Algebraic deformation for (S)PDEs

We introduce a new algebraic framework based on the deformation of pre-Lie products. This allows us to provide construction objects at play in regularity structures works by Bruned, Hairer and Zambotti (2019) Bruned Schratz (2022) for deriving general scheme dispersive PDEs low regularity. also explains how structure et al. cited above can be viewed as Butcher–Connes–Kreimer extraction-contraction Hopf algebras. start deforming various products via Taylor then we apply Guin–Oudom procedure which gives an associative product whose adjoint compared with known coproducts. work reveals that their central object study (S)PDEs.