Fig. 4.

Training energy barriers and transition rates. (A) After 18 iterations of our procedure, the energy barrier $\mathrm{\Delta }E$ is trained to within $0.2\%$ of the target barrier $\mathrm{\Delta }E*$. Shown is the error [$\mathrm{e}\mathrm{r}\mathrm{r}\mathrm{o}\mathrm{r}\left(\mathrm{\Delta }E\right)\equiv \left(\mathrm{\Delta }E-\mathrm{\Delta }E*\right)/\mathrm{\Delta }E*$] as a function of the target. (B) The transition rates measured via MD simulation ($k_{\mathrm{M}\mathrm{D}}$; black data) are not exactly proportional to $e^{-\beta \mathrm{\Delta }E*}$ (the dashed line has a slope of $-\beta$), indicating that the prefactor $\nu$ in Eq. 3 is not constant. However, this prefactor is captured reasonably well by the Kramers approximation ($k_{\mathrm{K}\mathrm{r}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s}}$; blue data). (C) After 18 iterations of training on the Kramers rate $k_{\mathrm{K}\mathrm{r}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s}}$, we obtain an accuracy within $0.2\%$ of the target rate $k*$. (D) The rates measured via MD simulation $k_{\mathrm{M}\mathrm{D}}$ agree very well with the target rate $k*$ (the solid line corresponds to $k_{\mathrm{M}\mathrm{D}}=k*$). Thus, we are able to accurately and quantitatively design the transition kinetics of the seven-particle clusters we consider.