  Physics-Informed Neural Networks (PINNs) have a wide range of applications as
an alternative to traditional numerical methods in plasma simulation. However,
in some specific cases of PINN-based modeling, a well-trained PINN may require
tens of thousands of optimizing iterations during training stage for complex
modeling and huge neural networks, which is sometimes very time-consuming. In
this work, we propose a meta-learning method, namely Meta-PINN, to reduce the
training time of PINN-based 1-D arc simulation. In Meta-PINN, the meta network
is first trained by a two-loop optimization on various training tasks of plasma
modeling, and then used to initialize the PINN-based network for new tasks. We
demonstrate the power of Meta-PINN by four cases corresponding to 1-D arc
models at different boundary temperatures, arc radii, arc pressures, and gas
mixtures. We found that a well-trained meta network can produce good initial
weights for PINN-based arc models even at conditions slightly outside of
training range. The speed-up in terms of relative L2 error by Meta-PINN ranges
from 1.1x to 6.9x in the cases we studied. The results indicate that Meta-PINN
is an effective method for accelerating the PINN-based 1-D arc simulation.
