# Swift sky localization of gravitational waves using deep learning seeded importance sampling

arXiv: https://arxiv.org/abs/2111.00833 · HTML: https://mlsanity.com/paper/2111.00833/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 49 references that are in the map.
- First posted on arXiv 1 Nov 2021.

## Builds on (most cited first, 11 of 11)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Real-time gravitational-wave science with neural posterior estimation](https://mlsanity.com/paper/2106.12594/) (2021)
- [Bayesian parameter estimation using conditional variational autoencoders for gravitational-wave astronomy](https://mlsanity.com/paper/1909.06296/) (2019)
- [Multivariate Uncertainty in Deep Learning](https://mlsanity.com/paper/1910.14215/) (2019)
- [Complete parameter inference for GW150914 using deep learning](https://mlsanity.com/paper/2008.03312/) (2020)
- [Deep Neural Networks to Enable Real-time Multimessenger Astrophysics](https://mlsanity.com/paper/1701.00008/) (2016)
- [Learning Bayesian posteriors with neural networks for gravitational-wave inference](https://mlsanity.com/paper/1909.05966/) (2019)
- [Lightning-Fast Gravitational Wave Parameter Inference through Neural Amortization](https://mlsanity.com/paper/2010.12931/) (2020)
- [Convolutional neural networks: a magic bullet for gravitational-wave detection?](https://mlsanity.com/paper/1904.08693/) (2019)

## Built on by (most cited first, 4 of 4)

- [Neural Importance Sampling for Rapid and Reliable Gravitational-Wave Inference](https://mlsanity.com/paper/2210.05686/) (2022)
- [Accelerated Bayesian parameter estimation and model selection for gravitational waves with normalizing flows](https://mlsanity.com/paper/2410.21076/) (2024)
- [Neuromorphic Intelligence](https://mlsanity.com/paper/2509.11940/) (2025)
- [Recent Advances in Simulation-based Inference for Gravitational Wave Data Analysis](https://mlsanity.com/paper/2507.11192/) (2025)

## Abstract (arXiv)

Fast, highly accurate, and reliable inference of the sky origin of gravitational waves would enable real-time multi-messenger astronomy. Current Bayesian inference methodologies, although highly accurate and reliable, are slow. Deep learning models have shown themselves to be accurate and extremely fast for inference tasks on gravitational waves, but their output is inherently questionable due to the blackbox nature of neural networks. In this work, we join Bayesian inference and deep learning by applying importance sampling on an approximate posterior generated by a multi-headed convolutional neural network. The neural network parametrizes Von Mises-Fisher and Gaussian distributions for the sky coordinates and two masses for given simulated gravitational wave injections in the LIGO and Virgo detectors. We generate skymaps for unseen gravitational-wave events that highly resemble predictions generated using Bayesian inference in a few minutes. Furthermore, we can detect poor predictions from the neural network, and quickly flag them.