Inpainting to search for premerger massive black hole binaries in realistic LISA datasets

The gist The authors demonstrate and compare two methods for premerger identification of massive black hole binaries; a zero-latency filter approach and, for the first time, an approach using an “inpainting” technique.

Introduction to Premerger Identification

A key science target for the Large Interferometer Space Antenna (LISA) is to carry out multimessenger observations of massive black hole binaries, observing the merger simultaneously in gravitational waves and with electromagnetic observatories Identifying that a merger is happening and providing an updating estimate of the sky location in the hours, days and weeks before the merger is critical to enable electromagnetic observations of the merger event Such pre-merger observations provide an early warning that a loud merger event is about to happen and can provide sky-localization estimates for these incredibly science-rich events The technique that we introduced in [13] offers a method for immediate analysis of LISA data It allows for the accurate computation of a matched filter using an acausal, zero-latency whitening filter that alleviates the need to wait (up to a day) for additional data to arrive before being able to filter However, our method is not robust to gaps in the LISA data and only searches for signals at discrete values of the gap to merger We therefore introduce a second possibility for premerger observation, applying the inpainting technique of [21] as an alternative to the zero-latency whitening filter.

The Sangria-HM Dataset

The Sangria-HM dataset consists of both a “training” and “blind” dataset, and we analyze here the training dataset to more easily compare the values of the signals to our results The MBHBs are simulated using the PhenomHM waveform model This foreground, made up of millions of white dwarf binaries in our galaxy which are nearly monochromatic in frequency, occupy the same frequency range as mergers of MBHBs The Galactic binary confusion noise overlaps with MBHB mergers in frequency space. We emphasize that our search is not for the mergers, rather the inspiral stage of the signal, many days before merger.

Zero-Latency Filter Search Results

We apply our previous zero-latency filter based search method to the Sangria-HM Training dataset to demonstrate its ability to observe premerger MBHBs We begin by taking the first 30 days of data and searching for mergers 0.5, 1, 4, 7 and 14 days from the end of that data (ie. signals that would merge 0.5, 1, 4, or a day in the future) By repeating this process by-hour, simulating how data might arrive in real time while continuously searching for premerger signals We consider a signal to be detected if we recover it with a signal-to-noise ratio larger than 10, which is more conservative than the thresholds we computed empirically in [13] but allows for some uncertainty in the noise model We remove each signal 2 hours before its corresponding merger time to avoid confusing actual mergers as premerger signals.

Inpainting Technique Application

The inpainting technique works by choosing appropriate values of the unwhitened data in the gap, such that after overwhitening all values in the gap are zero This results in the values of the overwhitened data in the gap not being zero The method allows us to simultaneously search for a signal matching a given template waveform at all times before merger We can see that as the inpainting search is not restricted to search at discrete times before merger we are able to detect some of the signals days earlier than our zerolatency search. For Signals 0 and 3 the zerolatency search identifies it 7 days before merger, whereas the inpainting search identifies it 14 days before merger We also observe that for Signals 2 - 5 are visibly overlapping in Figure 9.

Conclusion and Viability

We have demonstrated the application of two separate search techniques, one using a zero-latency whitening filter, and the other using inpainting, to identify premerger MBHB signals in the Sangria-HM Training dataset We believe that the methods presented here, being of negligible computing cost for the late 2030s and utilizing similar signal processing techniques to those developed over the last decades for ground-based analyses represent viable search strategies for premerger observation of MBHB after LISA launches. The authors are keen to continue to work closely with the LISA Ground Segment, and the “L2A” package in particular, to apply these methods to more realistic simulations of LISA data that the LISA Simulation Group will produce in the coming years.

How it works

1. Zero-latency filter approach: This method uses an acausal, zero-latency whitening filter that alleviates the need to wait (up to a day) for additional data to arrive before being able to filter.

2. Inpainting technique: This involves choosing appropriate values of the unwhitened data in the gap, such that after overwhitening all values in the gap are zero. The procedure is implemented in the PyCBC toolkit as described in [33].

3. Signal removal before merger: We remove each signal 2 hours before its corresponding merger time to avoid confusing actual mergers as premerger signals.

