In this talk, we will present a new numerical framework for dispersive equations based on algebraic methods for SPDEs.The main idea of the scheme is to embed the underlying resonance structure into the discretisation at low regularity. Using, a tailored decorated tree formalism, we control the nonlinear frequency interactions in the system up to arbitrary high order. We adapt SPDEs formalism to the context of dispersive PDEs by using a novel class of decorations {which encode the dominant frequencies}. The structure proposed in this paper is new and gives a variant of the Butcher-Connes-Kreimer Hopf algebra on decorated trees. This is a joint work with Katharina Schratz.