Figure 1.

(A) Model two-dimensional potential used to test EBMetaD, via an overdamped Langevin dynamics simulation. (B) Histogram of ξ as a function of the number of simulation steps (red lines), compared with the probability distribution associated with the model potential (gray), and with the target distribution (black). (Inset) Average biasing potential, versus $-\ln {\rho }_{\exp }\left(\xi \right)-F\left(\xi \right)$ (Eq. 6), with t_e = 5 × 10⁵ steps. $F\left(\xi \right)$ was calculated analytically, as $F\left(\xi \right)=-\ln \left[\int \text{d}\xi \text{'}\exp \left\{-U\left(\xi ,{\xi }^{\text{'}}\right)\right\}\right]+C$. (C) Histogram of ξ and ξ’ from EBMetaD (red isolines), overlaid on the ensemble-corrected potential calculated analytically (black isolines) (Eq. 3). Diffusion coefficients in ξ,ξ’ were set to 10, the integration time step was 10⁻⁵, and k_BT = 1. Gaussians of height 10⁻⁴k_BT and width 0.1 were added every 10³ steps. Equivalent results were obtained for a wide range of alternative values (Fig. S1).