  Synchrophasor data provide unprecedented opportunities for inferring power
system dynamics, such as estimating voltage angles, frequencies, and
accelerations along with power injection at all buses. Aligned to this goal,
this work puts forth a novel framework for learning dynamics after small-signal
disturbances by leveraging Gaussian processes (GPs). We extend results on
learning of a linear time-invariant system using GPs to the multi-input
multi-output setup. This is accomplished by decomposing power system swing
dynamics into a set of single-input single-output linear systems with narrow
frequency pass bands. The proposed learning technique captures time derivatives
in continuous time, accommodates data streams sampled at different rates, and
can cope with missing data and heterogeneous levels of accuracy. While Kalman
filter-based approaches require knowing all system inputs, the proposed
framework handles readings of system inputs, outputs, their derivatives, and
combinations thereof collected from an arbitrary subset of buses. Relying on
minimal system information, it further provides uncertainty quantification in
addition to point estimates of system dynamics. Numerical tests verify that
this technique can infer dynamics at non-metered buses, impute and predict
synchrophasors, and locate faults under linear and non-linear system models
under ambient and fault disturbances.
