  Computation of correlated ionic transport properties from molecular dynamics
in the Green-Kubo formalism is expensive as one cannot rely on the affordable
mean square displacement approach. We use spectral decomposition of the
short-time ionic displacement covariance to learn a set of diffusion eigenmodes
that encode the correlation structure and form a basis for analyzing the ionic
trajectories. This allows to systematically reduce the uncertainty and
accelerate computations of ionic conductivity in systems with a steady-state
correlation structure. We provide mathematical and numerical proofs of the
method's robustness, and demonstrate it on realistic electrolyte materials.
