提升长期时间序列预测性能，通过增强隐状态实现更灵活建模。
Augmented Invertible Koopman Autoencoder for long-term time series forecasting
- 引入非可逆编码器扩展隐空间维度，突破传统可逆模型限制。
- 在卫星图像和长窗口预测任务上均显著优于基准方法。
- 适合需要高精度长期预测的时序建模场景。
受动态模式分解及其众多扩展启发，近年来出现了多种基于神经自编码器的柯尔莫哥洛夫算子（Koopman operator）实现方法。这类方法在建模动力系统方面颇具潜力，既可用于状态演化的长期直接预测，也可作为下游任务的有效嵌入。特别是最近的工作提出了可逆柯尔莫哥洛夫自编码器（IKAE），利用基于耦合层的归一化流模型实现解析可逆编码器，从而精确重建输入状态。我们发现，归一化流所强制保持的维度一致性对IKAE模型构成限制，因此提出在隐状态中引入第二个非可逆编码器网络。由此得到的新模型称为增强型可逆柯尔莫哥洛夫自编码器（AIKAE）。我们在一系列长期时间序列预测实验中验证了AIKAE的有效性，涵盖卫星图像时序数据以及基于大回溯窗口观测的基准任务。
原文摘要 · Abstract (English)
Following the introduction of Dynamic Mode Decomposition and its numerous extensions, many neural autoencoder-based implementations of the Koopman operator have recently been proposed. This class of methods appears to be of interest for modeling dynamical systems, either through direct long-term prediction of the evolution of the state or as a powerful embedding for downstream methods. In particular, a recent line of work has developed invertible Koopman autoencoders (IKAEs), which provide an exact reconstruction of the input state thanks to their analytically invertible encoder, based on coupling layer normalizing flow models. We identify that the conservation of the dimension imposed by the normalizing flows is a limitation for the IKAE models, and thus we propose to augment the latent state with a second, non-invertible encoder network. This results in our new model: the Augmented Invertible Koopman AutoEncoder (AIKAE). We demonstrate the relevance of the AIKAE through a series of long-term time series forecasting experiments, on satellite image time series as well as on a benchmark involving predictions based on a large lookback window of observations.
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