标题： 用优化的高维混合储备计算预测二维时空混沌模式 显示英文标题

标题： Predicting two-dimensional spatiotemporal chaotic patterns with optimized high-dimensional hybrid reservoir computing

摘要： 作为一种替代方法，用于预测物理模型不再可靠的各种复杂动力系统，储备计算（RC）已变得流行。 混合方法被视为提高RC预测性能的一个有趣选择。 其理念是结合一个基于知识的模型（KBM）来支持完全数据驱动的RC预测。 RC有三种类型的混合方式，即全混合（FH）、输入混合（IH）和输出混合（OH），其中显示后者在低维混沌系统的预测准确性与鲁棒性方面更优。 在此，我们将该形式扩展到二维空间时间模式的预测。 为了克服这种极高维情况下的维度灾难，我们采用了局部状态假设，仅利用少数局部相邻的时间序列进行基于RC的预测。 使用描述心脏组织中混沌电波传播的Barkley模型的模拟数据，我们概述了高维混合RC的形式，并评估了不同混合方案的性能。 我们发现所有三种方法（FH、IH和OH）都比仅使用储备更好，当模型非常不准确时，改进较小。 对于小模型误差和小储备，FH和OH表现几乎同样好，并优于IH。 鉴于OH所需的CPU较少，尤其是其可解释性更好，因此应优先选择OH。 对于大储备，OH的性能会低于FH和IH。 一般来说，对于特定应用，可能建议测试三种配置，并选择在预测性能和CPU需求之间达到最佳平衡的配置。 显示英文摘要

摘要： As an alternative approach for predicting complex dynamical systems where physics-based models are no longer reliable, reservoir computing (RC) has gained popularity. The hybrid approach is considered an interesting option for improving the prediction performance of RC. The idea is to combine a knowledge-based model (KBM) to support the fully data-driven RC prediction. There are three types of hybridization for RC, namely full hybrid (FH), input hybrid (IH) and output hybrid (OH), where it was shown that the latter one is superior in terms of the accuracy and the robustness for the prediction of low-dimensional chaotic systems. Here, we extend the formalism to the prediction of spatiotemporal patterns in two dimensions. To overcome the curse of dimensionality for this very high-dimensional case we employ the local states ansatz, where only a few locally adjacent time series are utilized for the RC-based prediction. Using simulation data from the Barkley model describing chaotic electrical wave propagation in cardiac tissue, we outline the formalism of high-dimensional hybrid RC and assess the performance of the different hybridization schemes. We find that all three methods (FH, IH and OH) perform better than reservoir only, where improvements are small when the model is very inaccurate. For small model errors and small reservoirs FH and OH perform nearly equally well and better than IH. Given the smaller CPU needs for OH and especially the better interpretability of it, OH is to be favored. For large reservoirs the performance of OH drops below that of FH and IH. Generally, it maybe advisable to test the three setups for a given application and select the best suited one that optimizes between the counteracting factors of prediction performance and CPU needs.