Graphene Synthesis. Monolayer Gr was synthesized on liquid Cu at 1370 K via a previously established chemical vapor deposition (CVD) growth protocol using methane as a precursor in a reactor fitted with in situ characterization techniques that allow monitoring of the growth process . With further details provided in the supplementary information (SI), the in situ optical microscopy results in Figures and demonstrate that Gr nucleation is initiated after a "pulsed" high concentration methane burst at time 0 s, followed by continuous flake growth at lower methane concentration (pCH4/pH2 = 0.0127) as shown in Figures and. In the final growth stage, the large macroscopic flakes merge into a single-layer Gr sheet, as shown in Figure . The individual single-crystal flakes are characterized by a circular or hexagonal shape resulting from kinetically limited growth due to an overall precursor abundance at experimental conditions. This finally results in a flake-merging process leading to polycrystalline monolayer Gr composed of single-crystal domains with a size of a few hundred 𝜇𝑚 on average. More details on the growth procedures can be found in Ref. . X-ray Reflectivity Measurements. The adsorption height of the Gr monolayer above the liquid Cu surface ("gap") was determined by in situ XRR at the ID10 beamline of the ESRF synchrotron (Grenoble, France). The XRR scans were treated according to the method described recently in ref. , which not only accounts for the effect of the liquid surface curvature but also takes advantage of it. This, together with an improved reactor setup (e.g., larger sample surface) and measurement methodology, allowed to extract the normalized reflectivity profiles up to an unprecedented maximum value of the momentum transfer perpendicular to the surface, qz. Figure shows the resulting profiles before and after Gr growth (corresponding to Figures and, respectively). Employing the Parratt formalism, the reflectivity curves were fitted using a slab model consisting of one (in case of bare Cu) or three (in case of Cu covered with Gr) layers: signifying a Cu substrate, a void, and a carbon monolayer. With all details provided in the SI and Ref. , this fit yields the lateral average electron density profile against the surface depicted in Figure . From this profile, the "gap" distance is determined as the distance between the inflection point of the Cu density and the center of the Gr slab/layer, as indicated by the dashed lines in Figure . The advantage of using this Cu inflection point is a "gap" distance that does not dependent on the Cu roughness. Minor deviations of the below-quoted value compared to previous reports can be explained by the much shorter qz range available for fitting (between 0.4 -1.6 Å -1 ) in these preceding studies. Machine-Learning Potential. Moment Tensor Potentials (MTP) have been trained with DFT reference data to establish a numerically efficient ML surrogate model. The small number of hyperparameters involved in MTPs allows for a simple out-of-the-box application further described in the SI. The set of training and test structures (see Table ) is initially comprised of (strained) crystalline and liquid Cu bulk cells, (strained) free-standing periodic Gr sheets, and a finite Gr flake on a large liquid Cu slab. Interfacial information is subsequently provided by adding structures of a graphene sheet at various heights above a snapshot of a liquid Cu surface to the training set. All the liquid Cu structures were thereby taken as snapshots from preceding ab initio molecular dynamics work on this system . The DFT supercell calculations were performed with the full-potential, all-electron package FHI-aims , with all computational details provided in the SI. The entire set for training and test was computed with the Perdew-Burke-Ernzerhof (PBE) functional , once adding Tkatchenko-Scheffler (TS) and once adding MBD dispersion corrections, as well as with the rSCAN functional . This leads to four trained MTPs (MTP@PBE, MTP@PBE+TS, MTP@PBE+MBD, MTP@rSCAN) that all exhibit a high accuracy and transferability as expressed by root-mean-squared errors (RMSE) below 2 meV/atom (6.3 meV/atom) in energies and below 55 meV/Å (96 meV/Å) in the forces over the training (and test) set (see Figure and Table ). We note that the difference in RMSE between training and test sets indicates slight overfitting, yet without compromising accuracy.