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Register a new userGravitational-wave parameter estimation with autoregressive neural network flows
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We introduce the use of autoregressive normalizing flows for rapid likelihood-free inference of binary black hole system parameters from gravitational-wave data with deep neural networks. A normalizing flow is an invertible mapping on a sample space that can be used to induce a transformation from a simple probability distribution to a more complex one: if the simple distribution can be rapidly sampled and its density evaluated, then so can the complex distribution. Our first application to gravitational waves uses an autoregressive flow, conditioned on detector strain data, to map a multivariate standard normal distribution into the posterior distribution over system parameters. We train the model on artificial strain data consisting of IMRPhenomPv2 waveforms drawn from a five-parameter $(m_1, m_2, phi_0, t_c, d_L)$ prior and stationary Gaussian noise realizations with a fixed power spectral density. This gives performance comparable to current best deep-learning approaches to gravitational-wave parameter estimation. We then build a more powerful latent variable model by incorporating autoregressive flows within the variational autoencoder framework. This model has performance comparable to Markov chain Monte Carlo and, in particular, successfully models the multimodal $phi_0$ posterior. Finally, we train the autoregressive latent variable model on an expanded parameter space, including also aligned spins $(chi_{1z}, chi_{2z})$ and binary inclination $theta_{JN}$, and show that all parameters and degeneracies are well-recovered. In all cases, sampling is extremely fast, requiring less than two seconds to draw $10^4$ posterior samples.
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Gravitational waves from compact binaries measured by the LIGO and Virgo detectors are routinely analyzed using Markov Chain Monte Carlo sampling algorithms. Because the evaluation of the likelihood function requires evaluating millions of waveform models that link between signal shapes and the source parameters, running Markov chains until convergence is typically expensive and requires days of computation. In this extended abstract, we provide a proof of concept that demonstrates how the latest advances in neural simulation-based inference can speed up the inference time by up to three orders of magnitude -- from days to minutes -- without impairing the performance. Our approach is based on a convolutional neural network modeling the likelihood-to-evidence ratio and entirely amortizes the computation of the posterior. We find that our model correctly estimates credible intervals for the parameters of simulated gravitational waves.
Gravitational wave (GW) detection is now commonplace and as the sensitivity of the global network of GW detectors improves, we will observe $mathcal{O}(100)$s of transient GW events per year. The current methods used to estimate their source parameters employ optimally sensitive but computationally costly Bayesian inference approaches where typical analyses have taken between 6 hours and 5 days. For binary neutron star and neutron star black hole systems prompt counterpart electromagnetic (EM) signatures are expected on timescales of 1 second -- 1 minute and the current fastest method for alerting EM follow-up observers, can provide estimates in $mathcal{O}(1)$ minute, on a limited range of key source parameters. Here we show that a conditional variational autoencoder pre-trained on binary black hole signals can return Bayesian posterior probability estimates. The training procedure need only be performed once for a given prior parameter space and the resulting trained machine can then generate samples describing the posterior distribution $sim 6$ orders of magnitude faster than existing techniques.
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.
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.
Using the latest numerical simulations of rotating stellar core collapse, we present a Bayesian framework to extract the physical information encoded in noisy gravitational wave signals. We fit Bayesian principal component regression models with known and unknown signal arrival times to reconstruct gravitational wave signals, and subsequently fit known astrophysical parameters on the posterior means of the principal component coefficients using a linear model. We predict the ratio of rotational kinetic energy to gravitational energy of the inner core at bounce by sampling from the posterior predictive distribution, and find that these predictions are generally very close to the true parameter values, with $90%$ credible intervals $sim 0.04$ and $sim 0.06$ wide for the known and unknown arrival time models respectively. Two supervised machine learning methods are implemented to classify precollapse differential rotation, and we find that these methods discriminate rapidly rotating progenitors particularly well. We also introduce a constrained optimization approach to model selection to find an optimal number of principal components in the signal reconstruction step. Using this approach, we select 14 principal components as the most parsimonious model.
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