In this work, we propose a new method to solve partial differential equations (PDEs). Taking inspiration from traditional numerical methods, we view approximating solutions to PDEs as an iterative algorithm, and propose to learn the iterations from data. With respect to directly predicting the solution with a neural network, our approach has access to the PDE, having the potential to enhance the model's ability to generalize across a variety of scenarios, such as differing PDE parameters, initial or boundary conditions. We instantiate this framework and empirically validate its effectiveness across several PDE-solving benchmarks, evaluating efficiency and generalization capabilities, and demonstrating its potential for broader applicability.