# Learning Bayesian posteriors with neural networks for gravitational-wave inference

arXiv: https://arxiv.org/abs/1909.05966 · HTML: https://mlsanity.com/paper/1909.05966/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2019.

## Built on by (most cited first, 18 of 18)

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- [Inference-optimized AI and high performance computing for gravitational wave detection at scale](https://mlsanity.com/paper/2201.11133/) (2022)
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- [Swift sky localization of gravitational waves using deep learning seeded importance sampling](https://mlsanity.com/paper/2111.00833/) (2021)
- [AI and extreme scale computing to learn and infer the physics of higher order gravitational wave modes of quasi-circular, spinning, non-precessing binary black hole mergers](https://mlsanity.com/paper/2112.07669/) (2021)
- [Hyperparameter optimization of hp-greedy reduced basis for gravitational wave surrogates](https://mlsanity.com/paper/2310.15143/) (2023)
- [Accelerated Bayesian parameter estimation and model selection for gravitational waves with normalizing flows](https://mlsanity.com/paper/2410.21076/) (2024)
- [A Deep Learning Powered Numerical Relativity Surrogate for Binary Black Hole Waveforms](https://mlsanity.com/paper/2412.06946/) (2024)
- [Flexible Gravitational-Wave Parameter Estimation with Transformers](https://mlsanity.com/paper/2512.02968/) (2025)
- [Machine-Learning Love: classifying the equation of state of neutron stars with Transformers](https://mlsanity.com/paper/2210.08382/) (2022)
- [Enhancing the reliability of machine learning for gravitational wave parameter estimation with attention-based models](https://mlsanity.com/paper/2501.10486/) (2025)
- [Enhanced uncertainty quantification variational autoencoders for the solution of Bayesian inverse problems](https://mlsanity.com/paper/2502.13105/) (2025)
- [Recent Advances in Simulation-based Inference for Gravitational Wave Data Analysis](https://mlsanity.com/paper/2507.11192/) (2025)
- [Fast, accurate, and differentiable: a neural-network surrogate for NRSur7dq4 precessing binary black hole waveforms](https://mlsanity.com/paper/2607.24960/) (2026)

## Abstract (arXiv)

We seek to achieve the Holy Grail of Bayesian inference for gravitational-wave astronomy: using deep-learning techniques to instantly produce the posterior p(θ|D) for the source parameters θ, given the detector data D. To do so, we train a deep neural network to take as input a signal + noise data set (drawn from the astrophysical source-parameter prior and the sampling distribution of detector noise), and to output a parametrized approximation of the corresponding posterior. We rely on a compact representation of the data based on reduced-order modeling, which we generate efficiently using a separate neural-network waveform interpolant [A. J. K. Chua, C. R. Galley & M. Vallisneri, Phys. Rev. Lett. 122, 211101 (2019)]. Our scheme has broad relevance to gravitational-wave applications such as low-latency parameter estimation and characterizing the science returns of future experiments. Source code and trained networks are available online at https://github.com/vallis/truebayes.