Scramjet inlets are susceptible to unstart, leading to a sudden loss of thrust and control. A common reduced-order modeling approach for such flows is the Smart-Ortwerth model (2015), which predicts pseudoshock properties in backpressured ducts via three ODEs (p, M, A_c/A_0). While reduced-order models like this provide a good estimate, they rely on empirical coefficients that can introduce significant uncertainty. This research proposes a hybrid framework combining physics-informed neural networks (PINNs) with symbolic regression (SR) to discover interpretable correction terms for these governing equations. By embedding the Smart-Ortwerth ODEs directly into the network’s loss function and training on each dataset independently, we ensure physical consistency of the initial black-box terms produced by the PINN. This step essentially filters the raw data through the governing physics, reconciling sparse experimental wall pressure traces with high-fidelity numerical parameter sweeps generated via entropy-stable DGSEM code across varying inlet Mach numbers. We then use SR on these consolidated PINN datasets to identify the specific functional forms of the missing terms that account for unmodeled physics. This sequential process ensures that the resulting closed-form expressions respect the underlying physical scales. Our results demonstrate that this approach extracts interpretable correction terms with functional dependencies on local flow properties, maintaining physical consistency across the investigated Mach envelope. By identifying these dependencies, the framework accounts for unmodeled physics and empirical uncertainties that previously limited the accuracy of reduced-order models for pseudoshocks. The resulting model provides a reliable, data-driven tool for the identification of unknown terms in shock-train-dominated flows. This steady framework provides a baseline for future investigations into unsteady unstart dynamics and the design of resilient high-speed propulsion systems.