Abstract: Due to the high computational load of modern numerical simulation,there is a demand for approaches that would reduce the sizeof discrete problems while keeping the accuracy reasonable.In this work, we present an original algorithmto coarsen an unstructured grid basedon the concepts of differentiablephysics. We achieve thisby employing $k$-means clustering, autodifferentiation andstochastic minimization algorithms.We demonstrate performance of the designed algorithm on a linear parabolic equation which governsslightly compressible fluid flow in porous media.Our results show that in the considered scenarios, we reduced the number of grid points up to 10 times while preserving the modeled variable dynamics in the points of interest.The proposed approach can be applied to simulation of an arbitrary system described by evolutionary partial differential equations.