EAGER-DynamicData: Collaborative Research: Data-driven morphing of parsimonious models for the description of transient dynamics in complex systems

EAGER-DynamicData：协作研究：数据驱动的简约模型变形，用于描述复杂系统中的瞬态动力学

• 批准号: 1462241
• 负责人: Yannis Kevrekidis
• 金额: $ 7.5万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-09-15 至 2017-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1462241&HistoricalAwards=false
• 关键词: EAGER; DynamicData; Collaborative; Research; Data

Predicting and quantifying the behavior of complex systems in engineering and science is a topic of critical importance for many areas such as design, optimization, and safety. Even more critical is the forecast of extreme responses of these systems. Rare responses that can lead to catastrophic events manifest themselves in a wide range of systems such as geophysical phenomena, power and communication networks, and epileptic incidents in brain activity, just to mention a few. In all of these cases, accurate predictions are hampered by the fact that the exact dynamics of the system in nature is often poorly understood. This poor understanding is due to the large number of essentially coupled mechanisms that operate at different temporal and spatial scales. Although it is not always essential to predict the system with high accuracy over all these different levels, it is important to understand and model the effect of the unresolved mechanisms to the degrees of freedom we want to predict. This requires a reliable knowledge of the descriptive laws for these mechanisms as well as their coupling to the degrees-of-freedom of interest and this is clearly not always (well) done. This incomplete modeling of the dynamics leads to inevitable model error that is essential to be taken into account for reliable predictions. An obvious way that this can be done is by the utilization of available and dynamically incoming data. The goal of this work is the development of methods and algorithms to extend the capability for data-driven morphing (that is, data-driven adaptation) of parsimonious models. These will be able to adequately capture the instantaneously most significant dynamics of the system and utilize them to inexpensively perform informative prediction and uncertainty quantification. Such a development will be of critical importance for many fields where the modeling and predictive capacity is limited by the inadequate understanding of the underlying physical mechanisms.The aim of this proposal is to link machine learning with model reduction in a data-stream-driven environment, in order to formulate fundamentally novel methods for the probabilistic forecast of complex stochastic systems. Of particular interest is the quantification and prediction of extreme responses, by relying exclusively on the utilization of available data and with the minimum use of equations (or high fidelity solvers), if these are available. The effort is driven by the presence of serious obstacles associated with the prediction of such features in complex dynamical systems: non-negligible model error in the descriptive laws (if these are available), prohibitive cost for real time computations, sparse data or data with non-negligible error, and transient dynamics. These difficulties are manifest at a time when there is a great need for understanding and prediction of extreme responses in contexts such as climate dynamics, nonlinear waves, and networks of high dimensionality. The aim is to address several of theses challenges by constructing new stochastic prediction methods that will extend the existing state-of-the-art for data-driven modeling and prediction through the implementation (and appropriate extension) of machine learning / data mining techniques and the combination with stochastic order reduction and uncertainty quantification methods that dynamically adapt the reduced order subspace according to the dynamics. These efforts will be guided by a proof-of-concept application involving prediction of extreme, localized events in nonlinear waves. Adaptive reduced order models driven by data will be a key element for the inference of critical dynamical properties, which are otherwise "buried" in the complex responses. By linking machine learning techniques to adaptive reduced order models our research will catalyze new domains of numerical/mathematical analysis and it will extend the reach of more conventional mathematics-assisted modeling beyond some of its current limits.

预测和量化工程和科学中复杂系统的行为对于设计、优化和安全等许多领域至关重要。更重要的是对这些系统的极端响应的预测。可能导致灾难性事件的罕见反应表现在广泛的系统中，例如地球物理现象、电力和通信网络以及大脑活动中的癫痫事件，仅举几例。在所有这些情况下，准确的预测都受到人们对自然界系统的精确动力学知之甚少的事实的阻碍。这种理解不足是由于大量在不同时间和空间尺度上运行的本质上耦合的机制造成的。尽管在所有这些不同级别上高精度地预测系统并不总是必要的，但了解和建模未解决的机制对我们想要预测的自由度的影响非常重要。这需要对这些机制的描述定律以及它们与感兴趣的自由度的耦合有可靠的了解，但这显然并不总是（很好）完成。这种不完整的动力学建模会导致不可避免的模型误差，为了可靠的预测必须考虑到这一点。实现此目的的一个明显方法是利用可用的动态传入数据。这项工作的目标是开发方法和算法来扩展简约模型的数据驱动变形（即数据驱动适应）的能力。这些将能够充分捕获系统的瞬时最重要的动态，并利用它们以低成本执行信息预测和不确定性量化。这样的发展对于许多领域来说至关重要，这些领域的建模和预测能力因对底层物理机制的理解不足而受到限制。该提案的目的是将机器学习与数据流驱动的环境中的模型简化联系起来，以便为复杂随机系统的概率预测制定根本性的新颖方法。特别令人感兴趣的是极端响应的量化和预测，完全依赖于可用数据的利用，并尽可能少地使用方程（或高保真解算器）（如果有的话）。这项工作是由于与复杂动力系统中的此类特征的预测相关的严重障碍的存在而推动的：描述性定律中不可忽略的模型错误（如果有的话）、实时计算的成本高昂、数据稀疏或数据稀疏不可忽略的误差和瞬态动态。当非常需要理解和预测气候动力学、非线性波和高维网络等背景下的极端响应时，这些困难就显现出来了。目的是通过构建新的随机预测方法来解决其中的几个挑战，该方法将通过机器学习/数据挖掘技术的实现（和适当的扩展）来扩展现有的最先进的数据驱动建模和预测结合随机降阶和不确定性量化方法，根据动态动态调整降阶子空间。这些工作将以概念验证应用为指导，涉及非线性波中极端局部事件的预测。由数据驱动的自适应降阶模型将成为推断关键动态特性的关键要素，否则这些特性将被“埋藏”在复杂的响应中。通过将机器学习技术与自适应降阶模型联系起来，我们的研究将促进数值/数学分析的新领域，并将扩展更传统的数学辅助建模的范围，超越其当前的一些限制。