Paper: Compositional Search of Stable Crystalline Structures in Multi-Component Alloys Using Generative Diffusion Models (ICLR-2024)

Reviewer comment (Experiments):
In "Dataset creation with MD", it is unclear what one data point in the dataset represents. Is it a graph with node features? A clear definition of the sample space is missing.

Author response:
One data point is a crystal graph: apart from the node features (atom types), it is equipped with lattice vectors - those are three vectors along which the nodes repeat periodically. Lattice vectors can be seen as the features of the entire structure (graph), similarly to other input parameters: the value of the property (bulk modulus), and - for P-CDVAE - also a label that describes the phase (whether it’s an FCC or BCC structure). The output of the model has the same format and while theoretically, the sample space is not constrained to graphs of a certain size, in practice, all training examples were composed of 54 atoms, just like the training examples.

Reviewer comment (Reproducibility):
The statement "Diffusion autoencoders are trained in a self-supervised manner, by removing the artificially induced noise of varying magnitudes from the data" is unclear. What is the input to the model, and how is the self-supervision task formed?

Author response:
The input to the model is a crystal structure. The model is trained on the task of data denoising/reconstruction - after the structure is encoded, Gaussian noise is applied to the representation. The model learns to reconstruct the input graph and a loss function is applied based on the errors in reconstructed, which can be seen as a self-supervised task: in absence of external labels, a reconstruction task is performed based solely on the input data.

Reviewer comment (Reproducibility):
Regarding the training of "P-CDVAE", it is unclear whether the phase is an observed variable so that the denoising model can be trained to predict the phase.

Author response:
The crystal phase of the training examples (FCC or BCC) was straightforward to assess - the results of MD simulations aligned perfectly with the composition-to-phase relation visualized in FIG. 2, based on (Wu et al., 2017). Therefore, the structures in the dataset were annotated with corresponding crystal phase labels based purely on the composition. To assess the phase of the output structures, OVITO software was used. A loss function was applied to the model’s fully connected subnetwork to enforce correct prior phase prediction (against the phase labels). The training didn’t involve the loss function that explicitly punishes the mismatch between the phase of the emergent output structure and the label (or uses the phase of the output structure in any other way), but it did involve the coordinate loss. In that sense, the observation of the phase of output structure was not a part of the machine learning pipeline and was only conducted to analyze the results (fig. 4)

Reviewer comment (Writing):
In "Local search for data augmentation", the described approach seems different from typical data augmentation in machine learning. Here, local search is used to optimize some property of the structure rather than to increase training data.

Author response:
The goal of the operation was indeed to enrich the dataset with optimized structures that cannot be simply seen as sampled from uniform distribution (in terms of initial conditions, that then converge to locally stable spatial distribution). In hindsight, we admit that “augmentation” strikes as an inadequate name for this procedure - given that the goal of augmentation is usually to add examples to the dataset through simpler operations in order to account for simple feats (e.g. symmetries) of already existing cases.

Reviewer comment (Theory):
In the statement "In order to cover the random ordering of the atoms in a specific point in the composition space," it is unclear why node ordering should play a role.

Author response:
We’re sorry to admit that this is one of the very unfortunate phrases that make the ideas behind the methodology obscure. A paraphrase that better conveys what was meant here is: “In order to cover more arbitrary orderings of atoms that are possible for a given atomic composition”.