4.15. Descriptor "se_e3_tebd"

Note

Supported backends: PyTorch , JAX , DP

The notation of se_e3_tebd is short for the three-body embedding descriptor with type embeddings, where the notation se denotes the Deep Potential Smooth Edition (DeepPot-SE). The embedding takes bond angles between a central atom and its two neighboring atoms (denoted by e3) and their type embeddings (denoted by tebd) as input.

4.15.1. Theory

The three-body embedding DeepPot-SE descriptor with type embeddings incorporates bond-angle and type information, making the model more accurate. The descriptor \(\mathcal{D}^i\) can be represented as

\[ \mathcal{D}^i = \frac{1}{N_c^2}(\mathcal{R}^i(\mathcal{R}^i)^T):\mathcal{G}^i,\]

where \(N_c\) is the expected maximum number of neighboring atoms, which is the same constant for all atoms over all frames. \(\mathcal{R}^i\) is constructed as

\[ (\mathcal{R}^i)_j = \{ \begin{array}{cccc} s(r_{ij}) & \frac{s(r_{ij})x_{ij}}{r_{ij}} & \frac{s(r_{ij})y_{ij}}{r_{ij}} & \frac{s(r_{ij})z_{ij}}{r_{ij}} \end{array} \},\]

where \(s(r_{ij})\) is the switch function between central atom \(i\) and neighbor atom \(j\), which is the same as that in se_e2_a.

Currently, only the full information case of \(\mathcal{R}^i\) is supported by the three-body embedding. Each element of \(\mathcal{G}^i \in \mathbb{R}^{N_c \times N_c \times M}\) comes from \(M\) nodes from the output layer of an NN function \(\mathcal{N}_{e,3}\). If tebd_input_mode is set to concat, the formulation is:

\[ (\mathcal{G}^i)_{jk}=\mathcal{N}_{e,3}((\theta_i)_{jk}, \mathcal{A}^j, \mathcal{A}^k)\]

Otherwise, if tebd_input_mode is set to strip, the angular and type information will be taken into two separate NNs \(\mathcal{N}_{e,3}^{s}\) and \(\mathcal{N}_{e,3}^{t}\). The formulation is:

\[ (\mathcal{G}^i)_{jk}=\mathcal{N}_{e,3}^{s}((\theta_i)_{jk}) + \mathcal{N}_{e,3}^{s}((\theta_i)_{jk}) \odot ( \mathcal{N}_{e,3}^{t}(\mathcal{A}^j, \mathcal{A}^k) \odot s(r_{ij}) \odot s(r_{ik}))\]

where \((\theta_i)_ {jk} = (\mathcal{R}^i)_ {j,\\{2,3,4\\}}\cdot (\mathcal{R}^i)_ {k,\\{2,3,4\\}}\) considers the angle form of two neighbours (\(j\) and \(k\)). The type embeddings of neighboring atoms \(\mathcal{A}^j\) and \(\mathcal{A}^k\) are added as an extra input of the embedding network. The notation \(:\) in the equation indicates the contraction between matrix \(\mathcal{R}^i(\mathcal{R}^i)^T\) and the first two dimensions of tensor \(\mathcal{G}^i\).

4.15.2. Instructions

A complete training input script of this example can be found in the directory

$deepmd_source_dir/examples/water/se_e3_tebd/input.json

The training input script is very similar to that of se_e2_a. The only difference lies in the descriptor section

	"descriptor": {
      "type": "se_e3_tebd",
      "sel": 40,
      "rcut_smth": 0.5,
      "rcut": 4.0,
      "neuron": [
        2,
        4,
        8
      ],
      "tebd_dim": 8,
      "tebd_input_mode": "concat",
      "activation_function": "tanh"
	},

The type of the descriptor is set by the key type.

4.15.3. Type embedding

Type embedding is within this descriptor with the tebd_dim argument.

4.15.4. Model compression

Model compression is not supported.