Industrially widespread laser processes such as laser cutting and laser welding are nowadays usually only monitored and at best controlled in partial areas such as process aborts. On the other hand, process data can be obtained with the aid of acoustic and optical sensors as well as thermal cameras and then processed further. Process data obtained in this way are linked to quality characteristics such as burr formation and edge roughness in cutting and structure depth and spacing in micro structuring on the one hand, and to process parameters such as laser power, feed rate, focus size and position on the other. A prerequisite for controlled laser processes is whether AI-supported algorithms can be used to make reliable predictions about the expected process result based on the process data. Within an internal Fraunhofer project "AI Beam", large amounts of data originating from cutting and welding are used to train an AI (and the correct selection of the appropriate mathematical method) and linked to quality criteria. First results of this project related to cutting will be presented. In another research project, similar approaches for laser micro structuring are being pursued together with industrial partners. Results from this ongoing project will also be presented.