Generating valid Euclidean distance matrices
This work addresses the challenge of generating molecular structures efficiently for applications in chemistry or materials science, but it appears incremental as it builds on existing symmetry-invariant neural network methods.
The paper tackled the problem of generating point clouds like molecular structures with arbitrary rotations and translations by introducing an architecture that produces valid Euclidean distance matrices, which are inherently invariant to these transformations, and used it in a Wasserstein GAN to generate molecular structures in a one-shot manner.
Generating point clouds, e.g., molecular structures, in arbitrary rotations, translations, and enumerations remains a challenging task. Meanwhile, neural networks utilizing symmetry invariant layers have been shown to be able to optimize their training objective in a data-efficient way. In this spirit, we present an architecture which allows to produce valid Euclidean distance matrices, which by construction are already invariant under rotation and translation of the described object. Motivated by the goal to generate molecular structures in Cartesian space, we use this architecture to construct a Wasserstein GAN utilizing a permutation invariant critic network. This makes it possible to generate molecular structures in a one-shot fashion by producing Euclidean distance matrices which have a three-dimensional embedding.