Sparse-coded Time-delay Graph DMD for Prediction of River Water Level Distribution

This paper proposes a method for predicting river water level distribution using time-delay dynamic mode decomposition (tdDMD) and sparse modeling with graph filter banks (GFB). As a previous work, sparse-coded dynamic mode decomposition on graph (SC-DMD-G) was proposed with dynamic mode decomposition (DMD) to derive data-driven time-evolution equations for water level changes on a graph and to predict river water level distributions at multiple locations. However, the prediction performance of SC-DMD-G for nonlinear dynamical systems is not sufficient to represent nonlinear and complex river water levels. Therefore, this work aims to derive a data-driven time-evolving equation that exceeds the performance of SC-DMD-G in predicting river water level distribution. The proposed method can model nonlinear dynamical systems with high accuracy by introducing tdDMD, which enables linear representation of nonlinear dynamics. In order to verify the significance of the proposed method, water level observation data are collected from the Internet by web scraping and river water level distribution prediction is performed for a period of no rainfall on web scraping data. The performance evaluation results show that the proposed method is superior to the tdDMD and the SC-DMD-G.