Embedding Layers for Accurate Direct Deep Learning Force Models

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Abstract

The evaluation of atomic forces and total energy is a key challenge for large-scale atomistic simulations of materials.

In recent years, machine learning techniques are successfully used to predict potential energies and derive the atomic forces through their gradient. In such methods, the training data is produced by quantum calculations, typically Density Functional Theory (DFT). The direct prediction of atomic forces by deep learning (DL) models was demonstrated by other groups and us.

It has the advantage of being local and slightly faster while still maintaining state of the art mean absolute error (MAE). A disadvantage is that the forces might be non-conserving.

Like models that predict the energy, direct force models should behave well under symmetry operations and permutation of atoms. Here, we show how the use of self-learned embedding layers and data augmentation help to achieve both goals.

We evaluate the model's reliability by several measures: the resulting mean average error (MAE), the calculation of phonons spectra in several solids, the behavior of force derivatives under atom movement, and finally, the resulting radial distribution function (RDF) after molecular dynamics runs which use the model forces at several temperature values.

We show that the MAE alone is not a sufficient measure for a successful model.