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.

了解复杂系统如何响应扰动对于科学研究和实际应用至关重要。复杂性是各种自然、工程和社会系统的基本特征，如生态系统、经济、社交网络和气候。复杂系统的特点是波动发生在广阔的空间和时间尺度上。天气在短时间尺度上变化不定，气候系统在平稳变化时期与临界点之间交替演变。我们中的许多人可能在新闻中读到过，我们有可能在有生之年经历亚马逊森林的崩溃或大西洋赤道翻转环流。关键是要找到系统的自然波动与强迫存在导致的强迫响应之间的稳健关系。找到气候多变性和气候变化之间的严格联系意味着能够更好地从地球系统的历史中预测其未来状态。数据科学革命正在改变我们对复杂系统建模的方式，人们认识到必须将基于理论的方法和数据驱动的方法相结合。这两种方法都在迅速发展，并发现了令人惊讶的共同点。虽然我们可以获得大量的数据，但重要的是要注意，如H.庞加莱库普曼主义是一个理论框架，它允许通过研究描述可观测演化的线性算子的性质来理解复杂系统如何随时间变化。这种方法非常强大，可以通过挑选出其内在的波动模式来对系统进行准确的数据驱动分析。我们最近已经能够找到一个理论之间的联系库普曼表示的自然变化的系统和响应运营商描述其响应扰动。为复杂系统构造精确的响应算子在理论和计算上都具有挑战性。当系统接近临界行为时，问题变得更加困难，这与这些算子的发散有关。LINK项目的目的是发展这一非常有前途的科学思想，利用Koopmanism提出的概念性多尺度气候模式的角度，以简洁而有意义的方式描述大气和海洋的耦合演变，构建计算效率高、准确的响应算子。因此，我们将自由波动和强迫波动联系起来。这种模型的特点是亚稳态行为，与临界点的存在有关。然后，我们将研究响应操作员如何标记临界状态的接近，从而更好地理解所谓的早期预警指标，通常与系统对扰动的敏感性增加和更长的记忆有关。LINK的结果将与一般复杂系统的研究相关，并将导致使用观测和更高复杂性模型研究和理解气候危机的新工具。LINK是根据两个工作包构建的，每个工作包都包含旨在实现特定目标的活动，详细信息见本应用程序的专用表格。LINK将涉及PI，PDRA（John Moroney，目前在都柏林的Trinity学院）和两个外部合作伙伴- M.D.来自以色列魏茨曼研究所的Chekroun和N.来自NORDITA（瑞典）的Zagli。外部合作伙伴已承诺投入资源和时间来支持这一科学合作，并将在整个项目期间（每两周一次的会议）远程指导和监督PDRA，并在英国、瑞典和以色列进行科学访问期间亲自指导和监督PDRA。