FastEMRIWaveforms

Overview

FastEMRIWaveforms (FEW) generates fully relativistic extreme mass-ratio inspiral (EMRI) waveforms quickly enough for LISA data analysis — seconds on a CPU, and faster still on a GPU. The framework is modular: a trajectory module evolves the inspiral, an amplitude module supplies the mode amplitudes, and a summation module assembles the waveform. Modules can be swapped to trade accuracy against speed.

The Kerr eccentric equatorial produces waveforms that faithfully match (slow to generate) reference waveforms with a worst case overlap of $∼10^{−5}$ for inspirals with initial eccentricity $e_0 \le 0.85$. The figure below shows an example of the waveform produced by the model.

Installation

The CPU build installs from PyPI:

pip install fastemriwaveforms

GPU acceleration requires a build matched to your CUDA toolkit; see the full documentation for the right package and the supported model names.

Usage

Generate a waveform from a high-level model. Parameter names and conventions are detailed in the FEW documentation:

from few.waveform import GenerateEMRIWaveform

wave = GenerateEMRIWaveform("KerrEccEqFlux")

h = wave(
    M=1e6,      # primary mass (solar masses)
    mu=1e1,     # secondary mass (solar masses)
    a=0.5,      # primary spin
    p0=12.0,    # initial semi-latus rectum
    e0=0.3,     # initial eccentricity
    x0=1.0,     # cosine of the inclination
    dist=1.0,   # luminosity distance (Gpc)
    dt=10.0,    # time step (s)
    T=1.0,      # observation time (years)
)

h is the complex strain time series; take its real and imaginary parts for the two polarisations.

Examples

The documentation includes tutorial notebooks covering trajectory generation, individual modules, and GPU usage.

Authors and contributors

For a full list of people who have contributed to the development of FEW see the CONTRIBUTORS.md file in the repository.

Citing FastEMRIWaveforms

If you use FastEMRIWaveforms in your research, please acknowledge the Toolkit:

FastEMRIWaveforms also requests the following citations:

• Rapid generation of fully relativistic extreme-mass-ratio-inspiral waveform templates for LISA data analysis arXiv Inspire
  BibTeX

  @article{Chua:2020stf,
      author = "Chua, Alvin J. K. and Katz, Michael L. and Warburton, Niels and Hughes, Scott A.",
      title = "{Rapid generation of fully relativistic extreme-mass-ratio-inspiral waveform templates for LISA data analysis}",
      eprint = "2008.06071",
      archivePrefix = "arXiv",
      primaryClass = "gr-qc",
      doi = "10.1103/PhysRevLett.126.051102",
      journal = "Phys. Rev. Lett.",
      volume = "126",
      number = "5",
      pages = "051102",
      year = "2021"
  }

• FastEMRIWaveforms: New tools for millihertz gravitational-wave data analysis arXiv Inspire
  BibTeX

  @article{Katz:2021yft,
      author = "Katz, Michael L. and Chua, Alvin J. K. and Speri, Lorenzo and Warburton, Niels and Hughes, Scott A.",
      title = "{Fast extreme-mass-ratio-inspiral waveforms: New tools for millihertz gravitational-wave data analysis}",
      eprint = "2104.04582",
      archivePrefix = "arXiv",
      primaryClass = "gr-qc",
      doi = "10.1103/PhysRevD.104.064047",
      journal = "Phys. Rev. D",
      volume = "104",
      number = "6",
      pages = "064047",
      year = "2021"
  }

• Fast and Fourier: Extreme Mass Ratio Inspiral Waveforms in the Frequency Domain arXiv Inspire
  BibTeX

  @article{Speri:2023jte,
      author = "Speri, Lorenzo and Katz, Michael L. and Chua, Alvin J. K. and Hughes, Scott A. and Warburton, Niels and Thompson, Jonathan E. and Chapman-Bird, Christian E. A. and Gair, Jonathan R.",
      title = "{Fast and Fourier: Extreme Mass Ratio Inspiral Waveforms in the Frequency Domain}",
      eprint = "2307.12585",
      archivePrefix = "arXiv",
      primaryClass = "gr-qc",
      doi = "10.3389/fams.2023.1266739",
      month = "7",
      year = "2023"
  }

• The Fast and the Frame-Dragging: Efficient waveforms for asymmetric-mass eccentric equatorial inspirals into rapidly-spinning black holes arXiv Inspire
  BibTeX

  @article{Chapman-Bird:2025xtd,
      author = "Chapman-Bird, Christian E. A. and others",
      title = "{Efficient waveforms for asymmetric-mass eccentric equatorial inspirals into rapidly spinning black holes}",
      eprint = "2506.09470",
      archivePrefix = "arXiv",
      primaryClass = "gr-qc",
      doi = "10.1103/scbp-75pf",
      journal = "Phys. Rev. D",
      volume = "112",
      number = "10",
      pages = "104023",
      year = "2025"
  }

See how to cite for further guidance.