![]() ![]() #EXPECTATIONS MULTIPATCH RECEIVING BLANKET FULL#The utility of the algorithm is illustrated by studying the saddle points associated with (a) the isomerization transition of the alanine dipeptide using two coarse-grained variables, specifically the Ramachandran dihedral angles, and (b) the beta-hairpin structure of the alanine decamer using 20 coarse-grained variables, specifically the full set of Ramachandran angle pairs associated with each residue. The algorithm is capable of dealing with problems involving many coarse-grained variables. This is done by using the general strategy of the heterogeneous multi-scale method by applying a macro-scale solver, here the gentlest ascent dynamics algorithm, with the needed force and Hessian values computed on-the-fly using a micro-scale model such as molecular dynamics. #EXPECTATIONS MULTIPATCH RECEIVING BLANKET FREE#In this paper, we develop an algorithm for finding the saddle points on a high-dimensional free energy surface "on-the-fly" without requiring a priori knowledge the free energy function itself. For complex systems, where the free energy depends on many degrees of freedom, this is not feasible. For simple systems in which the free energy depends on a few variables, the free energy surface can be precomputed, and saddle points can then be found using existing techniques. These saddle points act as transition states and are the bottlenecks for transitions of the system between different metastable states. ![]() Many problems in biology, chemistry, and materials science require knowledge of saddle points on free energy surfaces. Samanta, Amit Chen, Ming Yu, Tang-Qing Tuckerman, Mark E, Weinan Sampling saddle points on a free energy surface We expect that this approach and future refinements will greatly accelerate searches for saddle points, as well as other searches on the potential energy surface, as machine-learning methods see greater adoption by the atomistics community. This approach can be systematized, and in two simple example problems we demonstrate a dramatic reduction in the number of ab initio force calls. ![]() When these training data are used to improve the machine-learning model, the estimates greatly improve. The saddle-point prediction can then be verified by an ab initio calculation if it is incorrect, this strategically has identified regions of the PES where the machine-learning representation has insufficient training data. Since machine-learning models can learn from, and thus mimic, atomistic simulations, the saddle-point search can be conducted rapidly in the machine-learning representation. In this work, we describe how machine learning (ML) can reduce the number of intermediate ab initio calculations needed to locate saddle points. This results in the vast majority of the computational effort being spent calculating the electronic structure of states not important to the researcher, and very little time performing the calculation of the saddle point state itself. ![]() However, the search for saddle points often involves hundreds or thousands of ab initio force calls, which are typically all done at full accuracy. In atomistic simulations, the location of the saddle point on the potential-energy surface (PES) gives important information on transitions between local minima, for example, via transition-state theory. Acceleration of saddle-point searches with machine learning. ![]()
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