Towards Combinatorial Generalization for Catalysts: A Kohn-Sham Charge-Density Approach

The Kohn-Sham equations underlie many important applications such as the discovery of new catalysts. Recent machine learning work on catalyst modeling has focused on prediction of the energy, but has so far not yet demonstrated significant out-of-distribution generalization. Here we investigate another approach based on the pointwise learning of the Kohn-Sham charge-density. On a new dataset of bulk catalysts with charge densities, we show density models can generalize to new structures with combinations of elements not seen at train time, a form of combinatorial generalization. We show that over 80% of binary and ternary test cases achieve faster convergence than standard baselines in Density Functional Theory, amounting to an average reduction of 13% in the number of iterations required to reach convergence, which may be of independent interest. Our results suggest that density learning is a viable alternative, trading greater inference costs for a step towards combinatorial generalization, a key property for applications. Perhaps the greatest difficulty of catalyst discovery is the combinatorial size of the search space of structures. Even when reducing the candidate set of elements to 55, as done in the Open Catalyst Project [8], the number of possible element combinations grows very quickly: we have 55 3 = 26, 235, 55 4 = 341, 055, and so forth. Additional factors like choice of crystal lattice, surface orientations, binding sites, and adsorbates further complicate matters, but nevertheless the number of possible element combinations is a dominating factor. Given the immensity of this search space, generalization to new combinations is a key aspect for the success of property-predicting models in applications. Put 37th Conference on Neural Information Processing Systems (NeurIPS 2023).