  Physics-informed neural networks (PINNs) as a means of discretizing partial
differential equations (PDEs) are garnering much attention in the Computational
Science and Engineering (CS&E) world. At least two challenges exist for PINNs
at present: an understanding of accuracy and convergence characteristics with
respect to tunable parameters and identification of optimization strategies
that make PINNs as efficient as other computational science tools. The cost of
PINNs training remains a major challenge of Physics-informed Machine Learning
(PiML) - and, in fact, machine learning (ML) in general. This paper is meant to
move towards addressing the latter through the study of PINNs on new tasks, for
which parameterized PDEs provides a good testbed application as tasks can be
easily defined in this context. Following the ML world, we introduce
metalearning of PINNs with application to parameterized PDEs. By introducing
metalearning and transfer learning concepts, we can greatly accelerate the
PINNs optimization process. We present a survey of model-agnostic metalearning,
and then discuss our model-aware metalearning applied to PINNs as well as
implementation considerations and algorithmic complexity. We then test our
approach on various canonical forward parameterized PDEs that have been
presented in the emerging PINNs literature.
