The authors suggest using a numerical method based upon the finite element analysis of the equations of continuous inhomogeneous media mechanics to describe thermophysical properties of transient motions of viscous gas through porous media with chemical changes and phase transitions in a solid phase. The model takes into account heat exchange between a solid frame and gas, changes in the phase volume and mass at interaction, the presence of oxidant diffusion. The software developed in FreeFem++ allows clear and vivid studying the process of gas combustion in solid porous medium with inhomogeneous combustion source at forced filtration in the course of time as well as modeling and analyzing a real experiment.

The problems of the non-stationary complex heat transfer have been considered in the work. An optimization algorithm based on machine learning methods has been proposed. The algorithm uses a neural network trained on a dataset of numerical experiments to predict the value of a chosen quality functional. Dual annealing method has been used to minimize neural network prediction function while varying boundary parameters. The obtained results are verified by comparison with numerical experiments.