type embedding

Since the Embedding Net of the DP model is $N^2$ times the number of element types $N$, it poses limitations on both the training and inference speed when there are a large number of element types in the system. Additionally, this also restricts the potential of the DP model in terms of scalability to larger models. Considering that the $N^2$ Embedding nets implicitly encode information about the element types, we can achieve similar effects by adjusting $S_{ij}$ and concatenating the physical property information of the element types with $S_{ij}$. This way, we only need a single Embedding Net instead of $N^2$.

For $S_{ij}$, where $i$ represents the central atom, we concatenate the physical properties of the element type corresponding to $j$ with $S_{ij}$ to form a vector of length 1 plus the number of physical properties. This vector is then fed into the Embedding Net. In our testing on the quinary alloy(Ru, Rh, Ir, Pd, Ni) dataset and the LiGePS quaternary dataset, the DP model based on this type embedding method achieved or exceeded the standard DP model's prediction accuracy while reducing training time by 27%. For detailed results, please refer to the performance test.

usage method

To initiate model training with the default physical properties, the user can include the $type\_embedding$ parameter in the JSON file used for training. Please refer to the project example example/LiGePS/ligeps.json for more details.

{
  "type_embedding": true
}

You can also specify the desired physical properties in the model parameter of the JSON file.

The force field calling method in Lammps is the same as the standard DP model calling method mentioned earlier.

Performance test

Accuracy

Comparison of prediction accuracy between Type embedding method and the standard DP model on the validation set of a quinary alloy mixed dataset (containing 9486 configurations with different atom types)

Fig 1. Energy error reduction on the validation set of the five element alloy system

Fig 2. Force error reduction on the validation set of the five element alloy system

Comparison of prediction accuracy between Type embedding method and the standard DP model on the validation set of a quaternary LiGePS configurations (consisting of 10,000 configurations at 1200K)

Fig 1. Energy error reduction on the validation set of the five element alloy system

Fig 2. Force error reduction on the validation set of the quaternary LiGePS system

Training time

Fig 1. Total training time for the five element alloy system

Fig 2. Total training time for the quaternary LiGePS system

Molecular dynamics time

(To be supplemented...)