Extreme learning machine as an observer for chaotic systems

Inferring unmeasured state variables from a limited set of measurements is a fundamental problem in the study of chaotic systems, with broad applications across science and engineering. We propose a data-driven observer based on the extreme learning machine (ELM), a single-hidden-layer feedforward network with randomly assigned input weights and analytically determined output weights. Trained on a short segment of fully measured data, the network can then use the incoming partial measurements to reconstruct the unmeasured variables in a closed-loop fashion. We validate the approach on three representative chaotic systems — the Rössler system, the Lorenz system, and the Chua circuit — where the ELM observer accurately reconstructs the unmeasured variables. We further show that the ELM observer exhibits robustness against noise and transferability across different parameter settings of the same system. Given its model-free nature and algorithmic simplicity, the proposed framework may find broad applications across science and engineering.