The DP descriptor
The vanilla non-smooth DP
Overview
The descriptor
- Radial information:
- Distance info: .
The smooth DP (DP-SE)
Overview
A simplified description of the process of constructing the energy is the following:
A more complete depiction can be seen in (Wen et al., 2022) as shown in the following figure:
Nomenclature
| Variable | Description | Dimension |
|---|---|---|
| the environment matrix for atom | ||
| the augmented matrix for atom | ||
| the embedding matrix | ||
| the smooth descriptors | ||
| the energy of atom |
More precisely, the map is given by (Lu et al., 2021):
where denotes the first “” columns of . Here, is of dimension and is of dimension where .
Variants of the descriptor
The superscript enclosed in parenthesis denote the variant of the descriptor, including
| Description | Embedding | Descriptor |
|---|---|---|
| Two-body embedding with radial distance between neighbouring atoms | ||
| Two-body embedding with coordinates of the neighbour atoms | ||
| Three-body embedding with the angle between neighbour atoms in the embedding term |
In the DeePMD-kit implementation, they are named se_e2_r, se_e2_a, and se_e3, respectively. The accuracy and resolution between the three descriptor variants are (Wen et al., 2022).
Implementation
The implementation details in DeePMD-kit are described in the API documentation for the following functions:
The specific shape of network (adjacent layers have same or twice the width) allows the use of ResNet (deep residual neural network) (He et al., 2015).
References
- Atom Type Embedding — DeePMD-kit documentation
- DeePMD 描述符 se_a 前向和反向
- deepmd_on_pytorch/model.py at master · shishaochen/deepmd_on_pytorch (github.com)
- deepmd-kit/network.py at 3e54fea7aedf5e1f68fa534f9c692f2be6077da9 · deepmodeling/deepmd-kit (github.com)
- deepmd.utils package — DeePMD-kit documentation (deepmodeling.com)
- 9.1. How to tune Fitting/embedding-net size? — DeePMD-kit documentation (deepmodeling.com)
- 3.1. Overall — DeePMD-kit documentation (deepmodeling.com)
- He, K., Zhang, X., Ren, S., & Sun, J. (2015). Deep Residual Learning for Image Recognition. ArXiv:1512.03385 [Cs]. http://arxiv.org/abs/1512.03385
- Lu, D., Jiang, W., Chen, Y., Zhang, L., Jia, W., Wang, H., & Chen, M. (2021). DP Train, then DP Compress: Model Compression in Deep Potential Molecular Dynamics. ArXiv:2107.02103 [Physics]. http://arxiv.org/abs/2107.02103
- Wen, T., Zhang, L., Wang, H., E, W., & Srolovitz, D. J. (2022). Deep Potentials for Materials Science. ArXiv:2203.00393 [Cond-Mat, Physics:Physics]. http://arxiv.org/abs/2203.00393
- Zhang, L., Han, J., Wang, H., Saidi, W. A., Car, R., & Weinan, E. (2018). End-to-end symmetry preserving inter-atomic potential energy model for finite and extended systems. Proceedings of the 32nd International Conference on Neural Information Processing Systems, 4441–4451. https://arxiv.org/abs/1805.09003