We present a novel dataset of simulations of the photodissociation region (PDR) in the Orion Bar and provide benchmarks of emulators for the dataset. Numerical models of PDRs are computationally expensive since the modeling of these changing regions requires resolving the thermal balance and chemical composition along a line-of-sight into an interstellar cloud. This often makes it a bottleneck for 3D simulations of these regions. In this work, we provide a dataset of 8192 models with different initial conditions simulated with 3D-PDR. We then benchmark different architectures, focusing on Augmented Neural Differential Equation (ANODE) based models. Obtaining fast and robust emulators can be included as preconditioners of classical codes or full emulators into 3D simulations of PDRs.