Accelerating physics-informed neural network based 1D arc simulation by meta learning

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.