Predicting extreme events and anomalous features using a statistical dynamical model and machine learning

Computational and Applied Mathematics Colloquium

Meeting Details

For more information about this meeting, contact Kristin Berrigan, John Harlim, Jinchao Xu.

Speaker: Di Qi, Courant Institute, New York University

Abstract: Understanding and predicting extreme events and their anomalous statistics are a grand challenge in complex natural systems. Recent controlled laboratory experiments in weakly turbulent shallow water with abrupt depth change exhibit a remarkable transition from nearly Gaussian statistics to extreme anomalous statistics with large positive skewness of the surface height. We develop a statisticaldynamical model to explain and quantitatively predict the anomalous statistical behavior. Incoming and outgoing waves are modeled by the truncated Korteweg–de Vries equations statistically matched at the depth change. The statistical matching of the knownnearly Gaussian incoming Gibbs state completely determines the predicted anomalous outgoing Gibbs state and successfully captures key features of the experiment. A deep learning strategy is proposed next to predict the extreme events that appear in the tKdVmodel. The neural network is trained using data only from the near-Gaussian regime without the occurrence of large extreme values. The optimized network demonstrates uniformly high skill in successfully capturing the solution structures in a wide variety ofstatistical regimes, including the highly skewed extreme events.

Room Reservation Information

Room Number: 114 McAllister

Date: 01/27/2020

Time: 12:20pm - 1:30pm