We present a novel scientific machine learning framework for reconstructing the hidden dynamics of the transmission rate in compartmental epidemic models. Accurate estimation of this key parameter is critical for reliable forecasting, as even small misestimations can severely compromise predictive performance. Our approach is designed to discover the latent differential laws governing the transmission rate, expressed as a function of exogenous variables—measurable external factors such as environmental conditions that influence disease spread. The proposed hybrid architecture integrates a data-driven component with a physics-based model. The data-driven component leverages neural ordinary differential equations to learn the time evolution of the parameters, conditioned on both exogenous variables and latent variables that capture the influence of unobserved external factors. The physics-based component is a standard compartmental model treating the reconstructed parameters as inputs. Training is performed in a fully end-to-end manner, with a loss function that measures the discrepancy between observed outputs and numerical predictions from the physics-based model. To further improve accuracy, we incorporate a data assimilation scheme that estimates sample-specific latent variables. We apply this architecture to model the transmission rate of seasonal influenza as a function of meteorological variables, specifically temperature and humidity. Our results highlight the ML framework’s ability to capture complex, time-varying relationships between environmental drivers and disease transmission, offering a promising tool for data-informed epidemic forecasting.