We apply a scientific machine learning framework to aid the prediction and understanding of nanomaterial formation processes via a joint spectral-kinetic model. We apply this framework to study nucleation and growth of 2D perovskite nanosheets. Colloidal nanomaterials have size-dependent optical properties, and can be observed in situ, all of which make them a good model for understanding the complex processes of nucleation, growth and phase transformation of 2D perovskites. Our results demonstrate that this model nanomaterial can form through two processes at the nanoscale: either via a layer-by-layer chemical exfoliation process from lead bromide nanocrystals or via direct nucleation from precursors. We utilize a phenomenological kinetic analysis to study the exfoliation process and scientific machine learning to study the direct nucleation and growth, and discuss the circumstances under which it is more appropriate to use phenomenological or more complex machine learning models. Data for both analysis techniques are collected through in-situ spectroscopy in a stopped flow chamber, incorporating over 500,000 spectra taken under more than 100 different conditions. More broadly, our research shows that the ability to utilize and integrate traditional kinetics and machine learning methods will greatly assist the understanding of complex chemical systems.