Applying Dynamic Mode Decomposition to Interconnected Systems for Forecasting and System Identification

Abstract

Dynamic Mode Decomposition (DMD) describes a family of dynamical systems analysis approaches that approximate complex, likely non-linear behaviors with a low-rank linear operator. DMD has traditionally been used in a systems-identification context and was originally developed as a method of modeling fluid flows using the Koopman Operator. In contrast to these original applications, this work explores DMD's ability to produce high-fidelity forecasts using small training sets in an effort to flexibly model two complex, real-world systems. In particular, a novel, iterative implementation of DMD is tested and validated on 18 years of trading price data for constituent companies of the S\&P 500 and on 2 years of per-capita COVID-19 case counts throughout the continental US. The novel combination of DMD with blocked time-series cross-validation described in this work was found to consistently produce forecasts with an average MAPE of approximately 0.1 (in the case of the financial model) and RMSE of approximately 0.2 cases per 1000 citizens (for the COVID-19 model). In addition to reliably predicting the complex behaviors characteristic of real-world systems, this approach was leveraged to identify robust, distinct dynamical trends and construct networks which provided insights into central system elements. This work has illustrated the utility of applying DMD in an iterative approach facilitates forecasting accuracy across a variety of systems without compromising its ability to uncover fundamental characteristics of these underlying systems.