Accelerating physics-informed neural network based 1D arc simulation by meta learning. (16th February 2023)

• Record Type: Journal Article
• Authors: Zhong, Linlin; Wu, Bingyu; Wang, Yifan
• Is Part Of: Journal of physics. Volume 56:Number 7(2023)
• Publication Date: 2023-02-16
• Subjects: physics-informed neural network -- plasma simulation -- meta learning -- deep learning; Physics -- Periodicals; 530
• DOI: 10.1088/1361-6463/acb604
• Languages: English
• ISSNs: 0022-3727

Abstract

Abstract: 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 1D 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 1D 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 L 2 error by Meta-PINN ranges from 1.1× to 6.9× in the cases we studied. The results indicate that Meta-PINN is an effective method for accelerating the PINN-based 1D arc simulation.