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Physics-informed neural networks (PINNs) as a means of discretizing partialdifferential equations (PDEs) are garnering much attention in the ComputationalScience and Engineering (CS&E) world. At least two challenges exist for PINNsat present: an understanding of accuracy and convergence characteristics withrespect to tunable parameters and identification of optimization strategiesthat make PINNs as efficient as other computational science tools. The cost ofPINNs training remains a major challenge of Physics-informed Machine Learning(PiML) - and, in fact, machine learning (ML) in general. This paper is meant tomove towards addressing the latter through the study of PINNs on new tasks, forwhich parameterized PDEs provides a good testbed application as tasks can beeasily defined in this context. Following the ML world, we introducemetalearning of PINNs with application to parameterized PDEs. By introducingmetalearning and transfer learning concepts, we can greatly accelerate thePINNs optimization process. We present a survey of model-agnostic metalearning,and then discuss our model-aware metalearning applied to PINNs as well asimplementation considerations and algorithmic complexity. We then test ourapproach on various canonical forward parameterized PDEs that have beenpresented in the emerging PINNs literature.

A Metalearning Approach for Physics-Informed Neural Networks (PINNs): Application to Parameterized PDEs