Delay embedding-a method for reconstructing dynamical systems by delay coordinates-is widely used to forecast nonlinear time series as a model-free approach. When multivariate time series are observed, several existing frameworks can be applied to yield a single forecast combining multiple forecasts derived from various embeddings. However, the performance of these frameworks is not always satisfactory because they randomly select embeddings or use brute force and do not consider the diversity of the embeddings to combine. Herein, we develop a forecasting framework that overcomes these existing problems. The framework exploits various "suboptimal embeddings" obtained by minimizing the in-sample error via combinatorial optimization. The framework achieves the best results among existing frameworks for sample toy datasets and a real-world flood dataset. We show that the framework is applicable to a wide range of data lengths and dimensions. Therefore, the framework can be applied to various fields such as neuroscience, ecology, finance, fluid dynamics, weather, and disaster prevention.

中文翻译：

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利用次优嵌入预测高维动力学。

延迟嵌入-一种通过延迟坐标重建动力学系统的方法-作为一种无模型方法，被广泛用于预测非线性时间序列。当观察到多元时间序列时，可以使用几种现有框架来产生单个预测，并结合从各种嵌入中得出的多个预测。但是，这些框架的性能并不总是令人满意，因为它们随机选择嵌入或使用蛮力并且不考虑嵌入的多样性来组合。在此，我们开发了一种克服这些现有问题的预测框架。该框架利用通过组合优化使样本内误差最小化而获得的各种“次优嵌入”。该框架在样本玩具数据集和现实洪水数据集的现有框架中取得了最佳结果。我们证明了该框架适用于各种数据长度和维度。因此，该框架可应用于神经科学，生态学，金融，流体动力学，天气和防灾等各个领域。