Fig. 5.

(A) Energy (in $k_{B}T$) along the steepest descent paths connecting a single starting structure with five adjacent structures, obtained through the DNEB method (Fig. 3 and SI Appendix). These results are after the simultaneous optimization of all 10 energy barriers (target energy barriers [in $k_{B}T$] are shown in the legend). The observed energy barriers are within $0.3\%$ of their targets. (B) The loss function after attempting to simultaneously control the dynamics of multiple transitions, as a function of the number of transitions. Due to the form of the loss function (Eq. 5), simultaneous control is successful when $L_{\mathrm{fi}\mathrm{n}\mathrm{a}\mathrm{l}}\to 0$. In practice, when we obtain $L_{\mathrm{fi}\mathrm{n}\mathrm{a}\mathrm{l}}<10^{-2}$, this can be further reduced by additional optimization with smaller learning rates, indicating that the transition dynamics can indeed be controlled to a desired precision. The data are colored according to the Hessian-based prediction discussed in the text: green (blue) data correspond to cases where we predicted that simultaneous control could be (could not be) obtained. (C) Histogram of $L_{\mathrm{fi}\mathrm{n}\mathrm{a}\mathrm{l}}$ for all data shown in B.