# A sequential sampling strategy for extreme event statistics in nonlinear dynamical systems

arXiv: https://arxiv.org/abs/1804.07240 · HTML: https://mlsanity.com/paper/1804.07240/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Apr 2018.

## Built on by (most cited first, 14 of 14)

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- [Measuring the rogue wave pattern triggered from Gaussian perturbations by deep learning](https://mlsanity.com/paper/2109.08909/) (2021)
- [A generalized likelihood-weighted optimal sampling algorithm for rare-event probability quantification](https://mlsanity.com/paper/2310.14457/) (2023)
- [Towards provable probabilistic safety for scalable embodied AI systems](https://mlsanity.com/paper/2506.05171/) (2025)
- [How Low Can You Go? Active Learning for Sparse Model Discovery in the Ultra-Low-Data Limit](https://mlsanity.com/paper/2606.12182/) (2026)

## Abstract (arXiv)

We develop a method for the evaluation of extreme event statistics associated with nonlinear dynamical systems, using 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 utilizes 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 utilizing 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 utilizes 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, i.e. order O(10). 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 three-dimensional irregular waves. It is demonstrated that the developed approach can accurately determine the extreme event statistics using limited number of samples.