Learning the Hamiltonian of Disordered Materials with Equivariant Graph Networks

Chen Hao Xia, Manasa Kaniselvan, Alexandros Nikolaos Ziogas, Marko Mladenovic, Alexander Maeder, Mathieu Luisier

Keywords: Materials modeling, atomic structure, electronic structure, density functional theory, graph neural networks, hamiltonian, amorphous systems

TL;DR: We developed methods to train equivariant graph neural networks to learn the ground state Hamiltonian of amorphous materials with large unit cells.

Abstract: Graph neural networks (GNNs) have shown promise in learning the ground-state electronic properties of molecules and crystalline materials, subverting computationally intensive density functional theory (DFT) calculations. Materials with structural disorder, however, are more challenging to learn as they exhibit higher complexity and a more extensive palette of local atomic environments, all of which require large (10+ Angstrom) cells to be accurately captured. In this work, we adapt efficient equivariant GNN approaches to learn disordered materials' electronic properties, represented by the Hamiltonian matrix ($\mathbf{H}$). Since creating a large graph corresponding to the whole structure of interest would be computationally prohibitive, we introduce an 'augmented partitioning' approach in which the graph is sliced into multiple partitions, each augmented with masked virtual nodes and edges. This method maintains correct atomic neighborhoods within a single message passing layer, allowing for the network to learn the electronic properties of amorphous HfO$_2$ materials with 3,000 nodes (atoms), 500,000+ edges, and $\sim$28 million orbital interactions (non-zero entries of $\mathbf{H}$).

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Submission Number: 7589