DeepAI AI Chat
Log In Sign Up

Data-driven multiscale decompositions for forecasting and model discovery

by   Daniel Dylewsky, et al.
University of Washington

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.


page 1

page 2

page 3

page 4


Dynamic mode decomposition for multiscale nonlinear physics

We present a data-driven method for separating complex, multiscale syste...

SRMD: Sparse Random Mode Decomposition

Signal decomposition and multiscale signal analysis provide many useful ...

Generalized and Multiscale Modal Analysis

This chapter describes modal decompositions in the framework of matrix f...

Kernel Analog Forecasting: Multiscale Test Problems

Data-driven prediction is becoming increasingly widespread as the volume...

Multiscale dictionary of rat locomotion

To effectively connect animal behaviors to activities and patterns in th...