改进水库观测器，提升非线性系统变量推断精度。
Reservoir observer enhanced with residual calibration and attention mechanism
- 引入残差校准与注意力机制优化水库观测器
- 在典型混沌系统中显著提升最差情况下的推断准确率
- 适合需要高可靠性状态估计的研究者
水库观测器为从可观测变量推断非线性动力系统中未测量变量提供了一种数据驱动方法。尽管以往研究已证明其广泛应用性，但其性能可能因输入变量不同而显著波动，甚至在最坏情况下损害可靠性。为提升推断性能，本文将残差校准模块与注意力机制融入水库观测器设计。残差校准模块利用估计残差信息优化输出，注意力机制则捕捉数据的时间依赖性以增强水库内部动态表征。在典型混沌系统上的实验表明，该方法显著提升了推断准确性，尤其改善了传统水库观测器在最差情况下的表现。同时，通过引入转移熵概念，解释了输入依赖性导致的观测偏差及其改进机制的有效性。
原文摘要 · Abstract (English)
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.
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