Deep Probabilistic Koopman: Long-term time-series forecasting under periodic uncertainties

Abstract

This paper introduces general mathematical techniques for stable long-term forecasts with calibrated uncertainty measures. For most time series models, the difficulty of obtaining accurate probabilistic future time step predictions increases with the prediction horizon. We propose a surprisingly simple class of models that characterizes time-varying distributions and enables reasonably accurate predictions thousands of time steps into the future. This technique, called Deep Probabilistic Koopman (DPK), is based on recent advances in linear Koopman operator theory and does not require time stepping for future time predictions. We demonstrate the long-term forecasting performance of these models on a diversity of domains, including electricity demand forecasting, atmospheric chemistry, and neuroscience. Our domain-agnostic technique outperforms all 177 domain-specific competitors in the most recent Global Energy Forecasting Competition for electricity demand modelling.