The demand for integrated modeling of a tokamak disruption has motivated the embedding of a runaway electron (RE) model into magnetohydrodynamic (MHD) simulations. Such an integrated model can be deployed to estimate the damage from unmitigated disruptions, and the effectiveness of different mitigation strategies. Challenges associated with an integrated MHD-RE description are the computationally prohibitive demands from a first-principles description, or uncertainties that come packaged with reduced models. To this end, a novel path towards an efficient and high-fidelity integrated model of a tokamak disruption is presented. Specifically, an adjoint treatment of the relativistic Fokker-Planck equation is utilized to form the runaway probability function (RPF)[1], which allows for the mechanisms of RE generation to be described. The adjoint approach is then used in combination with physics-constrained deep learning approaches to provide an efficient means of predicting the number of REs formed from different mechanisms. In particular, a physics-informed neural network (PINN) is shown to efficiently learn the parametric solution over a broad range of relevant plasma parameters, thus predicting RE formation in milliseconds. As a result, the adjoint-PINN framework can efficiently describe the RE formation processes relevant to tokamak disruptions, such as the hot-tail seed[2], avalanche[3], and the decay[4] of runaway electrons. The end result is DeepRunAway: a fluid RE model that can be incorporated into a broader framework that describes a tokamak disruption. As an initial application, DeepRunAway is deployed into a zero-dimensional description of a tokamak disruption. [1] C. F. Karney and N. J. Fisch, The Physics of Fluids 29, 180 (1986). [2] C. J. McDevitt, Physics of Plasmas 30, 092501 (2023). [3] J. S. Arnaud, T. B. Mark, and C. J. McDevitt, Journal of Plasma Physics 90, 905900409 (2024). [4] C. J. McDevitt, J. S. Arnaud, and X.-Z. Tang, Physics of Plasmas 32, 042503 (2025).