Graph neural networks (GNNs) have shown promise in learning the ground-state electronic properties of materials, subverting ab initio density functional theory (DFT) calculations when the underlying lattices can be represented as small and/or repeatable unit cells (i.e., molecules and periodic crystals). Realistic systems are, however, non-ideal and generally characterized by higher structural complexity. As such, they require large (10+ {Å}) unit cells and thousands of atoms to be accurately described. At these scales, DFT becomes computationally prohibitive, making GNNs especially attractive. In this work, we present a strictly local equivariant GNN capable of learning the electronic Hamiltonian (H) of realistically extended materials. It incorporates an augmented partitioning approach that enables training on arbitrarily large structures while preserving local atomic environments beyond boundaries. We demonstrate its capabilities by predicting the electronic Hamiltonian of various systems with up to 3,000 nodes (atoms), 500,000+ edges, 28 million orbital interactions (nonzero entries of H), and $\leq$0.53% error in the eigenvalue spectra. Our work expands the applicability of current electronic property prediction methods to some of the most challenging cases encountered in computational materials science, namely systems with disorder, interfaces, and defects.

Simulating emerging resistive switching memory devices, such as memristors, requires modeling frameworks that can treat the motion of point defects across nanoscale domains. Field-driven Kinetic Monte Carlo (d-KMC) methods that simulate the discrete structural evolution of atomic coordinates in the presence of external potential and heat fields can be used for this purpose. While physically similar to conventional KMC methods, field-driven approaches present different computational motifs and introduce global communication. Here, we develop the first scalable d-KMC code for resistive memory arrays at atomistic resolution. We accelerate this latency-sensitive simulation on the GPU partition of the LUMI Supercomputer, exploiting the high-speed interconnects between GPUs on the same node. Applied to the technologically relevant HfOx material stack, our code enables the first atomistic simulation of $3 \times 3$ arrays of resistive switching memory cells with more than 1 million atoms, matching the dimensions of fabricated structures.