Data-assisted reduced-order modeling of extreme events in complex dynamical systems.
Data-assisted reduced-order modeling of extreme events in complex dynamical systems.
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DOI：
10.1371/journal.pone.0197704
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发表时间：
2018
期刊：
影响因子：
3.7
通讯作者：
Sapsis T
中科院分区：
文献类型：
--
作者：
Wan ZY;Vlachas P;Koumoutsakos P;Sapsis T
从雪崩和干旱到海啸和流行病等极端事件的预测取决于对相关的复杂动力系统的制定和分析。这种动力系统的特点是具有高内在维数，极端事件具有与平均值相差几个标准差的罕见转变形式。由于潜在吸引子的大内在维数以及瞬态事件的复杂性，这种系统不适合通过控制方程投影的经典降阶方法。另外，数据驱动技术旨在通过利用数据流和使用延迟坐标扩展降阶模型的维数来量化特定的关键模式的动态。反过来，这些方法在具有稀疏数据的相空间区域有很大的局限性，这是极端事件的情况。在这项工作中，我们开发了一个新的混合框架，补充了一个不完美的降阶模型，通过循环神经网络（RNN）架构集成了数据流。降阶模型的形式是将方程投影到低维子空间中，该子空间仍然包含系统的重要动态信息，并通过长短期记忆（LSTM）正则化进行扩展。LSTM-RNN通过分析不完美模型与数据流之间的不匹配来训练，并将其投射到降阶空间中。数据驱动模型在数据可用的区域辅助不完美模型，而对于数据稀疏的位置，不完美模型仍然为系统状态的预测提供基线。我们在两个具有挑战性的展示极端事件的原型系统上评估开发的框架。我们表明，与单独使用数据流或不完美模型的方法相比，混合方法提高了性能。值得注意的是，在数据稀少的与极端事件相关的地区，这种改善更为显著。
The prediction of extreme events, from avalanches and droughts to tsunamis and epidemics, depends on the formulation and analysis of relevant, complex dynamical systems. Such dynamical systems are characterized by high intrinsic dimensionality with extreme events having the form of rare transitions that are several standard deviations away from the mean. Such systems are not amenable to classical order-reduction methods through projection of the governing equations due to the large intrinsic dimensionality of the underlying attractor as well as the complexity of the transient events. Alternatively, data-driven techniques aim to quantify the dynamics of specific, critical modes by utilizing data-streams and by expanding the dimensionality of the reduced-order model using delayed coordinates. In turn, these methods have major limitations in regions of the phase space with sparse data, which is the case for extreme events. In this work, we develop a novel hybrid framework that complements an imperfect reduced order model, with data-streams that are integrated though a recurrent neural network (RNN) architecture. The reduced order model has the form of projected equations into a low-dimensional subspace that still contains important dynamical information about the system and it is expanded by a long short-term memory (LSTM) regularization. The LSTM-RNN is trained by analyzing the mismatch between the imperfect model and the data-streams, projected to the reduced-order space. The data-driven model assists 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 state. We assess the developed framework on two challenging prototype systems exhibiting extreme events. We show that the blended approach has improved performance compared with methods that use either data streams or the imperfect model alone. Notably the improvement is more significant in regions associated with extreme events, where data is sparse.
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影响因子：
8.6
作者：
FARMER, JD;SIDOROWICH, JJ
通讯作者：
SIDOROWICH, JJ
影响因子：
--
作者：
Lagaris, IE;Likas, A;Fotiadis, DI
通讯作者：
Fotiadis, DI
影响因子：
2.4
作者：
Berry, Tyrus;Giannakis, Dimitrios;Harlim, John
通讯作者：
Harlim, John
影响因子：
8.6
作者：
Kim, E.;Li, F.;Kevrekidis, P. G.
通讯作者：
Kevrekidis, P. G.
DOI：
10.1073/pnas.1517384113
发表时间：
2016-04-12
影响因子：
11.1
作者：
Brunton, Steven L.;Proctor, Joshua L.;Kutz, J. Nathan
通讯作者：
Kutz, J. Nathan