This study proposes a physics-enhanced neural network, PENTAGON, as an inference framework for volumetric tomography applications. By leveraging the synergistic combination of data-prior and forward-imaging model, we can accurately predict 3D optical fields, even when the number of projection views decreases to three. PENTAGON is proven to overcome the generalization limitation of data-driven deep learning methods due to data distribution shift, and eliminate distortions introduced by conventional iteration algorithms with limited projections. We evaluated PENTAGON using numerical and experimental results of a flame chemiluminescence tomography example. Results showed that PENTAGON can potentially be generalized for inverse tomography reconstruction problems in many fields.