Bridging Dynamics and Statistics: Transfer Entropy, Nonlinear Interactions and Transient Growth in Spatio-Temporal Extremes

Extreme events such as heat waves and wildfire outbreaks can threaten lives, property, ecosystems, infrastructure, and economic activity. These events often occur quite suddenly, are clustered in space, and arise from complicated interactions among weather, ecosystem, land, and ocean processes. Current forecasting methods can have difficulty detecting when ordinary conditions may rapidly develop into damaging extremes, especially when multiple hidden drivers interact over space and time. This project develops new statistical and deep learning modeling and computational tools to improve understanding and prediction of such events. By linking data-driven forecasting with scientific knowledge about how dynamic systems grow and interact, the work seeks to provide earlier warning of hazards that affect public safety, emergency preparedness, agriculture, energy systems, water resources, and community resilience. The project also advances the national interest by strengthening the mathematical, statistical, machine learning, and artificial intelligence foundations needed to anticipate high-impact risks, producing open-source software for use by other researchers and practitioners, and training students with multidisciplinary expertise spanning statistics, dynamical systems, and artificial intelligence. The resulting methods and tools may also benefit other fields in which rare but extreme events occur, including neuroscience, cardiology, economics, and national security applications involving complex dynamic systems. This project develops a unified framework for modeling and forecasting extremes in spatio-temporal systems by integrating spatio-temporal statistics, extreme value theory, dynamical systems theory, information theory, and neural estimation. The first goal is to characterize transient extremes through efficient statistical proxies for complex nonlinear systems, using linear systems with non-normal transition behavior and heavy-tailed innovation processes. This work develops theory showing how the interaction between transient growth and heavy-tailed disturbances can lead to extremes that are not well represented by standard stationary spatio-temporal dynamic models. The second goal is to identify directed information flow and latent forcing mechanisms that influence both typical behavior and extreme outcomes. The project develops a tail-emphasized spatio-temporal transfer entropy approach, supported by efficient probabilistic density estimation using reservoir computing via echo state networks with heavy-tailed mixture density network output layers. A temporal permutation importance framework is used to identify information gain from potential dynamic drivers of extreme responses. The methods are evaluated through applications to long-lead forecasting of extreme heat waves and wildfire risk. Expected contributions include new theory for transient spatio-temporal extremes, interpretable methods for discovering nonlinear drivers of rare events, and the foundation of a forecasting approach for environmental hazards. The project will produce open-source software, and educational activities that prepare graduate students to work at the intersection of statistics, dynamical systems, information theory, and artificial intelligence. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria. NSF Award ID: 2610253 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Christopher Wikle | Institution: University of Missouri-Columbia, COLUMBIA, MO | Award Amount: $270,000 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2610253 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2610253.html