This paper presents a novel methodology for characterizing and creating a digital twin of turbid media without the need for reference beams, employing a unique architecture for the physics-informed neural network. Unlike previous approaches utilizing various deep neural network architectures that often function as black boxes, our method prioritizes interpretability, offering a clearer understanding of the underlying processes of light propagation through turbid media. Additionally, unlike classical solutions relying on reference beams, our approach eliminates the dependence on beam quality and associated issues prevalent in both internal and external reference-based methods. The possibility and use case of gradient calculation through this presented digital twin are showcased by solving the reverse problem to retrieve the initial wavefront shape of the light that passed through this medium, known as image transmission. Surprisingly, the results surpassed the accuracy of models directly optimized for this task, underscoring the precision of the proposed digital twin. This capability represents a pivotal advancement for future developments in neuromorphic and deep learning computation and training using such a photonic and optical systems.