Intravital microscopy in small animals growingly contributes to the visualization of short- and long-term mammalian biological processes. Miniaturized fluorescence microscopy has revolutionized the observation of live animals' neural circuits. The technology's ability to further miniaturize to improve freely moving experimental settings is limited by its standard lens-based layout. Typical miniature microscope designs contain a stack of heavy and bulky optical components adjusted at relatively long distances. Computational lensless microscopy can overcome this limitation by replacing the lenses with a simple thin mask. Among other critical applications, Flat Fluorescence Microscope (FFM) holds promise to allow for real-time brain circuits imaging in freely moving animals, but recent research reports show that the quality needs to be improved, compared with imaging in clear tissue, for instance. Although promising results were reported with mask-based fluorescence microscopes in clear tissues, the impact of light scattering in biological tissue remains a major challenge. The outstanding performance of deep learning (DL) networks in computational flat cameras and imaging through scattering media studies motivates the development of deep learning models for FFMs. Our holistic ray-tracing and Monte Carlo FFM computational model assisted us in evaluating deep scattering medium imaging with DL techniques. We demonstrate that physics-based DL models combined with the classical reconstruction technique of the alternating direction method of multipliers (ADMM) perform a fast and robust image reconstruction, particularly in the scattering medium. The structural similarity indexes of the reconstructed images in scattering media recordings were increased by up to 20% compared with the prevalent iterative models. We also introduce and discuss the challenges of DL approaches for FFMs under physics-informed supervised and unsupervised learning.