Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 115, Issue 44, Pages 11138-11143Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1813263115
Keywords
extreme events; adaptive sampling; sequential experimental design
Categories
Funding
- Office of Naval Research [N00014-15-1-2381]
- Air Force Office of Scientific Research Grant [FA9550-16-1-0231]
- Army Research Office [W911NF-17-1-0306]
- American Bureau of Shipping
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We develop a method for the evaluation of extreme event statistics associated with nonlinear dynamical systems from a small number of samples. From an initial dataset of design points, we formulate a sequential strategy that provides the next-best data point (set of parameters) that when evaluated results in improved estimates of the probability density function (pdf) for a scalar quantity of interest. The approach uses Gaussian process regression to perform Bayesian inference on the parameter-to-observation map describing the quantity of interest. We then approximate the desired pdf along with uncertainty bounds using the posterior distribution of the inferred map. The next-best design point is sequentially determined through an optimization procedure that selects the point in parameter space that maximally reduces uncertainty between the estimated bounds of the pdf prediction. Since the optimization process uses only information from the inferred map, it has minimal computational cost. Moreover, the special form of the metric emphasizes the tails of the pdf. The method is practical for systems where the dimensionality of the parameter space is of moderate size and for problems where each sample is very expensive to obtain. We apply the method to estimate the extreme event statistics for a very high-dimensional system with millions of degrees of freedom: an offshore platform subjected to 3D irregular waves. It is demonstrated that the developed approach can accurately determine the extreme event statistics using a limited number of samples.
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