  We exploit the properties of chain mapping transformations of bosonic
environments to identify a finite collection of modes able to capture the
characteristic features, or fingerprint, of the environment. Moreover we show
that the countable infinity of residual bath modes can be replaced by a
universal Markovian closure, namely a small collection of damped modes
undergoing a Lindblad-type dynamics whose parametrization is independent of the
spectral density under consideration. We show that the Markovian closure
provides a quadratic speed-up with respect to standard chain mapping techniques
and makes the memory requirement independent of the simulation time, while
preserving all the information on the fingerprint modes. We illustrate the
application of the Markovian closure to the computation of linear spectra but
also to non-linear spectral response, a relevant experimentally accessible many
body coherence witness for which efficient numerically exact calculations in
realistic environments are currently lacking.
