To obtain w os (r) and w ss (r) in MLS2 using a NN, we employ a similar architecture as for the ML2 model (see Sec. III and Fig. ) with some crucial differences. First, unlike the MP2 correlation energy, the true correlation energy is not scale invariant in general . This allows us contrary to ML2 (see Eq. 9 and the preceding paragraph) to incorporate also density-based features, specifically, the Wigner-Seitz radius. Second, the output layer of the NN is connected via a sigmoid logistic activation function (more details on the activation functions between the layers are given in Sec. VI), constraining the MLS2 weights to values between 0 and 1. We further scale the resulting NN weights w os (r) and w ss (r) by a constant factor of 10 before applying them in Eq. 11. This scaling is necessary to allow the MLS2 model to account for situations where the actual correlation energy (in absolute terms) is much larger than what κMP2 predicts (see Sec. S2 in the SI for more details). Finally, we use e κMP2 c (r) and e κMP2 c,os (r) quantities normalized by ρ -1/3 (r)e x (r) as extra MLS2 dimensionless features (see Sec. S5 in the SI for a detailed list of features).