Model-free forecasting of partially observable spatiotemporally chaotic systems

Vikrant Gupta; Larry K B Li; Shiyi Chen; Minping Wan

doi:10.1016/j.neunet.2023.01.013

Model-free forecasting of partially observable spatiotemporally chaotic systems

Neural Netw. 2023 Mar:160:297-305. doi: 10.1016/j.neunet.2023.01.013. Epub 2023 Jan 23.

Authors

Vikrant Gupta¹, Larry K B Li², Shiyi Chen³, Minping Wan⁴

Affiliations

¹ Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, 518055, PR China; Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications, Southern University of Science and Technology, Shenzhen, 518055, PR China.
² Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Hong Kong, China; Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications, Hong Kong University of Science and Technology, Hong Kong, China.
³ Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, 518055, PR China; Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications, Southern University of Science and Technology, Shenzhen, 518055, PR China; Eastern Institute for Advanced Study, Ningbo, 315200, PR China.
⁴ Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, 518055, PR China; Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications, Southern University of Science and Technology, Shenzhen, 518055, PR China; Jiaxing Research Institute, Southern University of Science and Technology, Jiaxing, 314031, PR China. Electronic address: wanmp@sustech.edu.cn.

PMID: 36716509
DOI: 10.1016/j.neunet.2023.01.013

Abstract

Reservoir computing is a powerful tool for forecasting turbulence because its simple architecture has the computational efficiency to handle high-dimensional systems. Its implementation, however, often requires full state-vector measurements and knowledge of the system nonlinearities. We use nonlinear projector functions to expand the system measurements to a high dimensional space and then feed them to a reservoir to obtain forecasts. We demonstrate the application of such reservoir computing networks on spatiotemporally chaotic systems, which model several features of turbulence. We show that using radial basis functions as nonlinear projectors enables complex system nonlinearities to be captured robustly even with only partial observations and without knowing the governing equations. Finally, we show that when measurements are sparse or incomplete and noisy, such that even the governing equations become inaccurate, our networks can still produce reasonably accurate forecasts, thus paving the way towards model-free forecasting of practical turbulent systems.

Keywords: Chaos; Echo-state networks; Machine learning; Reservoir computing; Time-series forecasting; Turbulence.