  Correlations of an environment are crucial for the dynamics of non-Markovian
quantum systems, which may not be known in advance. In this paper, we propose a
gradient algorithm for identifying the correlations in terms of time-varying
damping rate functions in a time-convolution-less master equation for spin
chains. By measuring time trace observables of the system, the identification
procedure can be formulated as an optimization problem. The gradient algorithm
is designed based on a calculation of the derivative of an objective function
with respect to the damping rate functions, whose effectiveness is shown in a
comparison to a differential approach for a two-qubit spin chain.
