We then adapt our protocol and perform an automated search of an optimal set of bonded parameters for calibrating the building blocks of lipid models using Representation 2 (Fig. ). The hypothesis motivating this alternative representation is that while attempting to better preserve degrees of freedom during the coarse-graining process, using exclusively regular beads in the bulk of all saturated tails remains mandatory for preserving the thermodynamic properties of the lipids in both the liquid and gel phases (n.b. tails are differentiated by using next to ester groups either a small bead with 3-to-1 mapping or a regular bead with 5-to-1 mapping). We include in the training set the same 8 PC lipids as in the previous experiment, for which we simulate patches of lamellar bilayers in the liquid phase at the same temperatures as previously, but this time we directly include bilayer simulations in the tilted gel phase (Lβ') for DMPC, DPPC and DSPC (273K, 293K and 308K, respectively). This provides more information for guiding the optimization and introduces additional constraints enforcing the transferability of the bonded building blocks across phase states. We calibrate equilibrium values and force constants for all bonds and all angles defined in the lipid models, totaling 48 parameters across 13 bond types and 12 angle types (Fig. , equilibrium values remain set to 180 degrees for 2 angle types). The swarm of particles is initialized randomly within the 48dimensional search space, except for the first particle that is provided with knowledge from AA-mapped MD simulations (initialized using average equilibrium values computed for all bond and angle types) and from previous Martini lipid models (initialized within relevant ranges of force constants known to be adequate). The steady decrease of the loss (Fig. : green curve) indicates the bonded parameters of the models are adapted successfully until the optimization converges at swarm iteration 28. The presence of noise in the evaluation of the APL and Dʜʜ thickness for DMPC at 273K and DSPC at 308K indicates that the sets of parameters explored during optimization did not systematically trigger the formation of a gel phase (Fig. : light yellow and blue curves). At convergence, the models overall correctly approach the APL and Dʜʜ experimental measurements defined as target (Fig. : yellow and blue curves converging towards reference black line, set to 0), indicating Representation 2 allows to describe the thermodynamic properties of various types of lipids. The optimization problem now includes more and different constraints on the bonded parameters, introduced by adding in the training set the simulations of DMPC and DSPC in the tilted gel phase (Lβ'), as well as by reducing the number of beads in the lipid tails notably for PUFA-containing lipids (i.e. slightly lower resolution than Representation 1). The APL is very well fitted to experimental data for all pairs of lipid type and simulation temperature, both in the liquid and gel phases, while the Dʜʜ thicknesses remain slightly less fitted on average. The OT-B distances here also are minimized effectively, overall reproducing within the CG models the structural features present in the reference AA-mapped MD trajectories (Figs. ).