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

Nature Physics volume 18, pages 112–117 (2022)Cite this article

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Abstract

With the improving sensitivity of the global network of gravitational-wave detectors, we expect to observe hundreds of transient gravitational-wave 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 h and 6 d. For binary neutron star and neutron star–black hole systems prompt counterpart electromagnetic signatures are expected on timescales between 1 s and 1 min. However, the current fastest method for alerting electromagnetic follow-up observers can provide estimates in of the order of 1 min on a limited range of key source parameters. Here, we show that a conditional variational autoencoder pretrained 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 around six orders of magnitude faster than existing techniques.

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Fig. 1: The configuration of the CVAE neural network.
Fig. 2: Posterior results for one example test dataset.
Fig. 3: One-dimensional probability–probability plots.
Fig. 4: JS divergence values for all 250 test samples.

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Data availability

We provide the input test data waveforms as well as the trained ML model on the Harvard Dataverse at the following publicly available link: https://doi.org/10.7910/DVN/DECSMV

Code availability

We have made the entirety of the code used to produce the results (and Bilby posteriors) publicly available at the following GitHub repository: https://github.com/hagabbar/vitamin_c

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Acknowledgements

We acknowledge valuable input from the LIGO–Virgo Collaboration, specifically from W. Farr, T. Dent, J. Kanner, A. Nitz, C. Capano and the parameter estimation and machine-learning working groups. We additionally thank S. Marka for posing this challenge to us. We thank Nvidia for the generous donation of a Tesla V100 GPU used in addition to LIGO–Virgo Collaboration computational resources. We also gratefully acknowledge the Science and Technology Facilities Council of the UK. C.M. and I.S.H. are supported by the Science and Technology Research Council (grant ST/ L000946/1) and the European Cooperation in Science and Technology (COST) action CA17137. F.T. acknowledges support from Amazon Research and EPSRC grant EP/M01326X/1, and R.M.-S. EPSRC grants EP/M01326X/1, EP/T00097X/1 and EP/R018634/1.

Author information

Authors and Affiliations

  1. SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow, UK

    Hunter Gabbard, Chris Messenger & Ik Siong Heng

  2. School of Computing Science, University of Glasgow, Glasgow, UK

    Francesco Tonolini & Roderick Murray-Smith

Authors
  1. Hunter Gabbard
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Contributions

All authors contributed equally to the work of this manuscript. The work was primarily supervised by C.M., I.S.H. and R.M.-S.

Corresponding author

Correspondence to Hunter Gabbard.

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The authors declare no competing interests.

Additional information

Peer review information Nature Physics thanks Danilo Jimenez Rezende, Rory Smith and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 The cost as a function of training epoch.

The cost as a function of training epoch. We show the total cost function (magenta) together with its component parts: the KL-divergence component (purple) and the reconstruction component (blue) which are simply summed to obtain the total. The dark curves correspond to the cost computed on each batch of training data and the lighter curves represent the cost when computed on independent validation data. The close agreement between training and validation cost values indicates that the network is not overfitting to the training data. The change in behaviour of the cost between 102 and 3 × 102 epochs is a consequence of gradually introducing the KL cost term contribution via an annealing process.

Extended Data Table 1 The VItamin network hyper-parameters.

The VItamin network hyper-parameters. Dashed lines ‘—’ indicate that convolutional layers are shared between all 3 networks. Each column from left to right is representative of the \({r}_{{\theta }_{1}}(z| y)\), \({r}_{{\theta }_{2}}(x| y,z)\) and qϕ(z∣x, y) networks and each row denotes a different layer. a The shape of the data [one-dimensional dataset length, No. channels]. b One-dimensional convolutional filter with arguments (filter size, No. channels, No. filters). c L2 regularization function applied to the kernel weights matrix. textrmd The activation function used. e Striding layer with arguments (stride length). f Take the multichannel output of the previous layer and reshape it into a one-dimensional vector. g Append the argument to the current dataset. h Fully connected layer with arguments (input size, output size). i The \({r}_{{\theta }_{1}}\) output has size [latent space dimension, No. modes, No. parameters defining each component per dimension]. j Different activations are used for different parameters. For the scaled parameter means we use sigmoids and for log-variances we use negative ReLU functions. k The \({r}_{{\theta }_{2}}\) output has size [physical space dimension+additional cyclic dimensions, No. parameters defining the distribution per dimension]. The additional cyclic dimensions account for the 2 parameters where each cyclic parameter is represented in the abstract 2D plane. l The qϕ output has size [latent space dimension, No. parameters defining the distribution per dimension].

Extended Data Table 2 Benchmark sampler configuration parameters.

Benchmark sampler configuration parameters. Columns are denoted from left to right as the sampler name and the run configuration parameters for that sampler. Each row is representative of a different sampler. Parameter values were chosen based on a combination of their recommended default parameters11 and private communication with the Bilby development team.

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Gabbard, H., Messenger, C., Heng, I.S. et al. Bayesian parameter estimation using conditional variational autoencoders for gravitational-wave astronomy. Nat. Phys. 18, 112–117 (2022). https://doi.org/10.1038/s41567-021-01425-7

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