Interactions between light and matter during short-pulse laser materials processing are highly nonlinear, and hence acutely sensitive to laser parameters such as the pulse energy, repetition rate, and number of pulses used. Due to this complexity, simulation approaches based on calculation of the underlying physical principles can often only provide a qualitative understanding of the inter-relationships between these parameters. An alternative approach such as parameter optimisation, often requires a systematic and hence time-consuming experimental exploration over the available parameter space. Here, we apply neural networks for parameter optimisation and for predictive visualisation of expected outcomes in laser surface texturing with blind vias for tribology control applications. Critically, this method greatly reduces the amount of experimental laser machining data that is needed and associated development time, without negatively impacting accuracy or performance. The techniques presented here could be applied in a wide range of fields and have the potential to significantly reduce the time, and the costs associated with laser process optimisation.