Current, realistic numerical simulations of the solar atmosphere reproduce observations in a statistical sense; they do not exactly reproduce observations such as a movie of solar granulation. Physics-informed neural networks (PINNs) offer a new approach to solving the time-dependent radiative hydrodynamics equations that easily includes observations as boundary conditions. PINNs approximate the solution of the integro-differential equations with a deep neural network. The parameters of this network are determined by minimizing the residuals with respect to the physics equations and the observations. Ever increasing advances in machine learning make it now possible to tackle this massive optimization problem even on a laptop computer. The resulting PINN models are continuous in all dimensions, can zoom into local areas of interest in space and time, and provide information on physical parameters that are not necessarily observed such as horizontal velocities within granules. PINNs can also extrapolate in space and time beyond the directly observed domain, all while using only a small fraction of the storage space of classical numerical models. I will present the first results of this novel approach applied to synthetic observations of the solar photosphere, explain the underlying methodology and provide an outlook to applying the tool to actual solar observations and including additional physics such as magnetic fields. This is only the very first step in an exciting direction that has the potential to revolutionize the way we interpret solar observations, understand the underlying physics and approximate solar processes on small scales such that they can be efficiently included in simulations at much larger scales.