Physics-based multiple time-series univariate forecasting

Abstract

The Koopman operator theory provides a recipe for data-driven analysis of dynamical systems. The forecasting problem addresses the future value estimation of an observation from its recent past. One common modeling approach is producing forecasts via modeling the data-generating process, where observations are a function of the state variables of the data-generating process. One major challenge to this is the lack of knowledge of the data-generating process. Delay embedding is a common approach in dynamical system analysis to approximate the state-space manifold from a few state value measurements. In this work, we propose a deep learning framework that employs delay embedding, and Koopman operator theory in the context of univariate forecasting to produce a long-term stable forecast. In this work, we empirically show the correctness of the proposed framework. Our study shows the proposed model can generalize across data-set and is capable of producing a stable long-range forecast.