Training a neural network to rapidly identify candidate gravitational-wave events in the lower mass gap

This paper introduces GWSkyNet-MassGap, a neural network model trained to rapidly predict the probabilities of gravitational-wave candidates containing components in the lower mass gap or being neutron stars, achieving high accuracy for high-mass mergers while highlighting the need for mass ratio information to resolve degeneracies in lower-mass systems.

The Gist

The Big Picture: Filling the "Missing Link"

Imagine the universe has a family of heavyweights: Neutron Stars (the heaviest "normal" stars) and Black Holes (the absolute heavyweights). For a long time, astronomers thought there was a clear gap between them, like a missing rung on a ladder. They knew Neutron Stars weighed up to about 2 tons (in solar mass units), and Black Holes started at about 5 tons. But what about the stuff in between (2 to 5 tons)? It was a "Lower Mass Gap"—a mysterious empty space where no one knew if anything lived.

Recently, gravitational wave detectors (like LIGO and Virgo) started hearing "thuds" from colliding stars that seemed to live right in this gap. The big question is: Is the object in the middle a heavy Neutron Star or a light Black Hole?

Why does this matter? Because if a Neutron Star is involved in a crash, it often explodes with a bright flash of light (like a firework) that telescopes can see. If it's a Black Hole, it usually just swallows everything silently. Knowing which one it is helps scientists decide whether to point their optical telescopes at the sky to catch a light show.

The Solution: A "Speedy Detective" AI

The problem is that gravitational wave data takes a long time to analyze properly. By the time scientists figure out the details, the light show might be over.

The authors of this paper built a new neural network (a type of AI) called GWSkyNet-MassGap. Think of this AI as a speedy detective who looks at a crime scene photo and instantly guesses:

1. Is there a "Gap" object here? (Probability of a Mass Gap component).
2. Is there a Neutron Star here? (Probability of a Neutron Star).

The goal is to give this answer in seconds, allowing telescopes to start looking immediately.

How the AI Was Trained

You can't train a detective by showing them only real crimes; you need to show them thousands of practice cases.

• The Practice Room: The team created 20,000 fake but realistic star crashes using a computer. They used the latest theories about how stars are born and die to make sure the fake data looked like the real universe.
• The Clues: Instead of waiting for a full, slow analysis, the AI was trained to look only at the quick, rough sketches provided by the detectors immediately after a crash. These sketches include things like "where in the sky it happened," "how far away it is," and "how loud the signal was."
• The Twist: Unlike previous AI models that forced a hard line (e.g., "If it weighs 3 tons, it's a Black Hole"), this AI was taught to be fuzzy. It learned that the boundary is blurry. It calculates the probability that an object is in the gap, rather than just saying "Yes" or "No."

What the AI Learned (and What It Missed)

The researchers tested the AI on a set of fake data and then on real data from the first part of the fourth observing run (O4a).

The Successes:

• The Heavyweights: When the crashing stars were very heavy (like two giant Black Holes), the AI was excellent. It correctly said, "No Neutron Star, no Mass Gap object here." It's like a detective who can instantly tell the difference between a bicycle and a semi-truck.
• The Speed: It works fast enough to help with real-time decisions.

The Struggles:

• The Middle Ground: The AI got confused when the stars were in the "middle weight" range (between 3 and 15 solar masses).
• The Analogy: Imagine you hear a car engine. If you only know the volume of the engine (the "chirp mass"), you can guess if it's a small car or a truck. But, a small car with a loud engine and a big truck with a quiet engine can sound the same.
  • The AI is great at guessing the "volume."
  • However, it struggles to guess the type of car (Neutron Star vs. Black Hole) because it doesn't have enough information about the mass ratio (how much heavier one star is than the other).
  • Without knowing the ratio, the AI can't break the tie. It often guesses "maybe" or defaults to a low probability, even if the answer is actually "yes."

The "Distance" Glitch:
In a few real-world cases, the AI made mistakes because the initial "quick sketch" of the distance was wrong. If the AI thinks a crash is closer than it really is, it thinks the stars are lighter than they are. This made it guess "Neutron Star" for events that were actually just heavy Black Holes.

The Bottom Line

The paper concludes that GWSkyNet-MassGap is a useful new tool for the astronomy community.

• It is open-source (anyone can use it).
• It uses public data (no secret codes needed).
• It is fast.

However, it is not perfect yet. It is very good at ruling out Neutron Stars in massive crashes, but it needs more training or better data to accurately identify the tricky, medium-weight objects in the "Mass Gap." The authors suggest that in the future, this tool could be upgraded to not just guess the type of star, but to quickly estimate the exact mass of the stars involved, which would solve the confusion.

In short: The AI is a fast, helpful assistant that can spot the obvious heavyweights, but it still needs a little help figuring out the mysterious middle-weighters.

Technical Summary

1. Problem Statement

The boundary between the most massive neutron stars (NSs) and the least massive black holes (BHs) is currently uncertain, creating a "lower mass gap" in the range of $\sim 2-5 M_\odot$. While gravitational-wave (GW) detections (e.g., GW190814, GW230529) suggest this gap is not empty, distinguishing whether a candidate event contains a component in this gap is critical for follow-up astronomy.

• Scientific Motivation: Events involving NSs (or NS-BH binaries where the NS is tidally disrupted) are prime candidates for electromagnetic (EM) counterparts (kilonovae, gamma-ray bursts).
• Operational Challenge: Rapidly determining if a candidate GW event has a component in the mass gap or is an NS is essential for real-time decision-making regarding EM follow-up.
• Current Limitations: Existing Low-Latency (LL) tools from the LIGO-Virgo-KAGRA (LVK) collaboration (e.g., HasNS, HasMassGap) rely on specific template parameters (masses, spins, SNR) that are not always available in the initial public alerts. Furthermore, traditional classification often relies on sharp mass cut-offs (e.g., $3 M_\odot$), which fails to capture the physical uncertainty of the NS-BH boundary.

