title: Accelerating gravitational-wave inference with machine learning
Creators: name: Williams, Michael J.
Publisher: name: University of Glasgow
Year: 2023

description: The future for gravitational-wave astronomy is bright, with improvements for existing ground-based interferometers of the LIGO-Virgo-KAGRA Collaboration (LVK) and new ground- and space-based interferometers planned for the near future. As a result, there will imminently be an abundance of data to analyse from these detectors, which will bring with it the chances to probe new regimes. However, this will also bring with it new challenges to address, such as the volume of data and need for new analysis techniques. Leveraging this data hinges on our ability to determine the characteristics of the sources that produce the observed gravitational-wave signals, and Bayesian inference is the method of choice. The main algorithms that have been used in these analyses are Markov Chain Monte Carlo and Nested Sampling. Each have their own advantages and disadvantages. However, both are computationally expensive when applied to gravitational-wave inference, typically taking of order days to weeks for shorter signals and up to months for longer signals, such as those from binary neutron star mergers. Furthermore, the cost of these analyses increases as additional physics is included, such as higher-order modes, precession and eccentricity. These factors, combined with the previously mentioned increase in data, and therefore number of signals, pose a significant challenge. As such, there is a need for faster and more efficient algorithms for gravitational-wave inference. In this work, we present novel algorithms that serve as drop-in replacements for existing approaches but can accelerate inference by an order of magnitude. Our initial approach is to incorporate machine learning into an existing algorithm, namely nested sampling, with the aim of accelerating it whilst leaving the underlying algorithm unchanged. To this end, we introduce nessai, a nested sampling algorithm that includes a novel method for sampling from the likelihood-constrained prior that leverages normalizing flows, a type of machine learning algorithm. Normalizing flows can approximate the distribution of live points during a nested sampling run, and allow for new points to be drawn from it. They are also flexible and can learn complex correlations, thus eliminating the need to use a random walk to propose new samples. We validate nessai for gravitational-wave inference by analysing a population of simulated binary black holes (BBHs) and demonstrate that it produces statistically consistent results. We also compare nessai to dynesty, the standard nested sampling algorithm used by the LVK, and find that, after some improvements, it is on average ∼ 6 times more efficient and enables inference in time scales of order 10 hours on a single core. We also highlight other advantages of nessai, such as the included diagnostics and simple parallelization of the likelihood evaluation. However, we also find that the rejection sampling step necessary to ensure new samples are distributed according to the prior can be a significant computational bottleneck. We then take the opposite approach and design a custom nested sampling algorithm tailored to normalizing flows, which we call i-nessai. This algorithm is based on importance nested sampling and incorporates elements from existing variants of nested sampling. In contrast to the standard algorithm, samples no longer have to be ordered by increasing likelihood nor distributed according to the prior, thus addressing the aforementioned bottleneck in nessai. Furthermore, the formulation of the evidence allows for it to be updated with batches of samples rather than one-by-one. The algorithm we design is centred around constructing a meta-proposal that approximates the posterior distribution, which is achieved by iteratively adding normalizing flows until a stopping criterion is met. We validate i-nessai on a range of toy test problems which allows us to verify the algorithm is consistent with both nessai and, when available, the analytic results. We then repeat a similar analysis to that performed previously, and analyse a population of simulated BBH signals with i-nessai. The results show that i-nessai produces consistent results, but is up to 3 times more efficient than nessai and more than an order of magnitude more efficient (13 times) than dynesty. We also apply i-nessai to a binary neutron star (BNS) analysis and find that it can yield results in less than 30 minutes whilst only requiring O(106 ) likelihood evaluations. Having developed tools to accelerate parameter estimation, we then apply them to real data from LVK observing runs. We choose to analyse all 11 events from O1 and small selection of events from O2 and O3 and find good agreement between our results and those published by the LVK This demonstrates that nessai can be used to analyse real gravitational-wave data. However, it also highlights aspects that could be improved to further accelerate the algorithm, such as how the orbital phase and multimodal likelihood surfaces are handled. We also show how i-nessai can be applied to real data, but ultimately conclude that further work is required to determine if the settings used are robust. Finally, we consider nessai in the context of next generation ground-based interferometers and highlight some of the challenges such analyses present. As a whole, the algorithms introduced in this work pave the way for faster gravitational wave inference, offering speed-ups of up to an order of magnitude compared to existing approaches. Furthermore, they demonstrate how machine learning can be incorporated into existing analyses to accelerate them, which has the additional benefit of providing drop-in replacements for existing tools.