A normalizing flow approach for the inference of star cluster properties from unresolved broadband photometry

I. Comparison to spectral energy distribution fitting

¹ Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Albert-Ueberle-Straße 2, 69120 Heidelberg, Germany
² Universität Heidelberg, Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, INF 225, 69120 Heidelberg, Germany
³ Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, 06000, Nice, France
⁴ Instituto de Astronomía, Universidad Nacional Autónoma de México, Unidad Académica en Ensenada, Km 103 Carr. Tijuana–Ensenada, Ensenada, B.C., C.P. 22860, Mexico
⁵ INAF – Arcetri Astrophysical Observatory, Largo E. Fermi 5, I-50125, Florence, Italy
⁶ Department of Physics and Astronomy, University of Wyoming, Laramie, WY 82071, USA
⁷ Research School of Astronomy and Astrophysics, Australian National University, Canberra, ACT 2611, Australia
⁸ Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, MD 21218, USA
⁹ Space Telescope Science Institute, Baltimore, MD, USA
¹⁰ Sub-department of Astrophysics, Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 1 August 2025
Accepted: 2 December 2025

Abstract

Context. Estimating properties of star clusters from unresolved broadband photometry is a challenging problem that is classically tackled using spectral energy distribution (SED) fitting methods that are based on simple stellar population models. However, grid-based methods suffer from computational limitations. Because of their exponential scaling, they can become intractable when the number of inference parameters grows. In addition, nuisance parameters in the model can make the computation of the likelihood function intractable. These limitations can be overcome by modern generative deep learning methods that offer flexible and powerful tools for modeling high-dimensional posterior distributions and fast inference from learned data.

Aims. We present a normalizing flow approach for the inference of cluster age, mass, and reddening parameters from Hubble Space Telescope broadband photometry. In particular, we explore our network’s behavior when dealing with an inference problem that has been analyzed in previous works.

Methods. We used the SED modeling code CIGALE to create a dataset of synthetic photometric observations for 5 × 10⁶ mock star clusters. Subsequently, this dataset was used to train a coupling-based flow in the form of a conditional invertible neural network to predict posterior probability distributions for cluster age, mass, and reddening from photometric observations.

Results. We predicted cluster parameters for the Physics at High Angular resolution in Nearby GalaxieS (PHANGS) Data Release 3 catalog. To evaluate the capabilities of the network, we compared our results to the publicly available PHANGS estimates and found that the estimates agree reasonably well.

Conclusions. We demonstrate that normalizing flow methods can be a viable tool for the inference of cluster parameters, and argue that this approach is especially useful when nuisance parameters make the computation of the likelihood intractable and in scenarios that require efficient density estimation.