Advances in ultra-intense laser technology have increased repetition rates and average power for chirped-pulse lasersystems which is promising for many applications including energetic proton sources. An important challenge is the needto optimize and control the proton source by changing the details of the laser-plasma interaction, which is where machinelearning can play an important role. Building upon our earlier work in Desai et al. 2024, we generate a large syntheticdata set for proton acceleration using a physics-informed analytic model that we improved to include pre-pulse physicsand we train different machine learning methods on this data set to determine which methods perform efficiently andaccurately. Generally we find that quasi-real time training of these models using single shot data from a kHz repetitionrate ultra-intense laser system should typically be feasible on a single GPU. We also find that less sophisticated modelscan be trained even faster, and that the accuracy of these models is still good enough to be useful. We provide our sourcecode and example synthetic data for others to test new machine learning methods and approaches to automated learningin this regime.