Abstract
Global optimization of the structure of atomic nanoparticles is often hampered by the presence of many funnels on the potential energy surface. While broad funnels are readily encountered and easily exploited by the search, narrow funnels are more difficult to locate and explore, presenting a problem if the global minimum is situated in such a funnel. Here, a divide-and-conquer approach is applied to overcome the issue posed by the multifunnel effect using a machine learning approach, without using a priori knowledge of the potential energy surface. This approach begins with a truncated exploration to gather coarse-grained knowledge of the potential energy surface. This is then used to train a machine learning Gaussian mixture model to divide up the potential energy surface into separate regions, with each region then being explored in more detail (or conquered) separately. This scheme was tested on a variety of multifunnel systems and yielded significant improvements to the times taken to locate the global minima of Lennard-Jones (LJ) nanoparticles, LJ75 and LJ104, as well as two metallic systems, Au55 and Pd88. However, difficulties were encountered for LJ98, providing insight into how the scheme could be further improved.Global optimization of the structure of atomic nanoparticles is often hampered by the presence of many funnels on the potential energy surface. While broad funnels are readily encountered and easily exploited by the search, narrow funnels are more difficult to locate and explore, presenting a problem if the global minimum is situated in such a funnel. Here, a divide-and-conquer approach is applied to overcome the issue posed by the multifunnel effect using a machine learning approach, without using a priori knowledge of the potential energy surface. This approach begins with a truncated exploration to gather coarse-grained knowledge of the potential energy surface. This is then used to train a machine learning Gaussian mixture model to divide up the potential energy surface into separate regions, with each region then being explored in more detail (or conquered) separately. This scheme was tested on a variety of multifunnel systems and yielded significant improvements to the times taken to locate the global minima of Lennard-Jones (LJ) nanoparticles, LJ75 and LJ104, as well as two metallic systems, Au55 and Pd88. However, difficulties were encountered for LJ98, providing insight into how the scheme could be further improved.