# Gravitational-wave parameter estimation with autoregressive neural network flows

arXiv: https://arxiv.org/abs/2002.07656 · HTML: https://mlsanity.com/paper/2002.07656/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Feb 2020.

## Built on by (most cited first, 19 of 19)

- [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)
- [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)
- [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)
- [Comparison of Affine and Rational Quadratic Spline Coupling and Autoregressive Flows through Robust Statistical Tests](https://mlsanity.com/paper/2302.12024/) (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)
- [Boosting the Efficiency of Parametric Detection with Hierarchical Neural Networks](https://mlsanity.com/paper/2207.11583/) (2022)
- [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)
- [Machine-Learning Love: classifying the equation of state of neutron stars with Transformers](https://mlsanity.com/paper/2210.08382/) (2022)
- [Towards a robust and reliable deep learning approach for detection of compact binary mergers in gravitational wave data](https://mlsanity.com/paper/2306.11797/) (2023)
- [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 the use of autoregressive normalizing flows for rapid likelihood-free inference of binary black hole system parameters from gravitational-wave data with deep neural networks. A normalizing flow is an invertible mapping on a sample space that can be used to induce a transformation from a simple probability distribution to a more complex one: if the simple distribution can be rapidly sampled and its density evaluated, then so can the complex distribution. Our first application to gravitational waves uses an autoregressive flow, conditioned on detector strain data, to map a multivariate standard normal distribution into the posterior distribution over system parameters. We train the model on artificial strain data consisting of IMRPhenomPv2 waveforms drawn from a five-parameter (m1, m2, φ0, tc, dL) prior and stationary Gaussian noise realizations with a fixed power spectral density. This gives performance comparable to current best deep-learning approaches to gravitational-wave parameter estimation. We then build a more powerful latent variable model by incorporating autoregressive flows within the variational autoencoder framework. This model has performance comparable to Markov chain Monte Carlo and, in particular, successfully models the multimodal φ0 posterior. Finally, we train the autoregressive latent variable model on an expanded parameter space, including also aligned spins (chi1z, chi2z) and binary inclination θJN, and show that all parameters and degeneracies are well-recovered. In all cases, sampling is extremely fast, requiring less than two seconds to draw 104 posterior samples.