Stormy sea with offshore platform and statistical distribution curve.

Unlocking the Secrets of Extreme Events: How a Smart Sampling Strategy Can Help

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Avery Sinclair in Tech & Innovation December 2025 • 5 min read.

"Discover how a novel sequential sampling strategy is revolutionizing our ability to predict and understand extreme events in complex dynamical systems, from rogue waves to economic shocks."


Extreme events are rare, high-impact occurrences that defy typical statistical expectations. These events, whether natural disasters, economic crashes, or technological failures, can have catastrophic consequences, making their prediction and understanding crucial. However, due to their rarity and the complexity of the systems in which they occur, accurately predicting extreme events remains a significant challenge.

Traditional methods for estimating the probability of extreme events often require vast amounts of data and extensive computational resources. Direct simulations or repeated experiments, while conceptually straightforward, become impractical when dealing with systems with inherent nonlinearity, broad energy spectra, and high dimensionality. This is because resolving the tails of probability distributions, where extreme events reside, demands an enormous number of samples to achieve statistical significance.

A new research paper introduces a sequential sampling strategy that dramatically reduces the amount of data needed to accurately estimate the statistics of extreme events in nonlinear dynamical systems. This innovative approach combines machine learning techniques with statistical inference to intelligently select the most informative data points, leading to rapid convergence and accurate predictions even with limited samples.

The Sequential Sampling Strategy: A Smarter Way to Predict the Unpredictable

Stormy sea with offshore platform and statistical distribution curve.

The core idea behind this sequential sampling strategy is to learn from data in an iterative process. Instead of randomly sampling the system's parameter space, the algorithm strategically chooses the "next-best" data point that will maximally improve the estimate of the probability density function (pdf) for a chosen quantity of interest.

This strategy leverages Gaussian process regression (GPR), a powerful machine learning technique, to perform Bayesian inference on the parameter-to-observation map. In simpler terms, GPR helps to build a surrogate model that approximates the relationship between the system's inputs (parameters) and its outputs (the quantity of interest). This surrogate model is much cheaper to evaluate than the actual system, allowing the algorithm to efficiently explore the parameter space.

Here's a breakdown of the key steps involved:
  • Initial Dataset: Start with a small initial dataset of design points (parameter values).
  • Gaussian Process Regression: Use GPR to build a surrogate model that approximates the relationship between the parameters and the quantity of interest.
  • PDF Estimation: Estimate the probability density function (pdf) of the quantity of interest using the surrogate model, along with uncertainty bounds.
  • Next-Best Point Selection: Determine the next-best data point by optimizing a metric that minimizes the uncertainty between the estimated bounds of the pdf prediction. This optimization focuses on the tails of the pdf, where extreme events reside.
  • Iteration: Evaluate the system at the selected data point, add it to the dataset, and repeat steps 2-4 until the desired level of accuracy is achieved.
A key advantage of this method is its computational efficiency. The optimization process for selecting the next-best point relies solely on information from the inferred map, avoiding costly simulations or experiments. Furthermore, the special form of the optimization metric emphasizes the tails of the pdf, ensuring that rare events are adequately captured.

Real-World Applications and Future Directions

The research paper demonstrates the effectiveness of this sequential sampling strategy by applying it to a very high-dimensional system: an offshore platform subjected to 3D irregular waves. The results show that the method can accurately determine the extreme event statistics using only a limited number of samples, showcasing its potential for real-world applications where data acquisition is expensive or time-consuming. This approach paves the way for better risk assessment and design in various fields, from engineering and finance to climate science and medicine. By providing a more efficient and accurate way to predict extreme events, this research empowers us to build more resilient systems and mitigate the impact of unforeseen crises.

About this Article -

This article was crafted using a human-AI hybrid and collaborative approach. AI assisted our team with initial drafting, research insights, identifying key questions, and image generation. Our human editors guided topic selection, defined the angle, structured the content, ensured factual accuracy and relevance, refined the tone, and conducted thorough editing to deliver helpful, high-quality information.See our About page for more information.

Everything You Need To Know

1

What is the core innovation of the sequential sampling strategy for predicting extreme events?

The core innovation lies in its iterative approach to learning from data. Instead of random sampling, the algorithm strategically selects the "next-best" data point. This maximizes the improvement in estimating the probability density function (pdf) for a chosen quantity of interest. This targeted approach, using Gaussian process regression (GPR), ensures accurate predictions even with a limited number of samples, dramatically reducing the data requirements compared to traditional methods.

2

How does Gaussian Process Regression (GPR) contribute to the sequential sampling strategy?

GPR plays a crucial role in the sequential sampling strategy by constructing a surrogate model. This model approximates the relationship between the system's parameters (inputs) and the quantity of interest (outputs). This surrogate model is much more computationally efficient to evaluate than the actual system, allowing for efficient exploration of the parameter space. GPR facilitates Bayesian inference on the parameter-to-observation map, enabling the algorithm to estimate the pdf and guide the selection of the most informative data points, focusing on the tails where extreme events reside.

3

What are the key steps involved in the sequential sampling strategy?

The sequential sampling strategy involves these key steps: 1. **Initial Dataset:** Begin with a small initial dataset of design points (parameter values). 2. **Gaussian Process Regression:** Employ GPR to build a surrogate model mapping parameters to the quantity of interest. 3. **PDF Estimation:** Estimate the probability density function (pdf) using the surrogate model, including uncertainty bounds. 4. **Next-Best Point Selection:** Determine the next-best data point by optimizing a metric that minimizes uncertainty, focusing on the pdf's tails. 5. **Iteration:** Evaluate the system at the selected data point, add it to the dataset, and repeat steps 2-4 until the desired accuracy is achieved.

4

Why is the sequential sampling strategy more computationally efficient than traditional methods?

The sequential sampling strategy's computational efficiency stems from two key factors. First, the optimization process for selecting the next-best data point relies solely on information from the inferred map, avoiding costly simulations or experiments. Second, the optimization metric is specifically designed to emphasize the tails of the probability density function (pdf). This ensures adequate capture of rare events, which is where traditional methods struggle, requiring extensive data and computation, making it faster and less resource-intensive than traditional techniques.

5

What are the real-world applications and potential benefits of the sequential sampling strategy?

The sequential sampling strategy has the potential to transform risk assessment and design in various fields. For example, it was applied to an offshore platform subjected to 3D irregular waves. The method accurately determined extreme event statistics using a limited number of samples, highlighting its practicality. Its benefits include more accurate and efficient prediction of extreme events, which can lead to improved risk mitigation in engineering, finance, climate science, and medicine. By efficiently handling the complexities of nonlinear dynamical systems, this approach promotes building more resilient systems and reducing the impact of unforeseen crises.

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