Computational Neurobiology Laboratory, The Salk Institute for Biological Studies, 10010 North Torrey Pines Road, La Jolla, California 92037, USA.
CORIA, Rouen Normandie Université, Campus Universitaire du Madrillet, F-76800 Saint-Etienne du Rouvray, France.
Chaos. 2020 Oct;30(10):103113. doi: 10.1063/5.0015533.
Observability can determine which recorded variables of a given system are optimal for discriminating its different states. Quantifying observability requires knowledge of the equations governing the dynamics. These equations are often unknown when experimental data are considered. Consequently, we propose an approach for numerically assessing observability using Delay Differential Analysis (DDA). Given a time series, DDA uses a delay differential equation for approximating the measured data. The lower the least squares error between the predicted and recorded data, the higher the observability. We thus rank the variables of several chaotic systems according to their corresponding least square error to assess observability. The performance of our approach is evaluated by comparison with the ranking provided by the symbolic observability coefficients as well as with two other data-based approaches using reservoir computing and singular value decomposition of the reconstructed space. We investigate the robustness of our approach against noise contamination.
可观测性可以确定给定系统的哪些记录变量对于区分其不同状态是最优的。量化可观测性需要了解支配动力学的方程。当考虑实验数据时，这些方程通常是未知的。因此，我们提出了一种使用时滞微分分析（DDA）来数值评估可观测性的方法。给定一个时间序列，DDA 使用时滞微分方程来近似测量数据。预测数据与记录数据之间的最小二乘误差越低，可观测性越高。因此，我们根据相应的最小二乘误差对几个混沌系统的变量进行排序，以评估可观测性。我们通过与符号可观测性系数提供的排序以及使用储层计算和重构空间奇异值分解的两种其他基于数据的方法进行比较，来评估我们方法的性能。我们研究了我们的方法对噪声污染的鲁棒性。
