  Numerical modelling is an essential approach to understanding the behavior of
thermal plasmas in various industrial applications. We propose a deep learning
method for solving the partial differential equations in thermal plasma models.
In this method a deep feed-forward neural network is constructed to surrogate
the solution of the model. A loss function is designed to measure the
discrepancy between the neural network and the equations describing thermal
plasmas. A good neural network is obtained by minimizing this loss function. We
demonstrate the power of this deep learning method by solving a 1-D arc
decaying model which is consist of three cases: stationary arc, transient arc
without considering radial velocity, and transient arc with radial velocity
respectively. The results show that the deep neural networks have excellent
ability to express the differential equations describing thermal plasmas. This
could bring us a new and prospective numerical tool for thermal plasma
modelling.
