Deep learning methods offer the promise of drastically reducing the computational cost of evaluating a diverse range of plasma physics models. The application of deep learning methods to several plasma applications is, however, hindered by the often sparse data sets available. Physics-informed machine learning methods, whereby physical constraints are embedded into a neural network (NN), offer a path through which the quantity of data required to train a NN can be drastically reduced, or entirely eliminated. The present work employs a physics-informed neural network (PINN) to predict runaway electron (RE) formation during a tokamak disruption in the absence of any synthetic or experimental data. In particular, a PINN is developed to learn the parametric solution to the adjoint of the time dependent Relativistic Fokker-Planck (RFP) equation. Once trained, the PINN serves as a rapid surrogate of the adjoint RFP equation, which may in turn be used to describe the principal mechanisms of RE generation during tokamak disruptions. Specifically, the RFP PINN is employed to evaluate the `hot tail' seed that emerges during the thermal quench of a tokamak disruption. The accurate treatment of such a seed has posed a substantial challenge due to the inherently kinetic origin of this mechanism, and its extreme sensitivity to the time history of the temperature profile. In addition, the RFP PINN is able to predict the subsequent amplification of this RE seed by the avalanche mechanism, thus enabling an efficient description of the dominant RE generation processes in a disrupting plasma. The predictions of the RFP PINN are verified against first principle Monte Carlo simulations of RE generation, with excellent agreement observed across a broad range of disruption conditions. Ongoing work is focused on integrating this rapid surrogate of the adjoint RFP equation with the MHD evolution of the disrupting plasma.