Session: 11-62-01: Machine Learning for Thermal Transport

Paper Number: 112433

112433 - Enhanced Chaotic Transition Prediction Using Hierarchical Clustering for the Lorenz System 

In this research, we propose a novel way of using unsupervised machine learning clustering to improve the accuracy of predicting chaotic transitions in natural convection systems. Previous work has focused on the application of unsupervised machine learning methods to natural convection systems for understanding turbulent convection transitions. We build on the prior work using the Lorenz system to investigate the potential of machine learning models. The Lorenz system was selected due to its relatively simple equations and well-documented chaotic behavior. The Lorenz equations are a dynamic system for natural convection that are represented by a coupled system of ordinary differential equations. Prior work had confirmed that unsupervised machine learning can predict transitions for this system, but the accuracy of predicting transitions could be improved.

Prior research analyzed eight, expert-chosen features focused on descriptive statistics of the spectral density for the raw inputs to a machine learning algorithm. We modified the machine learning methods to cover a larger range of geometry and fluid parameters with high accuracy using only images of time series plots as the input to the algorithm. The images are phase plots consistent with those commonly observed in the Lorenz system’s strange attractors. To account for a larger range of geometry and fluid parameters, we converted high-dimensional time series data to phase plot images. This allowed us to capture intricate details within the data that might be missed using prior approaches. We then use deep neural networks to extract low-dimensional features for clustering, allowing us to identify hidden patterns and structures within the data.

This work builds upon our prior research that used k-means++ clustering to predict behavior in natural convection systems. However, our new approach goes beyond traditional flat clustering methods by using a convolutional neural network and density-based clustering with varying minimum cluster sizes to improve accuracy. The new method has also reduced the bias associated with selecting Rayleigh ratio values, improving the accuracy and reliability of our results. Our approach does not rely on expert selected statistical features either, a significant advantage for adapting the method to other natural convection systems.

The results are visually represented through histograms that show the key transitions in the chaotic system. We confirmed that the density-based cluster is a more efficient and accurate machine learning algorithm for this problem. The method presented in this paper also incorporates additional validation steps to ensure the accuracy and reliability of the results. The new method provides more detailed insights into the chaotic behavior of the Lorenz system, even at high Rayleigh ratios. This has important implications for a range of fields, including natural convection, meteorology, fluid dynamics, and chaos theory.

Presenting Author: Ben Tribelhorn University of Portland

Presenting Author Biography: Dr. Ben Tribelhorn is an Associate Professor of Computer Science at the University of Portland. He teaches courses and conducts research in artificial intelligence (AI), data structures, parallel computing and algorithms.

Authors:

Solmaz Seyed Monir University of Washington Tacoma
Juhua Hu University of Washington Tacoma
Ben Tribelhorn University of Portland
Heather Dillon University of Washington Tacoma