  A precise understanding of the influence of a quantum system's environment on
its dynamics, which is at the heart of the theory of open quantum systems, is
crucial for further progress in the development of controllable large-scale
quantum systems. However, existing approaches to account for complex
system-environment interaction in the presence of memory effects are either
based on heuristic and oversimplified principles or give rise to computational
difficulties. In practice, one can leverage on available experimental data and
replace first-principles simulations with a data-driven analysis that is often
much simpler. Inspired by recent advances in data analysis and machine
learning, we propose a data-driven approach to the analysis of the
non-Markovian dynamics of open quantum systems. Our method allows, on the one
hand, capturing the most important characteristics of open quantum systems such
as the effective dimension of the environment and the spectrum of the joint
system-environment quantum dynamics, and, on the other hand, reconstructing a
predictive model of non-Markovian quantum dynamics, and denoising the measured
quantum trajectories. We demonstrate the performance of the proposed approach
with various models of open quantum systems, including a qubit coupled with a
finite environment, a spin-boson model, and the damped Jaynes-Cummings model.
