Information Theory and Stochastics for Multiscale Nonlinear Systems

Dear Colleagues,

Complex multiscale nonlinear stochastic dynamical systems are ubiquitous complex systems in geoscience, engineering, neural and material sciences. They are a grand challenge in contemporary science and engineering. Key issues are their basic mathematical structural properties and qualitative features, their statistical prediction, uncertainty quantification (UQ) and sensitivity, their data assimilation (also known as state estimation or filtering), and coping with the inevitable model errors that arise in approximating such complex systems. These model errors arise through both the curse of small ensemble size for large systems and the lack of physical understanding. Effective reduced nonlinear stochastic models in recent years often blended ideas from information theory, Bayesian statistics, and statistical physics in an emerging paradigm for these grand challenges, including extreme events prediction. In addition to multiscale nonlinear stochastic differential equations, multiscale Markov jump process and Markov chains are also important in applications using this paradigm.

This Special Issue focuses on original and new results concerning information theory, stochastic modeling and complex multiscale nonlinear systems in the paradigm as described above. Contributions for this Special Issue can involve one or several disciplines including mathematics, Bayesian statistics, statistical physics and applications.

Prof. Andrew J. Majda
Dr. Nan Chen
Prof. Markos A. Katsoulakis
Guest Editors

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