Model-free forecasting of partially observable spatiotemporally chaotic systems.

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.