A method for unsupervised learning of coherent spatiotemporal patterns in multiscale data

Karl Lapo ¹, Sara M Ichinaga ², J Nathan Kutz ^2,3

⁰Department of Atmospheric and Cryospheric Sciences, University of Innsbruck, Innsbruck 6020, Austria.

Proceedings of the National Academy of Sciences of the United States of America +

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February 14, 2025

View abstract on PubMed

Summary

We developed a new algorithm, multiresolution coherent spatio-temporal scale separation (mrCOSTS), to automatically analyze complex multiscale data. This method successfully identifies hidden patterns in climate, neuroscience, and fluid dynamics.

Area Of Science

Multiscale data analysis
Complex systems science
Scientific data diagnosis

Background

Analyzing multiscale data is challenging due to simultaneous processes across dimensions, scales, and nonstationarity.
Existing methods often require manual intervention, tuning, or specific data period selection.
Unsupervised and principled diagnosis of multiscale data remains a significant obstacle in various scientific fields.

Purpose Of The Study

To present a hierarchical and automated algorithm for diagnosing coherent patterns in multiscale data.
Introduce the multiresolution coherent spatio-temporal scale separation (mrCOSTS) method.
Provide a robust approach for analyzing complex multiscale datasets without requiring training.

Main Methods

mrCOSTS is a variant of dynamic mode decomposition.
It decomposes data into spatial patterns with shared temporal dynamics.
The algorithm leverages the hierarchical nature of multiscale systems for unsupervised analysis.

Main Results

mrCOSTS successfully analyzed complex multiscale datasets from climate (sea surface temperature), neuroscience (neural signals), and fluid dynamics (wind).
The method trivially retrieved complex dynamics previously difficult to resolve.
Hitherto unknown patterns of activity embedded within the dynamics were extracted.

Conclusions

mrCOSTS offers a significant advancement for addressing multiscale data challenges across science and engineering.
The algorithm facilitates a deeper understanding of complex systems by revealing underlying patterns.
This unsupervised method enhances the diagnosis of multiscale phenomena in diverse scientific domains.

Keywords:

complex systems data-driven modeling discovery dynamic mode decomposition multiscale unsupervised learning