  Solving differential equations efficiently and accurately sits at the heart
of progress in many areas of scientific research, from classical dynamical
systems to quantum mechanics. There is a surge of interest in using
Physics-Informed Neural Networks (PINNs) to tackle such problems as they
provide numerous benefits over traditional numerical approaches. Despite their
potential benefits for solving differential equations, transfer learning has
been under explored. In this study, we present a general framework for transfer
learning PINNs that results in one-shot inference for linear systems of both
ordinary and partial differential equations. This means that highly accurate
solutions to many unknown differential equations can be obtained
instantaneously without retraining an entire network. We demonstrate the
efficacy of the proposed deep learning approach by solving several real-world
problems, such as first- and second-order linear ordinary equations, the
Poisson equation, and the time-dependent Schrodinger complex-value partial
differential equation.
