Dynamical systems with high intrinsic dimensionality are often characterized
by extreme events having the form of rare transitions several standard
deviations away from the mean. For such systems, order-reduction methods
through projection of the governing equations have limited applicability due to
the large intrinsic dimensionality of the underlying attractor but also the
complexity of the transient events. An alternative approach is data-driven
techniques that aim to quantify the dynamics of specific modes utilizing
data-streams. Several of these approaches have improved performance by
expanding the state representation using delayed coordinates. However, such
strategies are limited in regions of the phase space where there is a small
amount of data available, as is the case for extreme events. In this work, we
develop a blended framework that integrates an imperfect model, obtained from
projecting equations into a subspace that still contains crucial dynamical
information, with data-streams through a recurrent neural network (RNN)
architecture. In particular, we employ the long-short-term memory (LSTM), to
model portions of the dynamics which cannot be accounted by the equations. The
RNN is trained by analyzing the mismatch between the imperfect model and the
data-streams, projected in the reduced-order space. In this way, the
data-driven model improves the imperfect model in regions where data is
available, while for locations where data is sparse the imperfect model still
provides a baseline for the prediction of the system dynamics. We assess the
developed framework on two challenging prototype systems exhibiting extreme
events and show that the blended approach has improved performance compared
with methods that use either data streams or the imperfect model alone. The
improvement is more significant in regions associated with extreme events,
where data is sparse.

本文提出了一种混合框架，它将投影方程得到的不完美模型和基于数据流的递归神经网络 (LSTM) 相结合，在具有极端事件的挑战性系统中表现出更好的性能，特别是在数据稀疏的情况下。

复杂动态系统极端事件的基于数据协助的降阶建模

Data-assisted reduced-order modeling of extreme events in complex  dynamical systems

We present data-driven techniques to augment Bag of Words (BoW) models, which
allow for more robust modeling and recognition of complex long-term activities,
especially when the structure and topology of the activities are not known a
priori. Our approach specifically addresses the limitations of standard BoW
approaches, which fail to represent the underlying temporal and causal
information that is inherent in activity streams. In addition, we also propose
the use of randomly sampled regular expressions to discover and encode patterns
in activities. We demonstrate the effectiveness of our approach in experimental
evaluations where we successfully recognize activities and detect anomalies in
four complex datasets.

本文提供了基于数据驱动技术的 Bag of Words 模型技术来识别复杂长期活动的方法，成功运用于四个数据集中，具有很强的模式识别能力及异常检测能力，并提出使用随机采样正则表达式来发现和编码这些活动中的模式。