A method of generative model design based on irregular data in application to heat transfer problems

The paper presents the results of applying the generative design method to reconstruct a model driven by irregular data in the form of a partial differential equation. The problem of non-stationary heating of a metal rod is considered as an example. The finite element method is used to construct templates of possible elements of the derived differential equation. The optimization algorithm for determining a model design is based on the procedure of best subset selection. The efficiency of the method for derivating a model of the thermal conduction process based on irregular data is shown. As irregular data, data obtained on spatial meshes with alternating steps of different size, or a step changing in arithmetic progression, are considered.