Digital technologies and artificial intelligence are currently driving disruptive changes in the economy and research landscape. The integration of digital solutions with innovative laser beam sources, optical systems, sensors, and modern system technology offers a comprehensive approach to enhancing productivity, efficiency, and quality in laser material processing. Digital process optimization in laser materials processing encompasses the design of optical systems and the integration of sensors for data visibility, extending to self-learning machines that autonomously identify optimal process parameters or adapt to varying conditions. The synergy of digital system technology, inverse (physical) process models, and adaptive beam shaping facilitates such autonomous laser processing machines. Application-specific beam shaping is crucial, as improved energy deposition directly enhances quality and productivity in laser materials processing. To meet the requirements for desired target field distributions, we employ a method based on diffractive deep neural networks, interpreting a system of cascaded phase masks as a physical realization of an artificial neural network. We demonstrate how the combination of two Liquid Crystal on Silicon (LCoS) spatial light modulators is integrated into an ultra-short pulse micromachining platform for flexible beam shaping. This optical neural network approach provides unprecedented freedom for target design features, including optimization for multiple target planes, combined optimization of amplitude and phase, extension of effective working range, in-system aberration correction, and digital phase mask alignment. The presented design method exemplifies how artificial intelligence benefits the field of photonics.