Dimensional reduction of complex systems has been a subject of intense research in recent years. However, the construction of a reduced model is not the final step. The reduced model can be used for different tasks. In this talk I will present a simple mesh refinement algorithm which utilizes a reduced model and allows to detect singularities of time-dependent PDEs. The algorithm is inspired by renormalization constructions in the theory of phase transitions. Results for the inviscid Burgers, critical and supercritical nonlinear Schrodinger equations will be provided.