In recent years, there has been an increased demand for elaborate monitoring techniques in laser material processing. This has been driven by the need for fast and cost-efficient quality assurance processes. At the same time, the use of ultrashort-pulsed (USP) laser radiation has emerged as a promising technology for creating intricate microstructures in graphite anodes due to their high precision and the negligible thermal impact. However, the integration of process monitoring in USP applications for graphite anode structuring is still underexplored. There is a lack of clarity on suitable sensors, observable parameters, and extractable process-relevant insights. This study addresses this gap by demonstrating the efficacy of state-of-the-art photodiode-based monitoring systems in collecting process-relevant data and deriving valuable insights from the process. As an application case, the laser structuring of lithium battery electrodes, consisting of a porous, graphite-based, and multi-material system was selected. A sensor equipped with three photodiodes was employed to address these challenges. Exploratory data analysis techniques and machine learning methodologies were leveraged to develop a data pipeline for processing the acquired information. The data was used to train convolutional neural networks which were able to predicting the focal position with high accuracy. At the same time, the limitations of traditional regression approaches could be shown. The findings advance the understanding of the possibilities of process monitoring in USP laser applications and emphasize the significance of data-driven approaches in optimizing manufacturing processes.