Inference of Unknown Dynamical Components Using Next Generation Reservoir Computing: From Chaotic Systems to Climate Data

Abstract

We investigate next generation reservoir computing (NGRC) as a data-driven approach for inferring unseen components of dynamical systems. We compare NGRC with traditional reservoir computing (RC) using the Lorenz and R\"ossler system, where two unknown components are inferred from one given component. For both systems, NGRC achieves accurate results while requiring fewer training data and less computational time than RC. We identified an inverse proportional behavior between the number of time-delayed steps needed for NGRC and the temporal resolution, indicating that the physical time span covered by the delay interval is an important factor in determining the required number of delayed steps. Finally, we apply NGRC to the observational climate data of ENSO (El Ni\~no--Southern Oscillation) and infer one observable from the remaining variables. Despite the noise and complexity of the real-world data, the NGRC shows promising results. Our findings demonstrate the potential of NGRC for efficient inference of unseen components in both controlled dynamical systems and real-world data.