Prediction in projection.
Prediction in projection.
复制标题
投影中的预测。
作者：
Joshua Garland;Elizabeth Bradley
捕捉和使用状态空间动态结构的预测模型可能非常有效。然而，在实践中，人们很少能够获得关于该结构的全部信息，并且很少能够从标量时间序列数据准确地重建动态，例如，通过延迟-坐标嵌入-可能是一个真实的挑战。在本文中，我们展示了采用不完整动态重建的预测模型--即，不一定是真实嵌入的模型可以对动态系统的状态产生令人惊讶的准确预测。特别是，我们证明了一个简单的近邻预测技术的有效性，该技术与低维和高维动力系统的二维时间延迟重建。即使拓扑的正确性可能无法保证像这样的不完整重建，动态结构，他们捕捉允许准确的预测，在许多情况下，甚至比使用传统的嵌入生成的预测更准确。这在实时预测的上下文中可能非常有用，其中产生正确的延迟坐标嵌入所需的人力是禁止的。
Prediction models that capture and use the structure of state-space dynamics can be very effective. In practice, however, one rarely has access to full information about that structure, and accurate reconstruction of the dynamics from scalar time-series data-e.g., via delay-coordinate embedding-can be a real challenge. In this paper, we show that forecast models that employ incomplete reconstructions of the dynamics-i.e., models that are not necessarily true embeddings-can produce surprisingly accurate predictions of the state of a dynamical system. In particular, we demonstrate the effectiveness of a simple near-neighbor forecast technique that works with a two-dimensional time-delay reconstruction of both low- and high-dimensional dynamical systems. Even though correctness of the topology may not be guaranteed for incomplete reconstructions like this, the dynamical structure that they do capture allows for accurate predictions-in many cases, even more accurate than predictions generated using a traditional embedding. This could be very useful in the context of real-time forecasting, where the human effort required to produce a correct delay-coordinate embedding is prohibitive.