Discovering new photovoltaics using optimal transport theory

Abstract

Searching by chemical and structural analogy is one of the most commonly used and successful approaches to materials discovery. However, formulating this task for algorithmic implementation raises the question of how we define similar materials. Methods have been proposed for searching materials space using vectors based on chemical composition and functional fragments in the material. Descriptors for structural similarity have also been proposed. However, the question of how to incorporate and balance structural and compositional similarity measures in a single metric remains open. Here, we adapt methods developed for calculating distances between undirected graphs and apply them to crystalline materials similarity. The Fused Gromov-Wasserstein (FGW) metric uses optimal transport theory to map between two graphs considering a balance of the graph structure and the information present at the nodes of the graph (atoms in crystals). We apply the method to exploring new photovoltaic materials. We demonstrate that FGW is competitive with embeddings from an equivariant graph neural network, trained on $> 10^6$ materials, despite minimal training. We then apply FGW to a discovery campaign to identify materials from the Materials Project database that have not previously been explored as photovoltaics, but have similarities to known high-efficiency materials. After validating predictions with hybrid density functional theory, we identify seven previously unexplored high-efficiency photovoltaic absorber candidates, including Cs$_5$Sb$_8$, which is found to have a predicted SLME of $> 30\%$ and to be thermodynamically stable. The FGW approach demonstrates the power of strong inductive biases for developing metrics for materials exploration with minimal training data.

Figures (4)

• Figure 1: Heat maps of normalised, absolute distances in a, SLME space and b--e, FGW space, where the Gromov parameter $\alpha$ is increased from 0 to 1 in b to e to include more structural importance to the FGW distance. The rows and columns on the $x$- and $y$-axes correspond to the materials in the dataset.
• Figure 2: a, Plot of BCE loss against $\alpha$ for the parameter combination for each feature vector that resulted in the lowest minimum. Colours encode the feature vector, whilst dotted lines are the harmonic distance cost matrix and dashed lines use scaled atomic distances. Marker shapes indicate feature distance: circles for cosine distance, triangles for Euclidean distance, and crosses for Manhattan distance. Note the poor performances of the one-hot vector and the randomly generated distributed vector at $\alpha=0$ (composition-only). The one-hot curve extends to 18.1 here but was not shown for clarity. The legend lists the feature vectors from lowest minimum at the top (CrystaLLM) to highest at the bottom (Magpie), though there is very little difference between them (1.5%). b, The same FGW methods at the optimal $\alpha$ values applied to a $k$-NN regression task, compared to three baselines for distance metrics: Euclidean distance between structure-level embeddings with Magpie & MACE and the SOAP kernel distance.
• Figure 3: a, Plots to identify the optimal clustering number through an elbow plot of the total intra-clustering distance and of the silhouette score, both against the cluster number, $n$. The optimal $n$ is found through the Kneedle algorithm for the elbow plot and by finding the peak of the silhouette score. Note the small discrepancy between the two approaches. b, Visualisations of the 'seed' materials: the highest PV efficiency material from each cluster. Crystal axes $b$ and $c$ are shown for reference: $a$ varies based on bond angles.
• Figure 4: a, KDE plots showing the distribution of SLMEs for the entire dataset compared to the 20 nearest materials to high-PCE GaAs, using the best three FGW distance methods by BCE loss in Figure \ref{['bce_knn']}a. The small unphysical densities at high and low SLMEs are artefacts of the kernel smoothing. b, 'local enrichment' of the $k$-nearest neighbours of Pt_2TlS_3, the seed with the highest SLME, in FGW space.