Bayesian parameter estimation using conditional variational autoencoders for gravitational-wave astronomy

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.Comment: 13 pages, 5 figure

Lightning-Fast Gravitational Wave Parameter Inference through Neural Amortization

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.Comment: V1: First version; V2: Updated references; V3: Update references and camera-ready version; V4: Correct figure labels; V5: Updated reference

Generalised gravitational burst generation with Generative Adversarial Networks

We introduce the use of conditional generative adversarial networks forgeneralised gravitational wave burst generation in the time domain.Generativeadversarial networks are generative machine learning models that produce new databased on the features of the training data set. We condition the network on fiveclasses of time-series signals that are often used to characterise gravitational waveburst searches: sine-Gaussian, ringdown, white noise burst, Gaussian pulse and binaryblack hole merger. We show that the model can replicate the features of these standardsignal classes and, in addition, produce generalised burst signals through interpolationand class mixing. We also present an example application where a convolutional neuralnetwork classifier is trained on burst signals generated by our conditional generativeadversarial network. We show that a convolutional neural network classifier trainedonly on the standard five signal classes has a poorer detection efficiency than aconvolutional neural network classifier trained on a population of generalised burstsignals drawn from the combined signal class space

Unbiased likelihood-free inference of the Hubble constant from light standard sirens

Multi-messenger observations of binary neutron star mergers offer a promising path towards resolution of the Hubble constant ($H_0$) tension, provided their constraints are shown to be free from systematics such as the Malmquist bias. In the traditional Bayesian framework, accounting for selection effects in the likelihood requires calculation of the expected number (or fraction) of detections as a function of the parameters describing the population and cosmology; a potentially costly and/or inaccurate process. This calculation can, however, be bypassed completely by performing the inference in a framework in which the likelihood is never explicitly calculated, but instead fit using forward simulations of the data, which naturally include the selection. This is Likelihood-Free Inference (LFI). Here, we use density-estimation LFI, coupled to neural-network-based data compression, to infer $H_0$ from mock catalogues of binary neutron star mergers, given noisy redshift, distance and peculiar velocity estimates for each object. We demonstrate that LFI yields statistically unbiased estimates of $H_0$ in the presence of selection effects, with precision matching that of sampling the full Bayesian hierarchical model. Marginalizing over the bias increases the $H_0$ uncertainty by only $6\%$ for training sets consisting of $O(10^4)$ populations. The resulting LFI framework is applicable to population-level inference problems with selection effects across astrophysics.Comment: 19 pages, 8 figures, comments welcom

Probing High Energy Physics Through Gravitational Waves

Over the last few years, gravitational wave detections have become ubiquitous, giving the physics community vast information about fundamental physics. As some of the universe’s highest energy events, neutron mergers allow us to explore extreme matter states through the gravitational waves they emit. The gravitational waves from binary neutron star mergers allow us, among other things, to probe the physics of the densest matter, reveal the equation of state of neutron stars, learn about the mechanism behind gamma ray bursts, and test general relativity itself. At the same time, black holes also allow us to test general relativity and probe the fields in their surroundings. In particular, black holes could shine a light on massive boson fields proposed by extensions of the Standard Model. Massive boson under the right circumstances will form bound states around black holes. Under the right conditions, bosons will extract energy and angular momentum from spinning black holes through superradiance. This energy extraction mechanism, along with the bound bosons, causes a boson cloud to grow around the black hole which dissipates its energy through gravitational waves. Detecting these gravitational waves can then help us learn about the bosons bound to the black hole, thereby making the black hole akin to a particle detector. In this thesis we further the understanding of the dynamics of massive boson superradiance instability by extending previous studies to include the self-interactions of the bosons. We then propose a phenomenological model for binary neutron star post-merger waveforms. The proposed model is based on a machine learning technique that requires large amounts of data. We attempt to estimate how much data would be required to have a functional model and discuss the issues that arise when validating the model

Variational learning for inverse problems

Machine learning methods for solving inverse problems require uncertainty estimation to be reliable in real settings. While deep variational models offer a computationally tractable way of recovering complex uncertainties, they need large supervised data volumes to be trained, which in many practical applications requires prohibitively expensive collections with specific instruments. This thesis introduces two novel frameworks to train variational inference models for inverse problems, in semi-supervised and unsupervised settings respectively. In the former, a realistic scenario is considered, where few experimentally collected supervised data are available, and analytical models from domain expertise and existing unsupervised data sets are leveraged in addition to solve inverse problems in a semi-supervised fashion. This minimises the supervised data collection requirements and allows the training of effective probabilistic recovery models relatively inexpensively. This novel method is first evaluated in quantitative simulated experiments, testing performance in various controlled settings and compared to alternative techniques. The framework is then implemented in several real world applications, spanning imaging, astronomy and human-computer interaction. In each real world setting, the novel technique makes use of all available information for training, whether this is simulations, data or both, depending on the task. In each experimental scenario, state of the art recovery and uncertainty estimation were demonstrated with reasonably limited experimental collection efforts for training. The second framework presented in this thesis approaches instead the challenging unsupervised situation, where no examples of ground-truths are available. This type of inverse problem is commonly encountered in data pre-processing and information retrieval. A variational framework is designed to capture the solution space of inverse problem by using solely an estimate of the observation process and large ensembles of observations examples. The unsupervised framework is tested on data recovery tasks under the common setting of missing values and noise, demonstrating superior performance to existing variational methods for imputation and de-noising with different real data sets. Furthermore, higher classification accuracy after imputation are shown, proving the advantage of propagating uncertainty to downstream tasks with the new model