# Complete parameter inference for GW150914 using deep learning

arXiv: https://arxiv.org/abs/2008.03312 · HTML: https://mlsanity.com/paper/2008.03312/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Aug 2020.

## Built on by (most cited first, 25 of 25)

- [Flow Matching for Scalable Simulation-Based Inference](https://mlsanity.com/paper/2305.17161/) (2023)
- [Real-time gravitational-wave science with neural posterior estimation](https://mlsanity.com/paper/2106.12594/) (2021)
- [Rediscovering orbital mechanics with machine learning](https://mlsanity.com/paper/2202.02306/) (2022)
- [Learning Robust Statistics for Simulation-based Inference under Model Misspecification](https://mlsanity.com/paper/2305.15871/) (2023)
- [Investigating the Impact of Model Misspecification in Neural Simulation-based Inference](https://mlsanity.com/paper/2209.01845/) (2022)
- [Neural Importance Sampling for Rapid and Reliable Gravitational-Wave Inference](https://mlsanity.com/paper/2210.05686/) (2022)
- [Real-time gravitational-wave inference for binary neutron stars using machine learning](https://mlsanity.com/paper/2407.09602/) (2024)
- [A deep generative model for probabilistic energy forecasting in power systems: normalizing flows](https://mlsanity.com/paper/2106.09370/) (2021)
- [Group equivariant neural posterior estimation](https://mlsanity.com/paper/2111.13139/) (2021)
- [Advances in Machine and Deep Learning for Modeling and Real-time Detection of Multi-Messenger Sources](https://mlsanity.com/paper/2105.06479/) (2021)
- [Arbitrary Marginal Neural Ratio Estimation for Simulation-based Inference](https://mlsanity.com/paper/2110.00449/) (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)
- [Comparison of Affine and Rational Quadratic Spline Coupling and Autoregressive Flows through Robust Statistical Tests](https://mlsanity.com/paper/2302.12024/) (2023)
- [Swift sky localization of gravitational waves using deep learning seeded importance sampling](https://mlsanity.com/paper/2111.00833/) (2021)
- [Bayesian evidence estimation from posterior samples with normalizing flows](https://mlsanity.com/paper/2404.12294/) (2024)
- [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)
- [Flexible Gravitational-Wave Parameter Estimation with Transformers](https://mlsanity.com/paper/2512.02968/) (2025)
- [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)
- [When Attention Collapses: Residual Evidence Modeling for Compositional Inference](https://mlsanity.com/paper/2605.02323/) (2026)
- [Binary Black Hole Parameter Estimation with Hybrid CNN-Transformer Neural Networks](https://mlsanity.com/paper/2606.13941/) (2026)

## Abstract (arXiv)

The LIGO and Virgo gravitational-wave observatories have detected many exciting events over the past five years. As the rate of detections grows with detector sensitivity, this poses a growing computational challenge for data analysis. With this in mind, in this work we apply deep learning techniques to perform fast likelihood-free Bayesian inference for gravitational waves. We train a neural-network conditional density estimator to model posterior probability distributions over the full 15-dimensional space of binary black hole system parameters, given detector strain data from multiple detectors. We use the method of normalizing flows---specifically, a neural spline normalizing flow---which allows for rapid sampling and density estimation. Training the network is likelihood-free, requiring samples from the data generative process, but no likelihood evaluations. Through training, the network learns a global set of posteriors: it can generate thousands of independent posterior samples per second for any strain data consistent with the prior and detector noise characteristics used for training. By training with the detector noise power spectral density estimated at the time of GW150914, and conditioning on the event strain data, we use the neural network to generate accurate posterior samples consistent with analyses using conventional sampling techniques.