Linear Response and Koopman Modes: Prediction and Criticality - LINK

线性响应和库普曼模式：预测和临界性 - LINK

• 批准号: EP/Y026675/1
• 负责人: Valerio Lucarini
• 金额: $ 10.43万
• 依托单位: University of Leicester
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2024
• 资助国家: 英国
• 起止时间: 2024 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FY026675%2F1
• 关键词: Linear; Response; Koopman; Modes; Prediction

Understanding how complex systems respond to perturbations is crucial for scientific research and real-world applications. Complexity is a fundamental characteristic of various natural, engineered, and social systems, such as ecosystems, economics, social networks, and the climate. Complex systems feature fluctuations occurring over a vast range of spatial and temporal scales. The weather changes erratically on short time scales, and the climate system has evolved by alternating between periods of smooth change with the occurrence of tipping points. Many of us might have read in the news that we are at risk of experiencing within our lifetime the collapse of the Amazon Forest or of the Atlantic meridional overturning circulation. It would be key to find robust relations between the natural fluctuations of a system and its forced response resulting from the presence of forcings. Finding a rigorous link between climate variability and climate change would imply being able to better predict the future state of the Earth system from its history. The data science revolution is transforming how we model complex systems, and it is recognized that theory-based and data-driven methods must be integrated. Both approaches are rapidly advancing and discovering surprising commonalities. While we have access to vast amounts of data, it's important to note that data alone lacks significance without interpretation, as suggested by H. Poincaré. Koopmanism is a theoretical framework that allows to understand how complex systems change in time by studying the properties of a linear operator that describes the evolution of observable. This approach is very powerful and allows for accurate data-driven analysis of a system, by singling out its intrinsic modes of fluctuations. We have recently been able to find a theoretical link between the Koopman representation of the natural variability of a system and the response operators describing its response to perturbations. Constructing accurate response operators for complex system has proved to be challenging both theoretically and computationally. The problem becomes even more difficult when the system is close to critical behaviour, which is associated with the divergence of such operators. The LINK project aims at developing this very promising scientific idea by constructing computationally efficient and accurate response operators using the angle suggested by the Koopmanism on conceptual multiscale climate models describing in a succinct yet meaningful way the coupled evolution of the atmosphere and the ocean. Hence, we will link free and forced fluctuations. Such models feature metastable behaviour, associated with the presence of tipping points. We will then study how the response operators flag the proximity of criticality, hence better understanding the so-called early warning indicators, usually associated with the increase in the system's sensitivity to perturbations and longer memory.LINK's results will be of relevance for the study of complex systems in general and will lead to new tools for studying and understanding the climate crisis using observations and higher complexity models. LINK is structured according to two Workpackages, each containing the activities aimed at the achievement of a specific objectives, detailed in the dedicated form of this application. LINK will involve the PI, a PDRA (John Moroney, presently at Trinity College, Dublin), and two external partners - M.D. Chekroun from the Weizmann Institute (Israel) and N. Zagli from NORDITA (Sweden). The external partners have committed resources and time for supporting this scientific collaboration and will contribute to the mentoring and supervision of the PDRA both remotely throughout the project duration (fortnightly meetings) and in person during the scientific visits that will take place in UK, Sweden, and Israel.

了解复杂的系统对扰动的反应如何对于科学研究和现实世界的应用至关重要。复杂性是各种自然，工程和社会系统的基本特征，例如生态系统，经济学，社交网络和气候。复杂的系统特征波动发生在大量的空间和临时尺度上。天气在短时间尺度上错误地变化，气候系统通过随着倾斜点的出现而改变平稳变化的时期来发展。我们中的许多人可能已经在新闻中读到，我们有可能在亚马逊森林或大西洋子午倾覆流通的一生中体验的风险。找到系统的自然波动与其强迫响应是由强迫的存在引起的，这将是关键。在气候变化和气候变化之间找到严格的联系将意味着能够从其历史上更好地预测地球系统的未来状态。数据科学革命正在改变我们对复杂系统的建模方式，并且人们认识到必须集成基于理论的和数据驱动的方法。两种方法都在迅速发展并发现了惊喜的共同点。虽然我们可以访问大量数据，但要注意，正如H.Poincaré所建议的那样，仅数据就缺乏意义而没有解释。 Koopmanism是一个理论框架，它可以通过研究描述观察进化的线性操作员的特性来了解复杂系统如何在时间上变化。这种方法非常强大，可以通过挑出其内在波动模式来准确地对系统进行准确的数据驱动分析。最近，我们能够找到系统自然变异性的Koopman表示与描述其对扰动的响应的响应算子之间的理论联系。事实证明，复杂系统的准确响应算子在理论和计算上都受到挑战。当系统接近关键行为时，问题就变得更加困难，这与此类操作员的差异相关。该链接项目旨在通过使用Koopmanism在概念多尺度攀岩模型上构建计算高效且准确的响应操作员来发展这一非常有希望的科学思想，这些角度以简洁而有意义的方式描述了大气和海洋的耦合的演变。因此，我们将链接自由和强迫的波动。这样的模型具有亚稳态行为，与临界点的存在有关。然后，我们将研究响应运营商如何标记临界性的接近性，因此更好地理解所谓的预警指标，通常与系统对扰动和更长的内存敏感性的提高有关。Link的结果将与一般的复杂系统的研究相关，并将使用观测和更高复杂性模型进行研究和了解新工具，并了解新的工具。链接是根据两个工作包进行构造的，每个链接包含旨在实现特定目标的活动，并以本应用程序的专用形式详细介绍。 Link将参与PI，PDRA（John Moroney，在都柏林三一学院出席）和两个外部合作伙伴-Weizmann Institute（Israel）的M.D. Chekroun和N. Nordita（瑞典）的N. Zagli。外部合作伙伴已经为支持这项科学合作提供了资源和时间，并将在整个项目期间（每两周一次的会议）以及在英国，瑞典和以色列进行的科学访问中为PDRA的心理和监督做出贡献。