networks still
rely on accurately learning the initial and/or boundary conditions of the
system of differential equations they are solving. In contrast, standard
numerical methods involve such conditions in computations without needing to
learn them. In this study, we propose to improve current physics-informed deep
learning strategies such that initial and/or boundary conditions do not need to
be learned and are represented exactly in the predicted solution. Moreover,
this method guarantees that when a deep operator network is applied multiple
times to time-step a solution of an initial value problem, the resulting
function is at least continuous.
