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Temperature profiles of the hot galaxy cluster intracluster medium (ICM) havea complex non-linear structure that traditional parametric modelling may failto fully approximate. For this study, we made use of neural networks, for thefirst time, to construct a data-driven non-parametric model of ICM temperatureprofiles. A new deconvolution algorithm was then introduced to uncover the true(3D) temperature profiles from the observed projected (2D) temperatureprofiles. An auto-encoder-inspired neural network was first trained by learninga non-linear interpolatory scheme to build the underlying model of 3Dtemperature profiles in the radial range of [0.02-2] R$_{500}$, using a sparseset of hydrodynamical simulations from the THREE HUNDRED PROJECT. Adeconvolution algorithm using a learning-based regularisation scheme was thendeveloped. The model was tested using high and low resolution input temperatureprofiles, such as those expected from simulations and observations,respectively. We find that the proposed deconvolution and deprojectionalgorithm is robust with respect to the quality of the data, the morphology ofthe cluster, and the deprojection scheme used. The algorithm can recoverunbiased 3D radial temperature profiles with a precision of around 5\% overmost of the fitting range. We apply the method to the first sample oftemperature profiles obtained with XMM{\it -Newton} for the CHEX-MATE projectand compared it to parametric deprojection and deconvolution techniques. Ourwork sets the stage for future studies that focus on the deconvolution of thethermal profiles (temperature, density, pressure) of the ICM and the darkmatter profiles in galaxy clusters, using deep learning techniques inconjunction with X-ray, Sunyaev Zel'Dovich (SZ) and optical datasets.

CHEX-MATE: A non-parametric deep learning technique to deproject and deconvolve galaxy cluster X-ray temperature profiles