Fig. 2: The schematic of the working principle of the entire architecture.
From: Heterogeneous relational message passing networks for molecular dynamics simulations
a The entire architecture diagram of HermNet where {Z} is the set of atomic numbers, which will be passed through an embedding layer. Initial vectorial node features are all-zero vectors of fixed dimension. This layer is expected to receive a scalar node feature {s}, a vectorial node feature, and a vectorial edge feature, i.e. relative position vector \({\overrightarrow{r}}_{ij}\), and then output an updated scalar and vectorial node feature as the inputs of the next layer. The final scalar node features will be passed to a global pooling layer as feature of the graph. With the graph-level feature passing to a sequence of fully connected layers, the target to predict is achieved. b Sub-network for processing related subgraphs, i.e., homogeneous digraphs. The layer is composed of message passing layers hierarchically, such as radial message passing layer for two-body interactions, angular message passing layer for three-body interactions, and so on. Related message passing layers will be truncated according to the level of interactions to be modeled. The features or/and message passing layers with dotted line should be introduced in accordance with requirements. Several sub-networks which model different relations compose a single heterogeneous relational message passing layer. When the interactions are truncated to two-body interactions, the entire framework is termed HPNet. c and d are the schematic diagrams of HermConv module of HPNet and HTNet (HVNet), respectively. RMConv modules for different relations constitute the HermConv module. c Sub-network in HPNet for A-type when the system contains only two kinds of elements, specifically, A- and B-type. d The hidden states of A-type vertex derive from a sub-network that is truncated to three-body interactions for corresponding relations. The colors of the networks for different three-body interactions represent the parameters. If these colors are the same, which means the parameters are shared in all these three networks, the HermNet is termed HVNet. If not, then the HermNet is termed HTNet.
