astronomy/ai produced the result/Monthly Notices of the Royal Astronomical Society 2023 · v2
Neural networks speed up forecasts of what gravitational wave detections LISA will catch
Researchers trained two small neural networks to stand in for slow calculations of how loud a space-based gravitational wave signal would be, and used them to work out what a future survey of such signals could reveal.
spectrum · one line per step, placed by what the step does · bright lines used AI
Rapid determination of LISA sensitivity to extreme mass ratio inspirals with machine learning
Monthly Notices of the Royal Astronomical Society, 2023
doi:10.1093/mnras/stad1397 · record aix-00097 v2 · checked 2026-10-08
- AI was for
- Simulation surrogate, Property prediction
- Model family
- Multilayer perceptron
- Checked by
- Held-out208 tested
- Code
- available
The finding the paper is about came from the AI.
What this research was about
Gravitational waves are tiny ripples in space and time, given off when very heavy objects move around each other. One source of them is an extreme mass ratio inspiral, or EMRI: a small compact object, such as a stellar remnant, spiralling slowly into a massive black hole far heavier than itself. These signals are a target for LISA, a planned space-based detector. A detector only picks up signals that are loud enough against its own noise, and that loudness is usually summarised by a signal-to-noise ratio. Working out that ratio means modelling the waveform in detail, which is slow.
The slowness matters because astronomers want to go from a handful of detections to statements about the whole underlying population, such as how black hole masses are distributed. To do that honestly, you must account for the fact that the detector misses the quiet sources. That correction, known as a selection function, is the fraction of a given population that would be loud enough to detect, and estimating it normally means repeating the slow loudness calculation an enormous number of times.
Where AI came in
The researchers trained two multilayer perceptrons, a basic kind of neural network, from scratch. The first learned to take the parameters describing an EMRI and return its signal-to-noise ratio, using a training set of ratios computed the slow way from simulated waveforms at a fixed distance. In place of running a waveform simulation, the network returns an estimate directly; the record notes it can produce 10^5 estimates in under 0.1 seconds.
The second network learned the selection function itself, mapping the numbers that describe a candidate population to the fraction of it that would be detectable. Its training data came from random sampling using the first network. During the population analysis, this second network was called each time the statistical sampler needed the correction, replacing the conventional calculation. The reported precisions on the population properties, drawn from a simulated catalogue of 116 detections, come out of this arrangement, and a consistency test across 208 simulated populations was run to check the results.
Written by AIxSci from the checked record below, to give context for readers outside the field. It is not part of the record.
The work
Technical · from the record
The authors replaced the expensive signal-to-noise ratio calculation for extreme mass ratio inspiral (EMRI) gravitational wave signals with a multilayer perceptron trained on precomputed SNRs, and then trained a second multilayer perceptron to map population hyperparameters directly to the detectable fraction of a population. Using this selection-function estimator inside hierarchical Bayesian population inference, they analysed a simulated catalogue of 116 EMRI detections and reported that the massive black hole mass function slope is measured to 8.8% precision, the compact object mass function slope to 4.6%, the width of the spin magnitude distribution to 10% and the event rate to 12%. A probability–probability test over 208 simulated populations showed hyperposteriors consistent with the expected confidence intervals when their neural network correction was used, and inconsistent when selection effects were ignored or corrected using linear interpolation.
How AI was used
Two multilayer perceptrons were trained from scratch in PyTorch. The first takes EMRI source parameters and returns the optimal matched-filter signal-to-noise ratio, trained on a dataset of SNRs computed from FastEMRIWaveforms waveforms distributed uniformly in the EMRI parameter space at a fixed luminosity distance of 1 Gpc, with orbital phases dropped and distance scaling applied after interpolation; it was trained with an L1 loss, with inputs rescaled to a unit normal and the Adam optimiser, and network depth increased manually until overfitting appeared. The second network interpolates the selection function directly over population hyperparameters, trained on stochastic Monte Carlo selection function estimates produced using the first network and distributed uniformly in the hyperparameter space. During hierarchical inference the selection function network is evaluated, in vectorised form, once per hyperlikelihood call within a nessai nested sampling run. For comparison, grid-based nearest neighbour, linear and cubic spline interpolators were constructed on a regular grid of SNRs, and a selection function MLP was also trained on linear-interpolator SNR estimates.
The shape of the work
Structural · the record, drawn
no AI
Generate EMRI waveforms and compute SNRs for training data
Numerical or physics simulation, including where a learned surrogate replaces it.
we generate 10yr EMRI waveforms in the time domain with a sampling rate of 0.1Hzwhere the paper describes this · verbatim
AI
Train SNR interpolator network
Fitting model parameters, including fine-tuning an existing model. The AI stood in for simulation.
Using a neural network trained on a data set of SNRs distributed uniformly in the EMRI parameter spacewhere the paper describes this · verbatim
AI
Predict SNRs and estimate selection function by Monte Carlo
Running a trained model over new data to predict, classify or score. The AI stood in for simulation.
This network is capable of producing 105 SNR estimates in <0.1swhere the paper describes this · verbatim
AI
Train selection function network
Fitting model parameters, including fine-tuning an existing model. The AI stood in for conventional algorithm.
A second MLP trained prior to sampling can be used to interpolate directly over α(𝝀).where the paper describes this · verbatim
no AI
Simulate EMRI catalogue and event posteriors
Obtaining raw data, whether by measurement, download or retrieval.
After discarding the signals too faint to be detected, we obtain a catalogue of 116 EMRIs.where the paper describes this · verbatim
AI
Sample hyperposterior with selection correction
Running a trained model over new data to predict, classify or score. The AI stood in for conventional algorithm.
We sample the hyperposterior Eq. (2) with the nessai nested sampler, using default settings.where the paper describes this · verbatim
no AI
Probability–probability consistency test
Testing outputs against ground truth.
we opt for the probability–probability (P–P) plot testwhere the paper describes this · verbatim
What the record says
Technical · every part carries its own basis
+ in the paper~ our reading− not reported
How to read the quotations. A quotation shows where the paper describes something. It does not quote every value beside it: one passage locates a part of the work, and values without their own quotation are our reading of that passage.
The reported population-inference precisions depend on the neural network selection function; the paper's quantitative results are produced through the two MLPs
We opt for the multilayer perceptron (MLP) algorithm as it fits this specification.where the paper describes this · verbatim
we globally evaluate hyperposterior consistency by simulating 208 EMRI populations and checking the resultswhere the paper describes this · verbatim
(ii) the trained neural networks used to produce the results presented, along with the code required to use themwhere the paper describes this · verbatim
What this paper did not report
Technical · absence is published deliberately
- ComputeThe hardware or time used is not stated.
- Version of SNR interpolator MLPWhich version of the model was used is not stated.
- Version of Selection function MLPWhich version of the model was used is not stated.
About this article
Record aix-00097, version 2, checked by a person on 2026-10-08. The record describes the paper; it does not assess whether the paper's findings are right. The paper is published under CC-BY; quotations are at most 25 words. How we work · Report an error