Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Model

By Jaideep Pathak, Alexander Wikner, Rebeckah K. Fussell, Sarthak Chandra, Brian R. Hunt, Michelle Girvan, Edward Ott. Chaos, 2018

350 citations recorded by the source corpus.

A model-based 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 widely-used knowledge-based models to be inaccurate. Thus, we here propose a general method that leverages the advantages of these two approaches by combining a knowledge-based 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 low-dimensional chaotic system, as well as to a high-dimensional 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 machine-learning component or its model-based component alone.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e775751e215e783da6b388fd604e83484a27e5e1

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Citations in the corpus

Backpropagation algorithms and Reservoir Computing in Recurrent Neural Networks for the forecasting of complex spatiotemporal dynamics (2019, methodology): “In this work, a large RC with d h = 9000 nodes is employed for LS calculation in the Kuramoto– Sivashinsky equation with parameter L = 60 and D = 128 grid points as in Pathak, Hunt et al. (2018).”
Neural operators for accelerating scientific simulations and design (2023, neutral): “Previous developments such as sparse representation [7], recurrent neural networks [8], reservoir computing [9] and others have shown promise in modeling dynamical systems.”
Physics-informed machine learning: case studies for weather and climate modelling (2021, methodology): “Pathak et al. [65] and Watson [66] used ML coupled with a dynamical system model for improved accuracy and forecasting horizons of chaotic systems.”
Digital Twin: Values, Challenges and Enablers From a Modeling Perspective (2019, neutral): “[342] J.”