# Learning orbital dynamics of binary black hole systems from gravitational wave measurements

arXiv: https://arxiv.org/abs/2102.12695 · HTML: https://mlsanity.com/paper/2102.12695/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 68 references that are in the map.
- First posted on arXiv 25 Feb 2021.

## Builds on (most cited first, 10 of 10)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1708.00588/) (2017)
- [Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction](https://mlsanity.com/paper/2007.04439/) (2020)
- [ANODE: Unconditionally Accurate Memory-Efficient Gradients for Neural ODEs](https://mlsanity.com/paper/1902.10298/) (2019)
- [Bayesian Neural Ordinary Differential Equations](https://mlsanity.com/paper/2012.07244/) (2020)
- [NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data](https://mlsanity.com/paper/1908.03190/) (2019)
- [Numerical Aspects for Approximating Governing Equations Using Data](https://mlsanity.com/paper/1809.09170/) (2018)
- [Fast prediction and evaluation of gravitational waveforms using surrogate models](https://mlsanity.com/paper/1308.3565/) (2013)

## Built on by (most cited first, 6 of 6)

- [Gaussian process learning of nonlinear dynamics](https://mlsanity.com/paper/2312.12193/) (2023)
- [MOT-SR: Multi-Objective Tool-Augmented Scientific Equation Discovery with Large Language Models](https://mlsanity.com/paper/2607.29561/) (2026)
- [Neural Astrophysical Wind Models](https://mlsanity.com/paper/2306.11666/) (2023)
- [Finding the Underlying Viscoelastic Constitutive Equation via Universal Differential Equations and Differentiable Physics](https://mlsanity.com/paper/2501.00556/) (2024)
- [Bayesian Symbolic Regression for Missing Physics](https://mlsanity.com/paper/2603.14918/) (2026)
- [Experimental Design for Missing Physics](https://mlsanity.com/paper/2604.01231/) (2026)

## Abstract (arXiv)

We introduce a gravitational waveform inversion strategy that discovers mechanical models of binary black hole (BBH) systems. We show that only a single time series of (possibly noisy) waveform data is necessary to construct the equations of motion for a BBH system. Starting with a class of universal differential equations parameterized by feed-forward neural networks, our strategy involves the construction of a space of plausible mechanical models and a physics-informed constrained optimization within that space to minimize the waveform error. We apply our method to various BBH systems including extreme and comparable mass ratio systems in eccentric and non-eccentric orbits. We show the resulting differential equations apply to time durations longer than the training interval, and relativistic effects, such as perihelion precession, radiation reaction, and orbital plunge, are automatically accounted for. The methods outlined here provide a new, data-driven approach to studying the dynamics of binary black hole systems.