Descriptor "se_e2_r"

4.3. Descriptor "se_e2_r" TensorFlow PyTorch JAX DP#

Note

Supported backends: TensorFlow TensorFlow, PyTorch PyTorch, JAX JAX, DP DP

The notation of se_e2_r is short for the Deep Potential Smooth Edition (DeepPot-SE) constructed from the radial information of atomic configurations. The e2 stands for the embedding with two-atom information.

4.3.1. Theory#

The descriptor, using either radial-only information, is given by

\[ \mathcal{D}^i = \frac{1}{N_c} \sum_j (\mathcal{G}^i)_{jk},\]

where \(N_c\) is the expected maximum number of neighboring atoms, which is the same constant for all atoms over all frames. A matrix with a dimension of \(N_c\) will be padded if the number of neighboring atoms is less than \(N_c\).

Each row of the embedding matrix \(\mathcal{G}^i \in \mathbb{R}^{N_c \times M}\) consists of \(M\) nodes from the output layer of an NN function \(\mathcal{N}_ {g}\) of \(s(r_{ij})\):

\[ (\mathcal{G}^i)_j = \mathcal{N}_{e,2}(s(r_{ij})),\]

where \(\boldsymbol{r}_ {ij}=\boldsymbol{r}_ j-\boldsymbol{r}_ i = (x_{ij}, y_{ij}, z_{ij})\) is the relative coordinate and \(r_{ij}=\lVert \boldsymbol{r}_{ij} \lVert\) is its norm. The switching function \(s(r)\) is defined as

\[\begin{split} s(r)= \begin{cases} \frac{1}{r}, & r \lt r_s, \\ \frac{1}{r} \big[ x^3 (-6 x^2 +15 x -10) +1 \big], & r_s \leq r \lt r_c, \\ 0, & r \geq r_c, \end{cases}\end{split}\]

where \(x=\frac{r - r_s}{ r_c - r_s}\) switches from 1 at \(r_s\) to 0 at the cutoff radius \(r_c\). The switching function \(s(r)\) is smooth in the sense that the second-order derivative is continuous.

In the above equations, the network parameters are not explicitly written. \(r_s\), \(r_c\) and \(M\) are hyperparameters provided by the user. The DeepPot-SE is continuous up to the second-order derivative in its domain.[1]

4.3.2. Instructions#

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

$deepmd_source_dir/examples/water/se_e2_r/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_e2_r",
	    "sel":		[46, 92],
	    "rcut_smth":	0.50,
	    "rcut":		6.00,
	    "neuron":		[5, 10, 20],
        "type_one_side": true,
	    "resnet_dt":	false,
	    "seed":		1,
	    "_comment": " that's all"
	},

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

4.3.3. Type embedding support#

Type embdding is only supported in the TensorFlow backends.

4.3.4. Difference among different backends#

In the TensorFlow backend, env_protection cannot be set to a non-zero value. In the PyTorch, JAX, and DP backend, type_one_side cannot be set to false.

4.3.5. Model compression#

Model compression is supported when type embedding is not used.