Inference and forecast problems of the nonlinear dynamical system have arisen in a variety of contexts. Reservoir computing and deep sequential models, on the one hand, have demonstrated efficient, robust, and superior performance in modeling simple and chaotic dynamical systems. However, their innate deterministic feature has partially detracted their robustness to noisy system, and their inability to offer uncertainty measurement has also been an insufficiency of the framework. On the other hand, the traditional state-space model framework is robust to noise. It also carries measured uncertainty, forming a just-right complement to the reservoir computing and deep sequential model framework. We propose the unscented reservoir smoother, a model that unifies both deep sequential and state-space models to achieve both frameworks' superiorities. Evaluated in the option pricing setting on top of noisy datasets, URS strikes highly competitive forecasting accuracy, especially those of longer-term, and uncertainty measurement. Further extensions and implications on URS are also discussed to generalize a full integration of both frameworks.

翻译：非线性动力系统的推断与预测问题已在多种情境中出现。一方面，储层计算与深度序列模型在建模简单及混沌动力系统时展现出高效、稳健且卓越的性能。然而，其固有的确定性特征在一定程度上削弱了其对含噪声系统的鲁棒性，且无法提供不确定性度量也成为该框架的不足。另一方面，传统状态空间模型框架对噪声具有鲁棒性，并能提供可量化的不确定性，恰好弥补了储层计算与深度序列模型框架的缺陷。本文提出无迹储层平滑器，该模型统一了深度序列模型与状态空间模型，以兼具两种框架的优势。通过在含噪声数据集上的期权定价场景进行评估，URS在预测精度（尤其是长期预测）和不确定性度量方面均展现出高度竞争力。文中还讨论了URS的进一步扩展与应用前景，以推动两种框架的全面融合。