Reservoir observer enhanced with residual calibration and attention mechanism

arXiv cs.LG / 4/13/2026

💬 OpinionIdeas & Deep AnalysisModels & Research

共有:

Key Points

The paper proposes an enhanced reservoir observer for nonlinear dynamical systems that performs inference of unmeasured variables from observed signals.
It improves robustness by adding a residual calibration module that uses estimation residuals to refine the observer output, and an attention mechanism that captures temporal dependencies in the data.
Experiments on chaotic systems show substantial accuracy gains, with the biggest improvements occurring in worst-case scenarios where traditional reservoir observers can fail.
The authors use transfer entropy concepts to explain why performance discrepancies depend on the choice of input variables and why the new design is more effective.

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.