# Atomic energy mapping of neural network potential

## TL;DR

This paper investigates how neural network potentials infer atomic energies from total energies, revealing vulnerabilities and proposing methods to improve atomic energy mapping through careful training set selection and invariant point monitoring.

## Contribution

It introduces a framework for analyzing atomic energy mapping in neural network potentials and demonstrates how to enhance accuracy by strategic training practices.

## Key findings

- Neural network potentials can have incorrect atomic energy mappings despite accurate total energy training.
- Invariant points in feature space are useful for assessing atomic energy mapping.
- Careful training set selection and monitoring improve atomic energy inference.

## Abstract

We show that the intelligence of the machine-learning potential arises from its ability to infer the reference atomic-energy function from a given set of total energies. By utilizing invariant points in the feature space at which the atomic energy has a fixed reference value, we examine the atomic energy mapping of neural network potentials. Through a series of examples on Si, we demonstrate that the neural network potential is vulnerable to 'ad hoc' mapping in which the total energy appears to be trained accurately while the atomic energy mapping is incorrect in spite of its capability. We show that the energy mapping can be improved by choosing the training set carefully and monitoring the atomic energy at the invariant points during the training procedure.