There is an opportunity for deep learning to revolutionize science and technology by revealing its findings in a human interpretable manner. We develop a novel data-driven approach for creating a human-machine partnership to accelerate scientific discovery. By collecting physical system responses, under carefully selected excitations, we train rational neural networks to learn Green's functions of hidden partial differential equation. These solutions reveal human-understandable properties and features, such as linear conservation laws, and symmetries, along with shock and singularity locations, boundary effects, and dominant modes. We illustrate this technique on several examples and capture a range of physics, including advection-diffusion, viscous shocks, and Stokes flow in a lid-driven cavity.