2. Methodology

A. Data Simulation and Generation

The authors generated a robust dataset of $2 \times 10^4$ simulated binary merger events to train the model:

• Source Distribution: Component masses ($m_1, m_2$) and spins were sampled from the Power Law + Dip + Break (PDB) model (fit to GWTC-3), which models the entire compact binary population without assuming hard mass cut-offs.
• Waveforms: Signals were simulated using TaylorF2, SEOBNRv4-ROM, and IMRPhenomD waveform approximants to match LVK search pipelines.
• Detector Network: Events were injected into realistic O4 detector noise (LIGO-Hanford, LIGO-Livingston, Virgo) with specific duty cycles. Only multi-detector events with a network Signal-to-Noise Ratio (SNR) $\rho_{net} > 7$ and distance $d < 2.4$ Gpc were retained.
• Localization: The ligo.skymap package was used to generate Bayestar localization maps, simulating the low-latency alerts released to the community.

B. Labeling Strategy (Probabilistic Approach)

Instead of binary classification (NS vs. BH), the model predicts continuous probabilities:

• $P_{NS}$ (Probability of NS): Calculated by marginalizing over the posterior distribution of the maximum NS mass ($M_{NS,max}$) derived from Equation of State (EOS) constraints (Tolman–Oppenheimer–Volkoff limit).
• $P_{MassGap}$ (Probability of Mass Gap): Calculated by marginalizing over the posterior distributions of both $M_{NS,max}$ and the minimum BH mass ($M_{BH,min}$) derived from the Power Law + Peak model.
• Target: The model learns to predict the probability that a binary has at least one component in the mass gap or is an NS.

C. Model Architecture: GWSkyNet-MassGap

• Inputs: The model uses only data available in low-latency public alerts (Bayestar localization maps):
  1. 90% sky localization area.
  2. 90% volume localization.
  3. Mean estimated distance.
  4. Standard deviation of estimated distance.
  5. Log Bayes Signal-to-Noise (Log BSN).
  6. Log Bayes Coherence (Log BCI).
  7. Detector network configuration.
• Network Structure: A deep neural network with four hidden dense layers (32 neurons each), using ReLU activation. The output layer consists of two neurons with sigmoid activation to output $P_{MassGap}$ and $P_{NS}$ simultaneously.
• Ensemble Learning: To reduce uncertainty, the final model is an ensemble of 20 independently trained networks (Bagging), reporting the mean and standard deviation of predictions.

3. Key Contributions

1. Novel Input Space: Unlike LVK's internal ML tools that use template-matched parameters (masses/spins), GWSkyNet-MassGap operates solely on Bayestar localization data, making it a fully independent, open-source, and reproducible tool for the broader community.
2. Probabilistic Labeling: The training data avoids arbitrary mass cut-offs. Instead, it uses physically motivated probability distributions for the NS/BH boundary, reflecting the true astrophysical uncertainty.
3. Chirp Mass Inference: The study demonstrates that the model successfully infers the source chirp mass ($M_c$) from localization data (specifically distance and sky area) to make its predictions, effectively bypassing the need for explicit mass inputs.

4. Results and Performance

A. Test Set Performance

• High-Mass Events ($M_c \gtrsim 15 M_\odot$): The model performs excellently, correctly predicting near-zero probabilities for both Mass Gap and NS ($P \approx 0$).
• Low-Mass/Ambiguous Events ($3 M_\odot \lesssim M_c \lesssim 15 M_\odot$): Performance degrades significantly. The model struggles to distinguish between a low-mass-ratio BBH and a high-mass-ratio NSBH/MassGap event because the chirp mass alone does not uniquely determine the component masses (mass ratio degeneracy).
• Bias: The model shows a bias toward predicting lower probabilities for the Mass Gap (rarely predicting $P_{MassGap} > 0.5$), leading to a mean absolute error (MAE) of 17% for Mass Gap and 10% for NS on the test set.

B. Application to O4a Events (GWTC-4.0)

The model was tested on 69 multi-detector candidate events from the first part of the O4 run:

• Overall Accuracy: Mean prediction error of 9% for $P_{MassGap}$ and 6% for $P_{NS}$.
• Success Cases: Correctly identified the NSBH event GW230518 (predicted $P_{NS} = 0.98$ vs. true $\approx 1.0$) and the low-mass BBH GW230627 (predicted $P_{MassGap} = 0.17$ vs. true $0.17$).
• Failure Modes (Outliers): Three events (GW230922, GW231001, GW231223) with high true chirp masses ($>15 M_\odot$) were incorrectly predicted to have high Mass Gap/NS probabilities.
  • Cause: The low-latency Bayestar analysis significantly underestimated the distance for these events (by $>2\times$). Since the model infers chirp mass from distance, it falsely inferred a low chirp mass, leading to false positive predictions.

5. Significance and Future Outlook

• Real-Time Utility: GWSkyNet-MassGap provides a complementary, open-source tool for the EM follow-up community to assess the likelihood of NS involvement in GW events using only publicly available alert data.
• Limitations: The model's accuracy is fundamentally limited by the chirp mass degeneracy. Without knowledge of the mass ratio (which requires full parameter estimation, not available in low-latency), the model cannot perfectly distinguish between different source types in the ambiguous mass range.
• Future Work: The authors suggest the model could be refined to explicitly predict the source chirp mass as an intermediate step. Additionally, future iterations could incorporate spin effects and more flexible population models to better resolve the mass gap boundaries.
• Availability: The model and predictions for O4 candidates are made publicly available via a webpage and Git repository to facilitate immediate use in future observing runs (IR1, O5).