ICML 2025

Learning the Electronic Hamiltonian of Large Atomic Structures
Chen Hao Xia * 1 Manasa Kaniselvan * 1 Alexandros Nikolaos Ziogas 1 Marko Mladenovi´c 1 Rayen Mahjoub 1
Alexander Maeder 1 Mathieu Luisier 1
Abstract
Graph neural networks (GNNs) have shown
promise in learning the ground-state electronic
properties of materials, subverting ab initio den-
sity 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, how-
ever, non-ideal and generally characterized by
higher structural complexity. As such, they re-
quire large (10+ ˚A) unit cells and thousands of
atoms to be accurately described. At these scales,
DFT becomes computationally prohibitive, mak-
ing 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 pre-
serving local atomic environments beyond bound-
aries. We demonstrate its capabilities by predict-
ing 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 ≤0.53% error in the eigenvalue spec-
tra. Our work expands the applicability of current
electronic property prediction methods to some of
the most challenging cases encountered in compu-
tational materials science, namely systems with
disorder, interfaces, and defects.
1. Introduction
Graph neural networks (GNNs) have proven capable of
learning properties that are functions of molecular and
*Equal contribution
1Integrated Systems Laboratory, Depart-
ment of Information Technology and Electrical Engineering, ETH
Zurich, Zurich, Switzerland.
Correspondence to: Chen Hao
Xia <chexia@iis.ee.ethz.ch>, Manasa Kaniselvan <mkanisel-
van@iis.ee.ethz.ch>.
Proce...