Model-Agnostic Population Inference for Gravitational-Wave Astronomy: From LIGO to LISA

TL;DR

This work tackles the challenge of recovering intrinsic gravitational-wave source populations from biased, noisy catalogs. It introduces a Correlated Compound Mixture Density Network (CCMDN) trained with amortized variational inference using normalizing flows to learn population hyperparameters $\bm{\Lambda}$ while accounting for detector selection via $\alpha(\bm{\Lambda})$. The method is validated on realistic LISA SMBH mocks and real GWTC-3 BBH data, demonstrating accurate recovery of joint distributions and absolute merger rates across both space- and ground-/space-based detector regimes. Compared with traditional parametric MCMC, the nonparametric CCMDN remains robust under model misspecification and offers substantial computational efficiency, making it well suited for next-generation, multi-band gravitational-wave surveys.

Abstract

Inferring the intrinsic population of compact binary mergers is complicated by detector selection biases and measurement uncertainties. Traditional parametric methods are limited by the need to presuppose functional forms, introducing model-dependent biases. To overcome these limitations, we introduce an inference framework powered by deep generative modeling. We develop a flexible, data-driven population model using a Correlated Compound-Mixture Density Network. This architecture integrates mixture models to handle multimodality, Gaussian copulas for parameter dependencies, and a library of flexible marginal distributions. The network is trained to approximate the posterior distribution of the population's hyperparameters using amortized variational inference with Normalizing Flows on catalogs of gravitational-wave events. We demonstrate the framework's capabilities in two distinct regimes. First, using simulated catalogs of supermassive black hole binary mergers for the Laser Interferometer Space Antenna (LISA), we show that the method accurately recovers complex three-dimensional distributions and absolute merger rates from sparse datasets, effectively correcting for selection effects and measurement uncertainties. Second, we validate the framework on real observational data from the LIGO-Virgo-KAGRA GWTC-3 catalog, successfully inferring the population of stellar-mass binary black holes using an injection-based selection effect correction. Our results confirm that the method is robust, scalable, and applicable across different detector sensitivities and source populations.

Figures (9)

• Figure 1: Technical Architecture of the Flow-Guided Correlated Compound Mixture Density Network. The network processes the latent variable $z$ (Column 1) via an NF, unpacking it (Column 2) into parameters for specific mixture components (Column 3: Kumaraswamy, Truncated Normal, Truncated Pareto). The vertical "Data Bus" emphasizes that the observed data $X$ feeds directly into the physics-based mixture components. Finally, these components are aggregated (Column 4) to compute the log-likelihood. Note the clear separation between the neural variational guide (green) and the physics-based mixture model (orange).
• Figure 2: Validation of the density estimation network on the toy model (no selection effects). The corner plot compares the true intrinsic population (orange dashed lines/points) with the distribution learned by the network (blue contours/shaded regions).
• Figure 3: Projected distributions of the intrinsic ($N_{\text{int}}=50$) and detectable ($N_{\text{obs}}=42$) supermassive black hole binary merger populations in the LISA parameter space. The detectable events (dark slate blue) are distinguished from the undetectable events (plum). (a) Primary mass versus redshift. (b) Primary mass versus mass ratio. (c) Redshift versus mass ratio. Error bars represent 90% credible intervals derived from the Fisher Information Matrix.
• Figure 4: Scalability validation across LISA catalog sizes ($N_{\text{int}} \in \{20, 50, 200, 500\}$). Comparison between True Intrinsic distribution and BNN Reconstruction. The contours progressively refine as data volume increases, demonstrating data-adaptive capability.
• Figure 5: Validation of event count inference. Each panel shows posteriors for intrinsic count $N_{\text{int}}$ (blue) and expected observed count $N_{\text{obs}}$ (green), compared to ground truths (red lines). The framework accurately recovers intrinsic counts across all catalog sizes.