Finding all minima of a potential energy function is of essential importance in many chemical engineering problems, including protein folding, self-assembly, and plant design. Here, we combine tools for finding all critical points of a potential with data-mining of the results of the exploration. Using a dynamical systems approach , we first explore all critical points and connections thereof in an energy landscape. Then, treating the discovered minima network as a directed graph, we apply the Directed Graph Laplacian (DGL) algorithm  in order to discover a lower-dimensional underlying manifold and create an effective embedding . To illustrate this methodology, we use an example case of a two-scale potential. The DGL algorithm successfully identifies those minima that lie on an effective low-dimensional (here, one-dimensional) manifold. This combination of methods has the potential to enable dimensionality reduction in optimization problems with fine and coarse scale structure, where a surrogate lower-dimensional effective description is possible.
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