With the goal of “carbon peak and carbon neutrality,” the need for environmentally friendly gases to replace SF6, a high greenhouse effect gas, is urgent. C4F7N, as an environmentally friendly gas with the greatest potential to replace SF6 as an arc extinguishing medium in circuit breakers, can be mixed with CO2 to greatly improve the shortcomings of its high liquefaction temperature, and the calculation of the physical parameters of the mixed gas plasma is a prerequisite for the computational simulation of the arc process in the opening of circuit breakers. Because solving the physical parameters is expensive, based on the system of differential equations, this paper adopts several machine learning algorithms by mining the relationship between the data using the known physical parameter data to predict the results of the physical parameters to be solved under certain conditions, which greatly reduces the cost of computation. The machine learning algorithms used in this paper are K-nearest-neighbor regression, decision tree, random forest, support vector machine, and gradient boosting regression, of which for the support vector machine, hyperparameters find it difficult to determine the problem of optimization using the gray wolf algorithm. The prediction results of several algorithms show that they are more accurate and that the problem can be solved better by using the method of machine learning. Finally, the comparison results show that the support vector machine exhibits better performance in most cases and that the gray wolf algorithm can make the results of the support vector machine more accurate.