CR − M scaling relation at z = 0.21 in CAMELS/IllustrisTNG simulations and in their LDL surrogate, for the fiducial model. These plots were done with the CV test set: 6 boxes with a volume of (50h⁻¹ Mpc)³ each. Left: Direct comparison of hydrodynamical simulated clusters (blue crosses) and their LDL counterpart (red crosses). The plain lines and shaded region indicate respectively the mean relation and scatter for each method. The scaling relation is well reproduced by the LDL method. Middle: Deviation of hydrodynamical values and LDL prediction to the mean relation (blue points), and the 1:1 slope (dashed line). The strong correlation indicates that the LDL recovers more than just a scaling relation: it can learn why a specific cluster is over or under luminous, given its mass, thanks to its 3D DM distribution. Right: Histogram of CR prediction errors. At the cluster level, the LDL prediction appears unbiased, and with a scatter of 0.12 dex, smaller than the natural scatter of the CR − M relation.