Disentangling the Galactic binary zoo: Machine learning classification of stellar remnant binaries in LISA data

Author(s)

Tay, Irwin Khai Cheng, Korol, Valeriya, Lechien, Thibault

Abstract

The Laser Interferometer Space Antenna (LISA) will open a new observational window in the millihertz gravitational-wave band, enabling the detection of tens of thousands of compact stellar remnant binaries across the Milky Way. Most of LISA's sources will be double white dwarf (WDWD) systems, while neutron star-white dwarf (NSWD) binaries and higher-mass systems will be orders of magnitude rarer but of significant astrophysical interest. Disentangling these populations is challenging due to the strong overlap in their gravitational-wave features. In this work, we investigate the use of machine-learning techniques to classify LISA-detectable binaries based solely on LISA observables. Using mock catalogues of Galactic binaries constructed from population-synthesis studies, we evaluate a range of machine-learning classifiers. We find that ensemble-based methods-particularly gradient-boosting algorithms such as XGBoost-deliver the best performance on our highly imbalanced dataset. WDWD systems are identified with a recall of $\sim 99\%$, reflecting their dominant presence, and high-mass binaries are also classified with high recall ($\ge 85\%$). In contrast, NSWD systems remain the most challenging population to distinguish: their features overlap strongly with those of WDWD binaries, making them particularly prone to misclassification. Despite this, XGBoost correctly identifies 85.6% of NSWD systems in our simulated LISA detections, outperforming simple statistical approaches based on kernel density estimation. We further demonstrate that machine-learning classification can effectively support the interpretation of LISA data, enabling the identification of eccentric binaries and extremely rare subclasses.

Figures

Caption

Distributions of the ten features in the data used for the machine learning classifiers, coloured by true class. Black: WDWD binaries; orange: NSWD binaries; grey: BHBH binaries; red: BHNS binaries; and maroon: NSNS binaries. Each distribution is normalised independently.

Caption

Confusion matrix of the multi-class XGBoost classifier evaluated on the main catalogue’s test set. Each entry is row-normalised and colour-coded by value, with bracketed numbers indicating the absolute counts. The classifier demonstrates strong performance in separating the high-mass binaries (BHBH, BHNS, NSNS), while classification of the low-mass binaries (WDWD, NSWD) remains more challenging. The distinction between WDWD and NSWD is the most difficult, with approximately $25\%$ of NSWD class incorrectly predicted as WDWD.

Caption

Performance comparison of machine-learning classifiers evaluated on the test set including NSWD and WDWD binaries only. In both plots, the top-right corner represents the ideal performance.

Caption

Feature distributions for correctly (blue) and incorrectly (red) predicted low-mass binary systems (WDWD and NSWD) by XGBoost binary classifier evaluated on the main catalogue's test set. The inset in the upper-right corner shows a SHAP summary plot illustrating the impact of the ten input features on the classifier's output for each system in the low-mass component test set. The features are ranked on the y-axis in descending order of average absolute importance. The x-axis shows the SHAP value, indicating the feature's contribution to the output, where a positive value pushes the prediction towards the positive class (NSWD) and a negative value pushes it towards the other (WDWD). A SHAP value of 0, marked by the vertical grey line, represents the baseline and indicates the feature had no impact on that specific prediction. Each point corresponds to an individual system from the test set, coloured by its normalised feature value, from low (dark blue) to high (yellow).

Caption

Confusion matrices evaluated on the low-mass population test set for the XGBoost (purple) and KDE (grey) classifiers. Each entry is row-normalised and colour-coded by value, with bracketed numbers indicating the absolute counts. The results show that XGBoost performs significantly better, correctly predicting 85.6\% of NSWD systems compared to 62.2\% for KDE. For the same population, XGBoost predicts 360 NSWD systems, whereas KDE predicts 312.

Caption

Confusion matrices evaluated on the low-mass population test set for the XGBoost (purple) and KDE (grey) classifiers. Each entry is row-normalised and colour-coded by value, with bracketed numbers indicating the absolute counts. The results show that XGBoost performs significantly better, correctly predicting 85.6\% of NSWD systems compared to 62.2\% for KDE. For the same population, XGBoost predicts 360 NSWD systems, whereas KDE predicts 312.

Caption

LISA-detectable Galactic WDWD (grey) populations and NSWD (blue and red) populations of a four-year LISA observation period shown in the gravitational-wave frequency–characteristic strain parameter space, with the LISA sensitivity curve plotted and shaded in purple. The two NSWD scatter plots represent the correctly (blue) and incorrectly (red) predicted NSWD systems by the XGBoost classifier evaluated on the test catalogue.

Caption

The confusion matrices for the two experiments described in \cref{sec: eccaftergolbal}. Experiment 1 (top) presents the confusion matrix for the evaluation of the XGBoost classifier trained without the feature eccentricity, applied to classify WDWD and NSWD binaries. Experiment 2 (bottom) shows the confusion matrix for the classifier trained without the eccentricity feature but using labels \texttt{NoEcc} (for binaries with zero eccentricity) and \texttt{Ecc} (for binaries with non-zero eccentricity). Each entry is row-normalised and colour-coded by value, with bracketed numbers indicating the absolute counts.

Caption

The confusion matrices for the two experiments described in \cref{sec: eccaftergolbal}. Experiment 1 (top) presents the confusion matrix for the evaluation of the XGBoost classifier trained without the feature eccentricity, applied to classify WDWD and NSWD binaries. Experiment 2 (bottom) shows the confusion matrix for the classifier trained without the eccentricity feature but using labels \texttt{NoEcc} (for binaries with zero eccentricity) and \texttt{Ecc} (for binaries with non-zero eccentricity). Each entry is row-normalised and colour-coded by value, with bracketed numbers indicating the absolute counts.