In this talk, we consider deep learning methods for inverse problems of piecewise-continuous variable coefficients of partial differential equations (PDEs). We use two different neural networks: the solution and coefficient networks, and decomposes the complex training process into three stages according to all the information at hand. The solution network learns an initial approximation of the PDE solution in the first stage. Based on this approximation, the coefficient network estimates the unknown coefficients in the second stage. With the two networks learned in the first two stages, in the third stage, the two networks are trained together on newly constructed training sets. Our numerical tests show that the three staged physical informed neural networks (PINN) are effective and accurate for solving PDE inverse problems of various types of variable coefficients, including polynomial, trigonometric, exponential, space-time dependent, and piecewise-continuous functions.