Constructing the Neural Network Potential With the Energies of the Atom and Its Derivatives

Neural Network Potentials (NNPs) are highly anticipated as a possible breakthrough to overcome the trade-off between accuracy and speed in atomistic simulations. NNP learns the potential energy surface from the reference first principle calculations. The most widely used first principle calculation is based on the density functional theory (DFT) with the plane-wave basis, which does not provide atomic energy. Thus it is not possible to directly train the NNP to learn target atomic energy from plane-wave DFT. To overcome this limitation Behler and Parrinello designed high-dimensional NNP such that it represents the atomic energy as the sum of total energy.
However, the mapping of atomic energy from the total energy is not unique, and if not carefully considered, there could be a loss of information leading to errors. We call this ad-hoc mapping problem. In contrast, because a pseudo-atomic localized basis can define atomic energy by its decomposition formalism, it enables NNP to avoid the above problem. In this presentation, we demonstrate the advantages of training NNPs directly from atomic energy and its derivatives, free from the high dimensional structure.

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[2] Phys. Rev. Mater. 3, 093802 (2019)