Mathematical modeling in additive technologies used for topological optimization

Additive technologies exemplified well in the industry. As a rule, it is technologies called synthesis on a support material (selective laser melting and the like), that make it possible to create products with complex geometries, internal channels, etc Modern software allows significant expansion in the capabilities of such technologies. One of the directions of the development in this area is the generative artificial intelligence, for example, in case of topological optimization aimed at reducing the weight of the product without loss of strength characteristics. It is based on well-known mathematical models and numerical calculation methods. At the same time, it has now become possible to calculate several models in parallel, depending on the set parameters. At the moment, several algorithms are used for modeling and calculations, gaining the reputation of good results, but at the same time an additional verification of the results obtained before manufacturing, is required. This paper presents the main mathematical models and examines the features for optimization in additive technologies. It discusses examples of model combinations. Using the example of a promising optimization method, the existing limitations and the possibilities of overcoming them are studied. Due to the peculiarities of modeling, one of the tasks is to obtain the results closest to the real ones, therefore, an option for improving the work is proposed, taking into account the real values of experiments. A pattern to understand the specifics of the work of various methods is given, allowing a possible data calculation option depending on the available initial conditions.