# Statistically-informed deep learning for gravitational wave parameter estimation

arXiv: https://arxiv.org/abs/1903.01998 · HTML: https://mlsanity.com/paper/1903.01998/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2019.

## Built on by (most cited first, 14 of 14)

- [Real-time gravitational-wave science with neural posterior estimation](https://mlsanity.com/paper/2106.12594/) (2021)
- [Advances in Machine and Deep Learning for Modeling and Real-time Detection of Multi-Messenger Sources](https://mlsanity.com/paper/2105.06479/) (2021)
- [Interpretable AI forecasting for numerical relativity waveforms of quasi-circular, spinning, non-precessing binary black hole mergers](https://mlsanity.com/paper/2110.06968/) (2021)
- [Inference-optimized AI and high performance computing for gravitational wave detection at scale](https://mlsanity.com/paper/2201.11133/) (2022)
- [Adapting to noise distribution shifts in flow-based gravitational-wave inference](https://mlsanity.com/paper/2211.08801/) (2022)
- [A brief review of contrastive learning applied to astrophysics](https://mlsanity.com/paper/2306.05528/) (2023)
- [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)
- [Pointwise Metrics Mislead: An Evaluation Protocol for Multimodal Inverse Problems](https://mlsanity.com/paper/2605.22891/) (2026)
- [DeepSNR: A deep learning foundation for offline gravitational wave detection](https://mlsanity.com/paper/2207.04749/) (2022)
- [Convolutional Neural Networks for signal detection in real LIGO data](https://mlsanity.com/paper/2402.07492/) (2024)
- [Enhancing the reliability of machine learning for gravitational wave parameter estimation with attention-based models](https://mlsanity.com/paper/2501.10486/) (2025)
- [Recent Advances in Simulation-based Inference for Gravitational Wave Data Analysis](https://mlsanity.com/paper/2507.11192/) (2025)
- [Binary Black Hole Parameter Estimation with Hybrid CNN-Transformer Neural Networks](https://mlsanity.com/paper/2606.13941/) (2026)

## Abstract (arXiv)

We introduce deep learning models to estimate the masses of the binary components of black hole mergers, (m1,m2), and three astrophysical properties of the post-merger compact remnant, namely, the final spin, af, and the frequency and damping time of the ringdown oscillations of the fundamental ℓ=m=2 bar mode, (ωR, ωI). Our neural networks combine a modified textttWaveNet architecture with contrastive learning and normalizing flow. We validate these models against a Gaussian conjugate prior family whose posterior distribution is described by a closed analytical expression. Upon confirming that our models produce statistically consistent results, we used them to estimate the astrophysical parameters (m1,m2, af, ωR, ωI) of five binary black holes: textttGW150914, textttGW170104, textttGW170814, textttGW190521 and textttGW190630. We use textttPyCBC Inference to directly compare traditional Bayesian methodologies for parameter estimation with our deep-learning-based posterior distributions. Our results show that our neural network models predict posterior distributions that encode physical correlations, and that our data-driven median results and 90% confidence intervals are similar to those produced with gravitational wave Bayesian analyses. This methodology requires a single V100 textttNVIDIA GPU to produce median values and posterior distributions within two milliseconds for each event. This neural network, and a tutorial for its use, are available at the textttData and Learning Hub for Science.