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

arXiv: https://arxiv.org/abs/2310.18702 · HTML: https://mlsanity.com/paper/2310.18702/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 49 references that are in the map.
- First posted on arXiv 28 Oct 2023.

## Builds on (most cited first, 26 of 26)

- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Winoground: Probing Vision and Language Models for Visio-Linguistic Compositionality](https://mlsanity.com/paper/2204.03162/) (2022)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [The Open Catalyst 2020 (OC20) Dataset and Community Challenges](https://mlsanity.com/paper/2010.09990/) (2020)
- [Measuring abstract reasoning in neural networks](https://mlsanity.com/paper/1807.04225/) (2018)
- [GOOD: A Graph Out-of-Distribution Benchmark](https://mlsanity.com/paper/2206.08452/) (2022)
- [Language as an Abstraction for Hierarchical Deep Reinforcement Learning](https://mlsanity.com/paper/1906.07343/) (2019)
- [The Open Catalyst 2022 (OC22) Dataset and Challenges for Oxide Electrocatalysts](https://mlsanity.com/paper/2206.08917/) (2022)
- [Unifying machine learning and quantum chemistry -- a deep neural network for molecular wavefunctions](https://mlsanity.com/paper/1906.10033/) (2019)
- [By-passing the Kohn-Sham equations with machine learning](https://mlsanity.com/paper/1609.02815/) (2016)
- [Learning to Make Analogies by Contrasting Abstract Relational Structure](https://mlsanity.com/paper/1902.00120/) (2019)
- [Can stable and accurate neural networks be computed? -- On the barriers of deep learning and Smale's 18th problem](https://mlsanity.com/paper/2101.08286/) (2021)
- [Rotation Invariant Graph Neural Networks using Spin Convolutions](https://mlsanity.com/paper/2106.09575/) (2021)
- [Spherical Channels for Modeling Atomic Interactions](https://mlsanity.com/paper/2206.14331/) (2022)
- [An Introduction to Electrocatalyst Design using Machine Learning for Renewable Energy Storage](https://mlsanity.com/paper/2010.09435/) (2020)
- [AiiDA 1.0, a scalable computational infrastructure for automated reproducible workflows and data provenance](https://mlsanity.com/paper/2003.12476/) (2020)
- [AiiDA: Automated Interactive Infrastructure and Database for Computational Science](https://mlsanity.com/paper/1504.01163/) (2015)
- [Precision Machine Learning](https://mlsanity.com/paper/2210.13447/) (2022)
- [DeepDFT: Neural Message Passing Network for Accurate Charge Density Prediction](https://mlsanity.com/paper/2011.03346/) (2020)
- [Neuro-algorithmic Policies enable Fast Combinatorial Generalization](https://mlsanity.com/paper/2102.07456/) (2021)
- [Lost in Latent Space: Disentangled Models and the Challenge of Combinatorial Generalisation](https://mlsanity.com/paper/2204.02283/) (2022)
- [Deep Density: circumventing the Kohn-Sham equations via symmetry preserving neural networks](https://mlsanity.com/paper/1912.00775/) (2019)
- [Neural Constraint Satisfaction: Hierarchical Abstraction for Combinatorial Generalization in Object Rearrangement](https://mlsanity.com/paper/2303.11373/) (2023)
- [Workflows in AiiDA: Engineering a high-throughput, event-based engine for robust and modular computational workflows](https://mlsanity.com/paper/2007.10312/) (2020)
- [Design for a Darwinian Brain: Part 1. Philosophy and Neuroscience](https://mlsanity.com/paper/1303.7200/) (2013)

## Built on by (most cited first, 5 of 5)

- [Higher-Order Equivariant Neural Networks for Charge Density Prediction in Materials](https://mlsanity.com/paper/2312.05388/) (2023)
- [ELECTRA: A Cartesian Network for 3D Charge Density Prediction with Floating Orbitals](https://mlsanity.com/paper/2503.08305/) (2025)
- [A Recipe for Charge Density Prediction](https://mlsanity.com/paper/2405.19276/) (2024)
- [Generative artificial intelligence for computational chemistry: a roadmap to predicting emergent phenomena](https://mlsanity.com/paper/2409.03118/) (2024)
- [Global Plane Waves From Local Gaussians: Periodic Charge Densities in a Blink](https://mlsanity.com/paper/2601.19966/) (2026)

## Abstract (arXiv)

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.