The optimization trajectories of the replicates starting from 𝑁 = 5 initial points are shown in Figure , with the evaluated objective function of the previous simulation-only regularized least-squares optimization for comparison. We see that in most cases, the optimizer struggles initially, with a high percentage of solutions proposed and rejected in the first 8 steps. While these steps do not immediately yield an improved force field, the parameter vectors they propose are added to the pool of parameter vectors used to build surrogates, eventually "exploring" enough space to find an improved solution, with an average objective of 0.039 vs. an initial objective of 0.16, an average 𝜌 𝐿 training set RMSE of 0.016 g/mL (initial RMSE 0.027 g/mL), and an average Δ𝐻 𝑣𝑎𝑝 RMSE of 2.75 kJ/mol (initial RMSE 7.15 kJ/mol).