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Details of Grant 

EPSRC Reference: EP/Y026675/1
Title: Linear Response and Koopman Modes: Prediction and Criticality - LINK
Principal Investigator: Lucarini, Professor V
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Nordic Inst for Theoretic Phys NORDITA Weizmann Institute of Science
Department: Computing & Mathematical Sciences
Organisation: University of Leicester
Scheme: Standard Research - NR1
Starts: 01 February 2024 Ends: 31 January 2025 Value (£): 81,880
EPSRC Research Topic Classifications:
Non-linear Systems Mathematics Numerical Analysis
Statistics & Appl. Probability
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
07 Sep 2023 EPSRC Mathematical Sciences Small Grants Panel September 2023 Announced
Summary on Grant Application Form
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.

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Organisation Website: http://www.le.ac.uk