The method of generative model design (GMD) has been applied to reconstruct the structure and coefficients of a partial differential equation describing the target’s heating and its evaporation by laser radiation. The initial synthetic data includes heating scenarios corresponding to surface energy absorption or to volume one. It was shown that reconstructing the model correctly required the use of a preprocessing technique providing the exclusion of a part of the initial data if the volume absorption took place. A modification of the method that made it possible to take into account the temperature dependence of the coefficients of the reconstructed equation was put forward. The influence of various statistical criteria used in selecting the optimal subset of elements on the accuracy of reconstructing the equation structure was discussed. The efficiency of the GMD was demonstrated for a wide range of target heating parameters and different options for setting the energy input. The possibility of model generating by noisy data was shown.