The DP descriptor

The vanilla non-smooth DP


The descriptor

The rotation matrix that transforms the global coordinate to the local coordinate in the vanilla non-smooth DP. (Wen et al., 2022)

The smooth DP (DP-SE)


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:

The construction of the network (Wen et al., 2022).


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).


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).