An automated drilling system requires a real-time evaluation of the drilling bit during drilling to optimize operation and determine when to stop drilling and switch bits. Furthermore, in the dynamic modeling of drill strings, it is necessary to take into account the interactions between drilling bits and rock. To address this challenge, a hybrid approach that combines physics-based models with data analytics has been developed to handle downhole drilling measurements in real time. First, experimental findings were used to formulate mathematical models of cutter–rock interaction in accordance with their geometrical characteristics, rock properties, and drilling parameters. Specifically, these models represent the normal and contact forces of polycrystalline diamond compact cutters (PDCs). Experimental data are analyzed utilizing deep learning, nonlinear regression, and genetic algorithms to fit nonlinear equations to data points. Following this, the recursive least square was implemented as a data analytic method to integrate real-time drilling data, drilling bit models, and mathematical models. Drilling data captured by the along-string measurement system (ASM) is implemented to estimate cutting and normal forces, torque, and specific energy at the bit. The unique aspect of this research is our approach in developing a detailed cutter–rock interaction model that takes all design and operation parameters into account. In addition, the applicability of the algorithm is demonstrated by real-time assessments of drilling dynamics, utilizing downhole digital data, that enable the prediction of drilling events and problems related to drilling bits.