Synchrotron light is used for a wide variety of scientific disciplines ranging from physical chemistry to molecular biology and industrial applications. As the electron beam circulates, random single-particle collisional processes lead to decay of the beam current in time. We report a simulation study in which a combined neural network (NN) and first-principles (FP) model is used to capture the decay in beam current due to Touschek, Bremsstrahlung, and Coulomb effects. The FP block in the combined model is a parametric description of the beam current decay where model parameters vary as a function of beam operating conditions (e.g. vertical scraper position, RF voltage, number of the bunches, and total beam current). The NN block provides the parameters of the FP model and is trained (through constrained nonlinear optimization) to capture the variation in model parameters as operating condition of the beam changes. Simulation results will be presented to demonstrate that the proposed combined framework accurately models beam decay as well as variation to model parameters without direct access to parameter values in the model.