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Simulation-based Inference towards Gravitational-wave waveform systematics in Intermediate-Mass Binary Black Holes

Sama Al-Shammari, Alexandre Göttel, Masaki Iwaya, Vivien Raymond

Abstract

Parameter estimation for gravitational-wave signals is computationally demanding due to the high dimensionality of the parameter space and the cost of repeated waveform generation in traditional Bayesian inference. These analyses require on the order of 10^8 likelihood evaluations and waveform generations, resulting in inference times of hours to days per event. Furthermore, discrepancies between waveform models introduce systematic uncertainties that can bias inferred source properties. To address these challenges, we propose a novel framework based on Simulation-based Inference (SBI) and Neural Posterior Estimation (NPE) and apply it to signals from Intermediate-Mass Black Holes (IMBH). In this framework, we train a single amortised neural posterior estimator on a large simulated dataset generated using two state-of-the-art waveform approximants, IMRPhenomXPHM and SEOBNRv5PHM. By treating the waveform model index as a latent variable, the network learns to produce posterior distributions that are naturally marginalized over the discrepancies of the two waveform models. Once trained, the model enables direct posterior sampling in milliseconds per event, eliminating the need for likelihood evaluations while simultaneously accounting for model systematics. We demonstrate that this approach recovers accurate posterior distributions for IMBH signals injected into Gaussian noise, achieving close agreement with traditional nested-sampling results while reducing inference time by several orders of magnitude. Our results show that NPE can robustly incorporate waveform-model systematics within a unified framework, offering a scalable path toward rapid, systematics-aware gravitational-wave inference. Establishing these methods as promising alternatives to classical likelihood-based pipelines for current and future high-mass gravitational-wave observations.

Simulation-based Inference towards Gravitational-wave waveform systematics in Intermediate-Mass Binary Black Holes

Abstract

Parameter estimation for gravitational-wave signals is computationally demanding due to the high dimensionality of the parameter space and the cost of repeated waveform generation in traditional Bayesian inference. These analyses require on the order of 10^8 likelihood evaluations and waveform generations, resulting in inference times of hours to days per event. Furthermore, discrepancies between waveform models introduce systematic uncertainties that can bias inferred source properties. To address these challenges, we propose a novel framework based on Simulation-based Inference (SBI) and Neural Posterior Estimation (NPE) and apply it to signals from Intermediate-Mass Black Holes (IMBH). In this framework, we train a single amortised neural posterior estimator on a large simulated dataset generated using two state-of-the-art waveform approximants, IMRPhenomXPHM and SEOBNRv5PHM. By treating the waveform model index as a latent variable, the network learns to produce posterior distributions that are naturally marginalized over the discrepancies of the two waveform models. Once trained, the model enables direct posterior sampling in milliseconds per event, eliminating the need for likelihood evaluations while simultaneously accounting for model systematics. We demonstrate that this approach recovers accurate posterior distributions for IMBH signals injected into Gaussian noise, achieving close agreement with traditional nested-sampling results while reducing inference time by several orders of magnitude. Our results show that NPE can robustly incorporate waveform-model systematics within a unified framework, offering a scalable path toward rapid, systematics-aware gravitational-wave inference. Establishing these methods as promising alternatives to classical likelihood-based pipelines for current and future high-mass gravitational-wave observations.

Paper Structure

This paper contains 4 sections, 5 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Results
  4. Discussion

Figures (2)

  • Figure 1: Example posterior recovery for an IMBH injection of type IMRPhenomXPHM in Gaussian noise. We compare the waveform-marginalised NPE posterior (trained jointly on IMRPhenomXPHM and SEOBNRv5PHM) against evidence-weighted posteriors obtained from separate bilby--dynesty analyses using each waveform approximant. The agreement demonstrates that the amortised NPE network reproduces the combined waveform-marginalised inference while reducing inference time by orders of magnitude. The results obtained from the bilby--dynesty analysis using IMRPhenomXPHM and the evidence-weighted posterior are indistinuishable throughout the plot due to the low evidence value from the SEOBNRv5PHM analysis.
  • Figure 2: Percentile--percentile (PP) test for the waveform-marginalised NPE network using $10^4$ synthetic injections ($5000$ per waveform family). The diagonal corresponds to perfectly calibrated credible intervals, shaded bands indicate the expected statistical fluctuations under ideal calibration. The close agreement with the diagonal indicates well-calibrated posterior coverage across the 13 inferred parameters.