In the context of laser micromachining, the high complexity and non-linearity of the laser-matter interaction imply that theoretical models fail to give a complete and predictive description of experimental results. Each new process to be developed in the world of laser micromachining requires finding optimal machining parameters to achieve time and quality criteria through numerous experimental tests. This time-consuming phase, which requires machine and personnel time as well as materials, is linked to the high complexity and non-linearity of the laser-matter interaction. Therefore, the known theoretical models describing this interaction fail to provide a complete description of the experimental result for a given set of machining parameters. As a new tool to find sets of optimal parameters, we propose to use an artificial intelligence approximation model (XGboost or neural network) and a genetic algorithm. A large database of many different engraving parameters and the associated machining properties has been generated for 316L stainless steel. Tranfer learning technique was used to generalize the model to other metals: 304 stainless steel, brass, and titanium. The performances of XGboost, raw neural network, and the pre-trained neural network are discussed for each material and the issue of amount of data needed for models training is addressed.