  We present a data-driven method for separating complex, multiscale systems
into their constituent time-scale components using a recursive implementation
of dynamic mode decomposition (DMD). Local linear models are built from
windowed subsets of the data, and dominant time scales are discovered using
spectral clustering on their eigenvalues. This approach produces time series
data for each identified component, which sum to a faithful reconstruction of
the input signal. It differs from most other methods in the field of
multiresolution analysis (MRA) in that it 1) accounts for spatial and temporal
coherencies simultaneously, making it more robust to scale overlap between
components, and 2) yields a closed-form expression for local dynamics at each
scale, which can be used for short-term prediction of any or all components.
Our technique is an extension of multi-resolution dynamic mode decomposition
(mrDMD), generalized to treat a broader variety of multiscale systems and more
faithfully reconstruct their isolated components. In this paper we present an
overview of our algorithm and its results on two example physical systems, and
briefly discuss some advantages and potential forecasting applications for the
technique.
