Probing the baryonic--dark matter connection in galaxy clusters using X-rays with gated recurrent unit neural networks

Precise mass measurements are essential for cosmology, but traditional hydrostatic equilibrium (HSE) methods are prone to bias, particularly in dynamically disturbed systems. In this work, we introduce a deep learning approach based on a novel gated recurrent unit (GRU) that predicts the total three-dimensional mass profiles of galaxy clusters directly from the spherically symmetric radial profiles of the intracluster medium (ICM), including temperature, density, pressure, and enclosed gas mass. Treating these radial profiles as sequential data allows the GRU to capture physically motivated dependencies across radii while naturally handling profiles with different numbers of radial bins. We trained and validated our model on high-resolution hydrodynamical simulations from þethree, achieving a 1σ scatter of sim5% in cluster mass predictions from idealised three-dimensional profiles over most of the cluster region, which is substantially lower than what would be obtained with conventional HSE mass estimates. The model also provides robust radius-dependent uncertainty estimates, while observational uncertainties can be incorporated through a Monte Carlo approach. Our algorithm demonstrates robustness against variations in data quality and cluster morphology. We further demonstrate that the model generalises well across independent hydrodynamical simulation suites (GIZMO-SIMBA and GADGET-X) when trained jointly, recovering unbiased mass profiles in both cases. Feature importance analysis shows that enclosed gas mass dominates the predictions, with pressure and temperature shaping the radial structure, reflecting physically meaningful mass assembly. To examine mass estimates for observational data, we applied the GRU approach to the REXCESS and X-COP galaxy cluster samples observed with XMM-Newton. The GRU and HSE mass estimates show close agreement for the lower-mass REXCESS sample, while HSE masses are systematically lower than the GRU predictions for the higher-mass X-COP sample, an offset consistent with hydrostatic mass bias. This approach provides a powerful data-driven framework for precise and unbiased cluster mass estimation, bridging simulations and observations to improve the accuracy of cluster-based cosmological studies. Moreover, it can be readily extended to Sunyaev–Zel'dovich and optical datasets, making it a versatile tool for multi-wavelength cluster mass inference.