  In this work, we combine an established method for open quantum systems --
the time evolving density matrix using orthogonal polynomials algorithm
(TEDOPA) -- with the transfer tensors formalism (TTM), a new tool for the
analysis, compression and propagation of non-Markovian processes. This enables
the investigation of previously inaccessible long-time dynamics, such as those
ensuing from low temperature regimes with arbitrary, possibly highly
structured, spectral densities. We briefly introduce both methods, followed by
a benchmark to prove viability and combination synergies. Subsequently we
illustrate the capabilities of this approach at the hand of specific examples
and conclude our analysis by highlighting possible further applications of our
method.
