Moreover, we note that it was possible to construct the trainable part of both models using standard spline coupling layers, analogously to our previous work in isolated molecules. . As such, both models (C and H) used standard coupling layers that are not inherently equivariant to permutations of any DOFs. It was possible to use this approach in the current work because none of the water molecules in the supercells we compared did swapped lattice sites within the MD-accessible timescales that we sampled. We note that PGM architectures can be equipped with equivariant functionality by replacing the standard multilayered perceptrons with attentionbased coupling mechanisms. The following sections describe in detail the approach adopted in models C and H, respectively.