For calculating the bottom-up component of our loss function (𝑂𝑇-𝐵 𝑔𝑙𝑜𝑏𝑎𝑙 in Eq. 1), as preliminary steps we obtain well-sampled AA MD trajectories for each bilayer included in the training set (128 lipids and 1 µs of equilibrium AA MD simulation each). We then project (map) these trajectories according to our CG representations of interest (Fig. ) and compute all AA-mapped bond and angle distributions to be used as reference during optimization. The bond and angle types are defined respectively as all possible connected pairs and triplets of beads, mapping atomic connectivity into beads connectivity according to our CG representations (Fig. ). We evaluate the mismatch between corresponding CG vs. AA-mapped bond and angle distributions using the Wasserstein distance (a.k.a. Earth Movers' Distance, EMD), a metric based on optimal transport 33 (OT, Fig. ) having several useful properties: (i) multimodal distributions are well handled; (ii) distances are robust to noise; (iii) distances are quantified in interpretable units (e.g., Å, degrees); and (iv) their computations are inexpensive (via PyEMD ). This metrics (hereafter referred to as "OT-B metrics") has been already proven well-suited for parametrizing the bonded terms of CG models of complex and flexible molecules in a previous version of SwarmCG . The bottom-up component of the loss informs on how closely a putative set of FF parameters allows to match the AA description of the molecular systems included in the training set, and is calculated as