Reservoir observer enhanced with residual calibration and attention mechanism

TL;DR

This paper introduces an improved reservoir observer for nonlinear systems by integrating residual calibration and attention mechanisms, significantly enhancing inference accuracy especially in challenging scenarios.

Contribution

The novel combination of residual calibration and attention mechanisms in reservoir observers improves inference reliability and accuracy for nonlinear dynamical systems.

Findings

Substantial improvement in inference accuracy demonstrated on chaotic systems.

Enhanced performance in worst-case scenarios compared to traditional reservoir observers.

Use of transfer entropy to explain input-dependent observation discrepancies.

Abstract

Reservoir observers provide a data-driven approach to the inference of unmeasured variables from observed ones for nonlinear dynamical systems. While previous studies have demonstrated wide applicability, their performance may vary considerably with different input variables, even compromising reliability in the worst cases. To enhance the performance of inference, we integrate residual calibration and attention mechanism into the reservoir observer design. The residual calibration module leverages information from the estimation residuals to refine the observer output, and the attention mechanism exploits the temporal dependencies of the data to enrich the representation of reservoir internal dynamics. Experiments on typical chaotic systems demonstrate that our method substantially improves inference accuracy, especially for the worst cases resulting from the traditional reservoir observers. We also invoke the notion of transfer entropy to explain the reason for the input-dependent observation discrepancy and the effectiveness of the proposed method.