Implementing TensorNet in modelforge #116
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Description
TensorNet is a message-passing neural network with a unique way to satisfy equivariance under the orthogonal group. Previously, two approaches have dominated:
TensorNet uses Cartesian tensor representations and embeddings which are O(3) equivariant.
To re-implement this model, we need to modify our current Embedding module (which is built for embedding of scalar values) and implement the Interaction module.
Embedding
Following the default$r_c$ within a neighborhood $N(d_{ij} < r_c)$ :
modelforge
input preparation, the model gets as input (for a given radiusAdditional properties that need to be calculated for the Tensornet embedding:
Scalar features
Scalar feature will be initialized as$I_{0}^{ij} = \text{Id}$ , with $Id$ the identity matrix.
Vector features
Tensor features
The tensor feature will be initialized as the symmetric traceless tensor of the outer product of$r_{ij}'$ : $S_0^{ij} = r_{ij}'r_{ij}'^T - \frac{1}{3}Tr( r_{ij}'r_{ij}'^T)Id$ , with $Tr$ is the trace operator and $Id$ the identity matrix.
Interaction
Todos
Status