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Predictability of bursts of a recurrent nova using topological data analysis and machine learning

Ignacio Morales-Gil

TL;DR

The paper addresses predicting bursts in the recurrent nova RS Ophiuchi from optical lightcurves, tackling non-periodicity by applying topological data analysis (TDA). It builds persistence diagrams from ordinal partition networks of lightcurve segments and featurizes them with multiple representations, then uses tenfold cross-validated supervised classification to predict whether a burst will occur within $1$ year. Persistence landscapes offered the best performance, achieving approximately $0.93$ accuracy on the test set and around $0.96$ recall for pre-burst intervals, indicating strong predictive power and potential for targeted follow-up observations in astronomical surveys. The work demonstrates the practical value of TDA in astronomy, suggesting extensions to regression and other data modalities such as spectra and images, thereby enabling earlier and more reliable transient alerts.

Abstract

RS Oph is a recurrent nova, a kind of cataclismic variable that shows bursts in a period approximately shorter than a century. Persistent homology, a technique from topological data analysis, studies the evolution of topological features of a simplicial complex composed of the data points or an embedding of them, as some distance parameter is varied. For this work I trained a supervised learning model based on several featurizations, namely persistence landscapes, Carlsson coordinates, persistent images, and template functions, of the persistence diagrams of sections of the lightcurve of RS Oph. A tenfold cross validation of the model based on one of the featurizations, persistence landscapes, consistently shows high recalls and accuracies. This method serves the purpose of predicting whether RS Oph is bursting within a year.

Predictability of bursts of a recurrent nova using topological data analysis and machine learning

TL;DR

The paper addresses predicting bursts in the recurrent nova RS Ophiuchi from optical lightcurves, tackling non-periodicity by applying topological data analysis (TDA). It builds persistence diagrams from ordinal partition networks of lightcurve segments and featurizes them with multiple representations, then uses tenfold cross-validated supervised classification to predict whether a burst will occur within year. Persistence landscapes offered the best performance, achieving approximately accuracy on the test set and around recall for pre-burst intervals, indicating strong predictive power and potential for targeted follow-up observations in astronomical surveys. The work demonstrates the practical value of TDA in astronomy, suggesting extensions to regression and other data modalities such as spectra and images, thereby enabling earlier and more reliable transient alerts.

Abstract

RS Oph is a recurrent nova, a kind of cataclismic variable that shows bursts in a period approximately shorter than a century. Persistent homology, a technique from topological data analysis, studies the evolution of topological features of a simplicial complex composed of the data points or an embedding of them, as some distance parameter is varied. For this work I trained a supervised learning model based on several featurizations, namely persistence landscapes, Carlsson coordinates, persistent images, and template functions, of the persistence diagrams of sections of the lightcurve of RS Oph. A tenfold cross validation of the model based on one of the featurizations, persistence landscapes, consistently shows high recalls and accuracies. This method serves the purpose of predicting whether RS Oph is bursting within a year.
Paper Structure (10 sections, 1 equation, 5 figures, 2 tables)

This paper contains 10 sections, 1 equation, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Data acquisition and processing
  4. Choice of time intervals and labeling
  5. Computation of persistence diagrams
  6. Featurization and cross validation
  7. Results and discussion
  8. Conclusions
  9. Acknowledgements
  10. Appendix. Point summaries

Figures (5)

  • Figure 1: The red solid line is the burst time. The dotted line 0.8 years after the burst marks the approximate end of the decay.
  • Figure 2: Dashed vertical lines in red mark the bursts, pointed vertical lines mark the advance time. Areas shaded in red, green and orange mean intervals ending in these areas are labeled as 'pre', 'inter', and 'post', respectively. Some of the first bursts, not included the studied region, are not easily distinguishable.
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