Lattice Correlation Functions from Differential Equations

We discuss how methods developed in the context of perturbation theory can be applied to the computation of lattice correlation functions, in particular in the non perturbative regime. The techniques we consider are integration-by-parts identities (supplemented with symmetry relations) and the method of differential equations, cast in the framework of twisted co-homology. We report on calculations of correlation functions for a scalar $\lambda {\phi }^4$ theory and lattices of small size, both in Euclidean and Minkowskian signature.