Abstract: Machine learning and differentiable programming offer a new paradigm for scientific computing, with algorithms tuned by machines instead of by people. I’ll show how these approaches can be used to improve the heuristics underlying numerical methods, particularly for discretizing partial differential equations. We use high resolution simulations to create training data, which we train convolutional neural nets to emulate on much coarser grids. By building on top of traditional approaches such as finite volume schemes, we can incorporate physical constraints, ensure stability and allow for extracting physical insights. Our approach allows us to integrate in time a collection of nonlinear equations in one spatial dimension at resolutions 4-8x coarser than is possible with standard finite difference methods.