A Physics-Informed Neural Network Model for Temperature Inversion of Axisymmetric Gas Discharge Channel

The accurate measurement of gas discharge channel temperature is of great significance for the study of lightning physics. How to accurately solve the Abel equation and reduce the impact of noise accumulation is the key to the accurate inversion of the temperature. Physics-Informed Neural Networks (PINN) have shown promising future by combining the data driving nature of neural network with physical information guidance. In this paper, the schlieren image dataset is generated by assuming temperature distribution and simulations. With the dataset, the model is developed by training a PINN guided by inverse Abel transform, where the input is a schlieren image and the output is the distribution of relative gas destiny. After training, the results show that the accuracy of the proposed PINN method is close to that of other numerical algorithms, while PINN shows a significant improvement in computation speed. Moreover, compared with other methods, the accuracy of the PINN method remains stable under varying levels of noise, indicating its robustness, while the traditional methods are significantly affected by noise. The results of this paper indicate that PINN is more efficient in temperature inversion fields and more resistant to the effects of noise than previous methods, providing strong support for gas discharge temperature inversion.