Key Findings

"We demonstrate that the inpainting method can identify premerger signals even when gaps are present in the data, demonstrating the recovery of a signal even when three day-long data gaps are added to the 14 days preceding merger."

The inpainting procedure is doing what we expect, recovering signals at roughly the time before merger that we expect from Table I.

We notice that as the inpainting search is not restricted to search at discrete times before merger we are able to detect some of the signals days earlier than our zerolatency search.

Data Analysis Details

The analysis was performed on the “SangriaHM dataset” produced as part of the LISA Data Challenges. The training dataset is a year long and contains Gaussian instrumental noise, a foreground of Galactic binaries and MBHB systems, both with parameters derived from astrophysical models The analysis utilizes template banks created using stochastic bank placement. The template banks used in [13] used a modeled power spectral density without Galactic binary confusion noise. Inclusion of unresolvable Galactic binary foreground in the model increases bank size by a factor between 2.1 and 2.6. The authors show that the number of waveforms is relatively small, current template banks for ground based analysis are at least one order of magnitude larger than this.

Overlapping Signals Management

The proximity of signals can lead to some overlap between them We show results without any signal removal (9a), or with signal removal 2 hours before merger (9b) for the inpainting search. This highlights that it is important not just to remove the merger of these MBHB signals from the data when searching for other MBHBs, but to remove loud signals.

1. textbfThe Inpainting Technique for Gap Handling in Premerger Searches: Capabilities of Inpainting Search with Gaps adds the recovery of a signal even when three day-long data gaps are added to the 14 days preceding merger. This allows AI systems to robustly identify premerger signals even when realistic LISA data contains missing segments, overcoming limitations of fixed-time searches that fail in the presence of gaps.

2. textbfAdaptive Template Bank Construction: The paper suggests using stochastic placement where "we would draw the time before merger when selecting a proposal point, alongside the other parameters. We would then check if that signal would be recovered by the existing template bank and add it to the bank if it would not be recovered below a specified match threshold. This enables AI systems to build template banks capable of observing any signals in a given range of times before merger," improving detection efficiency beyond discrete time-before-merger searches.

3. textbfSignal Masking Mitigation: The paper demonstrates that removing signals 2 hours before merger allows for the identification of subsequent signals, showing that Signal 5 can now be seen in the oneday-before-merger results. This capability allows AI systems to perform a sequential search where they can reliably identify multiple signals in the data, even when they are overlapping or close in time.

4. textbfEnhanced Premerger Detection Timing: The comparison shows that the inpainting procedure is doing what we expect, recovering signals at roughly the time before merger that we expect from Table I, and that the search can detect some of the signals days earlier than our zerolatency search. This means AI systems can achieve improved sensitivity by utilizing data conditioning effects, such as applying a long taper to the waveform over the first ∼ day of data to avoid any abrupt start effects.

5. textbfNon-Gaussianity and Artifact Handling: The inpainting technique is adapted from ground-based analyses where the observation of the first binary neutron star merger, GW170817, was significantly hampered by the presence of a loud non-Gaussian artifact in the seconds before the merger. This enables AI systems to mitigate non-Gaussianities and other noise artifacts that might otherwise bias inference algorithms.

A key science target of the Large Interferometer Space Antenna (LISA) is to carry out multi-messenger observations of massive black hole binaries, observing the merger simultaneously in gravitational waves and with electromagnetic observatories. Identifying that a merger is happening and providing an updating estimate of the sky location in the hours, days and weeks before the merger is critical to enable electromagnetic observations of the merger event. In this work we demonstrate and compare two methods for premerger identification of massive black hole binaries; a zero-latency filter approach and, for the first time, an approach using an ``inpainting'' technique. We apply these methods to the LISA Data Challenge dataset 2a--Sangria-HM--and demonstrate the successful recovery of the 14 signals in the dataset that we expected to be identifiable at least half a day before merger. We show that the inpainting method can identify premerger signals even when gaps are present in the data, demonstrating the recovery of a signal even when 3 day-long data gaps are added to the 14 days preceding merger. Finally, we explore the challenge of overlapping signals, using a region of overlapping signals in the Sangria-HM dataset, all of which merge within a 10-day window, and show how removing signals that have been confidently identified from the data allows us to identify quieter signals in the same period.