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Register a new userGravitational wave population inference with deep flow-based generative network
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We combine hierarchical Bayesian modeling with a flow-based deep generative network, in order to demonstrate that one can efficiently constraint numerical gravitational wave (GW) population models at a previously intractable complexity. Existing techniques for comparing data to simulation,such as discrete model selection and Gaussian process regression, can only be applied efficiently to moderate-dimension data. This limits the number of observable (e.g. chirp mass, spins.) and hyper-parameters (e.g. common envelope efficiency) one can use in a population inference. In this study, we train a network to emulate a phenomenological model with 6 observables and 4 hyper-parameters, use it to infer the properties of a simulated catalogue and compare the results to the phenomenological model. We find that a 10-layer network can emulate the phenomenological model accurately and efficiently. Our machine enables simulation-based GW population inferences to take on data at a new complexity level.
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We construct few deep generative models of gravitational waveforms based on the semi-supervising scheme of conditional autoencoders and their variational extensions. Once the training is done, we find that our best waveform model can generate the inspiral-merger waveforms of binary black hole coalescence with more than $97%$ average overlap matched filtering accuracy for the mass ratio between $1$ and $10$. Besides, the generation time of a single waveform takes about one millisecond, which is about $10$ to $100$ times faster than the EOBNR algorithm running on the same computing facility. Moreover, these models can also help to explore the space of waveforms. That is, with mainly the low-mass-ratio training set, the resultant trained model is capable of generating large amount of accurate high-mass-ratio waveforms. This result implies that our generative model can speed up the waveform generation for the low latency search of gravitational wave events. With the improvement of the accuracy in future work, the generative waveform model may also help to speed up the parameter estimation and can assist the numerical relativity in generating the waveforms of higher mass ratio by progressively self-training.
The past four years have seen a scientific revolution through the birth of a new field: gravitational-wave astronomy. The first detection of gravitational waves---recognised by the 2017 Nobel Prize in Physics---provided unprecedented tests of general relativity while unveiling a previously unknown class of massive black holes, thirty times more massive than the Sun. The subsequent detection of gravitational waves from a merging binary neutron star confirmed the hypothesised connection between binary neutron stars and short gamma-ray bursts while providing an independent measurement of the expansion of the Universe. The discovery enabled precision measurement of the speed of gravity while shedding light on the origin of heavy elements. At the time of writing, the Laser Interferometer Gravitational-wave Observatory (LIGO) and its European partner, Virgo, have published the detection of eleven gravitational-wave events. New, not-yet-published detections are announced on a nearly weekly basis. This fast-growing catalogue of gravitational-wave transients is expected to yield insights into a number of topics, from the equation of state of matter at supra-nuclear densities to the fate of massive stars. The science potential of 3G observatories is enormous, enabling measurements of gravitational waves from the edge of the Universe and precise determination of the neutron star equation of state. Australia is well-positioned to help develop the required technology. The Mid-term Review for the Decadal plan for Australian astronomy 2016-2025 should consider investment in a scoping study for an Australian Gravitational-Wave Pathfinder that develops and validates core technologies required for the global 3G detector network.
We apply a machine learning algorithm, the artificial neural network, to the search for gravitational-wave signals associated with short gamma-ray bursts. The multi-dimensional samples consisting of data corresponding to the statistical and physical quantities from the coherent search pipeline are fed into the artificial neural network to distinguish simulated gravitational-wave signals from background noise artifacts. Our result shows that the data classification efficiency at a fixed false alarm probability is improved by the artificial neural network in comparison to the conventional detection statistic. Therefore, this algorithm increases the distance at which a gravitational-wave signal could be observed in coincidence with a gamma-ray burst. In order to demonstrate the performance, we also evaluate a few seconds of gravitational-wave data segment using the trained networks and obtain the false alarm probability. We suggest that the artificial neural network can be a complementary method to the conventional detection statistic for identifying gravitational-wave signals related to the short gamma-ray bursts.
The gravitational waveform of a merging stellar-mass binary is described at leading order by a quadrupolar mode. However, the complete waveform includes higher-order modes, which encode valuable information not accessible from the leading-order mode alone. Despite this, the majority of astrophysical inferences so far obtained with observations of gravitational waves employ only the leading order mode because calculations with higher-order modes are often computationally challenging. We show how to efficiently incorporate higher-order modes into astrophysical inference calculations with a two step procedure. First, we carry out Bayesian parameter estimation using a computationally cheap leading-order-mode waveform, which provides an initial estimate of binary parameters. Second, we weight the initial estimate using higher-order mode waveforms in order to fold in the extra information from the full waveform. We use mock data to demonstrate the effectiveness of this method. We apply the method to each binary black hole event in the first gravitational-wave transient catalog GWTC-1 to obtain posterior distributions and Bayesian evidence with higher-order modes. Performing Bayesian model selection on the events in GWTC-1, we find only a weak preference for waveforms with higher order modes. We discuss how this method can be generalized to a variety of other applications.
Time series analysis is ubiquitous in many fields of science including gravitational-wave astronomy, where strain time series are analyzed to infer the nature of gravitational-wave sources, e.g., black holes and neutron stars. It is common in gravitational-wave transient studies to apply a tapered window function to reduce the effects of spectral artifacts from the sharp edges of data segments. We show that the conventional analysis of tapered data fails to take into account covariance between frequency bins, which arises for all finite time series -- no matter the choice of window function. We discuss the origin of this covariance and show that as the number of gravitational-wave detections grows, and as we gain access to more high signal-to-noise ratio events, this covariance will become a non-negligible source of systematic error. We derive a framework that models the correlation induced by the window function and demonstrate this solution using both data from the first LIGO--Virgo transient catalog and simulated Gaussian noise.
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