Stan Osher (joint with H. Schaeffer, R. Caflisch and C. Hauck) We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced by simply applying soft thresholding to the coefficients of the basis approximation. As examples we used a Fourier approximation and soft thresholding to successfully reduce the dynamics of convection equations, diffusion equations, viscous shock approximations and vorticity equations with high frequency source terms.