Abstract: Example embodiments relate to machine-learned approximation techniques for numerical simulations. An example computer-implemented method for performing enhanced numerical simulations includes receiving a first vector field corresponding to a first solution of one or more differential equations at a first time step. The first vector field includes first values at each of a plurality of points along a mesh. The method also includes determining, using a machine-learned model, one or more refinement terms based on the first vector field, wherein the refinement terms represent effects of areas between points on the mesh. In addition, the method includes modifying one or more of the first values at one or more of the plurality of points along the mesh based on the one or more refinement terms. Further, the method includes generating a second vector field that includes second values at each of the plurality of points.