Automatic Feature Selection for Atom-Centered Neural\nNetwork Potentials Using a Gradient Boosting Decision Algorithm

Atom-centered neural network (ANN)\npotentials have shown high accuracy\nand computational efficiency in modeling atomic systems. A crucial\nstep in developing reliable ANN potentials is the proper selection\nof atom-centered symmetry functions (ACSFs), also known as atomic\nfeatures, to describe atomic environments. Inappropriate selection\nof ACSFs can lead to poor-quality ANN potentials. Here, we propose\na gradient boosting decision tree (GBDT)-based framework for the automatic\nselection of optimal ACSFs. This framework takes uniformly distributed\nsets of ACSFs as input and evaluates their relative importance. The\nACSFs with high average importance scores are selected and used to\ntrain an ANN potential. We applied this method to the Ge system, resulting\nin an ANN potential with root-mean-square errors (RMSE) of 10.2 meV/atom\nfor energy and 84.8 meV/Å for force predictions, utilizing only\n18 ACSFs to achieve a balance between accuracy and computational efficiency.\nThe framework is validated using the grid searching method, demonstrating\nthat ACSFs selected with our framework are in the optimal region.\nFurthermore, we also compared our method with commonly used feature\nselection algorithms. The results show that our algorithm outperforms\nthe others in terms of effectiveness and accuracy. This study highlights\nthe significance of the ACSF parameter effect on the ANN performance\nand presents a promising method for automatic ACSF selection, facilitating\nthe development of machine learning potentials.