Hybrid forecasting of chaotic processes: Using machine learning in conjunction with a knowledgebased model
Abstract
A modelbased approach to forecasting chaotic dynamical systems utilizes knowledge of the mechanistic processes governing the dynamics to build an approximate mathematical model of the system. In contrast, machine learning techniques have demonstrated promising results for forecasting chaotic systems purely from past time series measurements of system state variables (training data), without prior knowledge of the system dynamics. The motivation for this paper is the potential of machine learning for filling in the gaps in our underlying mechanistic knowledge that cause widelyused knowledgebased models to be inaccurate. Thus, we here propose a general method that leverages the advantages of these two approaches by combining a knowledgebased model and a machine learning technique to build a hybrid forecasting scheme. Potential applications for such an approach are numerous (e.g., improving weather forecasting). We demonstrate and test the utility of this approach using a particular illustrative version of a machine learning known as reservoir computing, and we apply the resulting hybrid forecaster to a lowdimensional chaotic system, as well as to a highdimensional spatiotemporal chaotic system. These tests yield extremely promising results in that our hybrid technique is able to accurately predict for a much longer period of time than either its machinelearning component or its modelbased component alone.
 Publication:

Chaos
 Pub Date:
 April 2018
 DOI:
 10.1063/1.5028373
 arXiv:
 arXiv:1803.04779
 Bibcode:
 2018Chaos..28d1101P
 Keywords:

 Computer Science  Machine Learning;
 Nonlinear Sciences  Chaotic Dynamics;
 Statistics  Machine Learning
 EPrint:
 doi:10.1063/1.5028373