SPECIAL MATHEMATICS COLLOQUIUM
Speaker: Andrew Majda
Abstract. Complex Turbulent Systems such as those in climate science and engineering turbulence are a grand challenge for prediction, state estimation, and uncertainty quantification (UQ). Such turbulent dynamical systems have an erroneous phase space with a large dimension of instability and crucial extreme events with major societal impact. Monte Carlo statistical predictions for complex turbulent dynamical systems are hampered by severe model error due to the curse of small ensemble size with the overwhelming expense of the forecast model and also due to lack of physical understanding. This lecture surveys recent strategies for prediction, state estimation, and UQ for such complex systems and illustrates them on prototype examples. The novel methods include physics constrained nonlinear regression strategies for low order models, calibration strategies for imperfect models combining information theory and statistical response theory, and novel state estimation algorithms. The talk uses many concrete examples to illustrate these phenomena.