Mathematical modeling of non-stationary heat transfer in selective laser melting based on machine learning

The article considers numerical modeling of thermal processes in 3D printing using selective laser melting technology based on machine learning. A mathematical model of non-stationary heat transfer in a rod with a variable cross section is developed as a partial differential equation describing the rod's temperature. An algorithm for numerically solving this equation is proposed, implemented using the Matlab system. It is shown that, for certain initial conditions, the temperature distribution becomes quasi-stationary, and for this case, a simple analytical expression for the temperature field is obtained. A neural network is constructed and trained using the TensorFlow library, with training data obtained from the analytical solution of the thermal problem. The neural network's calculation results align with the solutions of the original mathematical model. The article highlights that three-dimensional modeling of the printing process for real-world products demands substantial computational resources. It is shown that machine learning-based models can effectively approximate the temperature field in 3D printing with selective laser melting technology for components of similar geometry.