A neural network-based study on the growth rate of a shocked heavy gas layer

Numerical investigation of a shock wave impacting an upstream disturbed heavy gas layer is conducted by varying four initial physical parameters: the Mach numbers of incident shock, the Atwood numbers between the interior and exterior of the gas layer, the thickness–wavelength ratios of the gas layer, and the initial amplitude–wavelength ratios of the upstream interface. The neural network method is applied to model the growth rates of both the upstream and downstream interfaces. The growth rates of the two interfaces are illustrated on a two-dimensional graph comprising 25 unit images by an analysis of 3360 simulated cases, effectively demonstrating the influence of four sets of initial parameters. From a macroscopic perspective, the variation in the thickness of the gas layer exhibits minimal impact on the growth rate of the upstream interface at low Mach numbers. Conversely, at high Mach numbers, the growth rate of the upstream interface increases with increasing thickness, while the growth rate of the downstream interface initially decreases before subsequently increasing as thickness increases. For these nonlinear relationships, two neural network models with four hidden layers establish a mapping from the initial parameters to the growth rates and accurately predict the growth rates for two interfaces, significantly reducing computational time for future scientific and engineering applications. Furthermore, the partial derivatives of the predicted growth rates with respect to the four initial parameters are computed using backpropagation with the trained neural network models. These partial derivatives facilitate the optimization of growth rate's changes by allowing fine-tuning of one parameter while maintaining the other initial parameters constant.