# Fast, accurate, and differentiable: a neural-network surrogate for NRSur7dq4 precessing binary black hole waveforms

arXiv: https://arxiv.org/abs/2607.24960 · HTML: https://mlsanity.com/paper/2607.24960/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 113 references that are in the map.
- First posted on arXiv 27 Jul 2026.

## Builds on (most cited first, 24 of 24)

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- [BlackJAX: Composable Bayesian inference in JAX](https://mlsanity.com/paper/2402.10797/) (2024)
- [Real-time gravitational-wave inference for binary neutron stars using machine learning](https://mlsanity.com/paper/2407.09602/) (2024)
- [Learning Bayesian posteriors with neural networks for gravitational-wave inference](https://mlsanity.com/paper/1909.05966/) (2019)
- [Group equivariant neural posterior estimation](https://mlsanity.com/paper/2111.13139/) (2021)
- [Fast prediction and evaluation of gravitational waveforms using surrogate models](https://mlsanity.com/paper/1308.3565/) (2013)
- [Reduced-order modeling with artificial neurons for gravitational-wave inference](https://mlsanity.com/paper/1811.05491/) (2018)
- [Autoencoder-driven Spiral Representation Learning for Gravitational Wave Surrogate Modelling](https://mlsanity.com/paper/2107.04312/) (2021)
- [Deep Residual Error and Bag-of-Tricks Learning for Gravitational Wave Surrogate Modeling](https://mlsanity.com/paper/2203.08434/) (2022)
- [A Deep Learning Powered Numerical Relativity Surrogate for Binary Black Hole Waveforms](https://mlsanity.com/paper/2412.06946/) (2024)

## Abstract (arXiv)

We present a neural network surrogate model that emulates the NRSur7dq4 gravitational waveform model for precessing binary black hole mergers. The surrogate decomposes the waveform into constituent quantities and trains an independent multilayer perceptron (MLP) for each. We validate the surrogate against NRSur7dq4 on 10,000 waveforms spanning its full parameter space (1 ≤ q ≤ 4, |chiA,B| ≤ 0.8). For representative total masses between 60 and 300 M_odot, median sky-averaged frequency-domain mismatches range from 8.0 × 10-5 to 1.7 × 10-4, with 95th percentiles below 10-3. On an NVIDIA L40S GPU the JAX surrogate evaluates a single waveform in about 1 ms end-to-end, roughly 10 times faster than the LALSimulation C implementation of NRSur7dq4, and sustains about 140 times the LALSimulation throughput at batch size 64, making it well suited for both low-latency parameter-estimation samplers and large-scale waveform generation. The full NRSur7dq4 NN waveform-to-likelihood pipeline is implemented in JAX and is differentiable. This is the first neural-network surrogate of a precessing numerical-relativity waveform model to combine validated NR-faithful accuracy with a fully differentiable, GPU-accelerated inference pipeline, enabling gradient-based inference approaches via automatic differentiation including Fisher information matrices, GPU-accelerated nested sampling, gradient-based MCMC and importance sampling.