Enhancing the Performance of Global Optimization of Platinum Cluster Structures by Transfer Learning in a Deep Neural Network

Abstract

The global optimization of metal cluster structures is an important research field. The traditional deep neural network (T-DNN) global optimization method is a good way to find out the global minimum (GM) of metal cluster structures, but a large number of samples are required. We developed a new global optimization method which is the combination of the DNN and transfer learning (DNN-TL). The DNN-TL method transfers the DNN parameters of the small-sized cluster to the DNN of the large-sized cluster to greatly reduce the number of samples. For the global optimization of Pt9 and Pt13 clusters in this research, the T-DNN method requires about 3–10 times more samples than the DNN-TL method, and the DNN-TL method saves about 70–80% of time. We also found that the average amplitude of parameter changes in the T-DNN training is about 2 times larger than that in the DNN-TL training, which rationalizes the effectiveness of transfer learning. The average fitting errors of the DNN trained by the DNN-TL method can be even smaller than those by the T-DNN method because of the reliability of transfer learning. Finally, we successfully obtained the GM structures of Pt n (n = 8–14) clusters by the DNN-TL method.

Machine Learning for Experimental Reactivity of a Set of Metal Clusters toward C–H Activation

“…The global minimum (GM) structures of the 129 reactive clusters were investigated by density functional theory (DFT) computations combined with GM methods of genetic algorithm and deep neural network with transfer learning technique (see details in Supporting Information and Table S7). The photoelectron imaging spectra of seven typical clusters in the “active islands” were experimentally measured to select appropriate DFT functionals (Figures S8–S11, see Supporting Information for method details). The GM structures for the Rh x M y – clusters with six to nine atoms ( x + y = 6–9) are shown in Figure , and all others can be found in Figures S12–S16.…”

On the structure and electronic properties of Ptn clusters: new most stable structures for n = 16–17

“…40 The reported structures for Pt n clusters with n = 3–14 in different studies are well assigned and compared. 10,41,42 This is not the case, however, for n = 15–20, where the lowest energy structures and low lying isomers of Pt clusters have not been analyzed in detail. For example, we have recently found a new most stable structure for Pt 15 with a capped pyramid-like structure by performing simulated annealing based on molecular dynamics simulations.…”

Adsorption and Recombination of H+ and H3O+ on Graphene-Supported Pt1, Pt13, and Pt14 Nanoclusters: A First Principles Study

“…The coordination number of Pt atoms of such a cluster corresponded to 4. The position of the atoms in the Pt 14 cluster was taken from the paper where the geometry optimization was carried out using deep learning of a neural network [73].…”