Aug 2026· Proceedings of the 32nd ACM SIGKDD Conference on Knowledge Discovery and Data Mining V.2· 0 citations· 11 references
Abstract
Accurate prediction of electronic Hamiltonians would enable broad property inference while avoiding the high computational cost of Density Functional Theory (DFT). However, progress toward general-purpose materials foundation models is limited by a data bottleneck: existing Hamiltonian datasets are typically small, lack structural diversity, and often omit essential relativistic physics such as spin--orbit coupling (SOC). We therefore construct UniHam, a large-scale Hamiltonian dataset and benchmark suite comprising 100,000+ DFT-computed complex-valued Hermitian Hamiltonians with full SOC, covering 72 elements and a wide range of crystal geometries and symmetries (spanning diverse lattice types and space-group families). Building on UniHam, we benchmark two representative state-of-the-art models under a standardized protocol and introduce complementary evaluation metrics that jointly assess three dimensions: (i) Hamiltonian reconstruction accuracy, (ii) out-of-distribution (OOD) generalization across composition/symmetry shifts, and (iii) the ability to support downstream property prediction from the predicted Hamiltonians. Experiments on UniHam demonstrate that the proposed benchmark and metrics effectively differentiate model capabilities, revealing intrinsic SOC- and element-dependent failure modes, large variations in compositional OOD robustness, and the necessity of spectral-level evaluation to assess whether Hamiltonian predictions reliably support downstream electronic-structure properties. Overall, UniHam provides a reproducible, SOC-complete benchmark that can sharpen model comparisons and accelerate the development of next-generation foundation models for quantum materials.
Coupled-cluster theory defines the accuracy standard for molecular electronic-structure properties but scales too steeply for routine application, whereas density-functional theory is affordable yet systematically biased. We resolve this trade-off with a single equivariant network, MEHnet-MG, that predicts an effective one-electron Hamiltonian from one inexpensive B3LYP/def2-SVP calculation and derives a broad suite of properties from it (energy, optical gap, dipole, quadrupole, polarizability, Mulliken atomic charges, and Mayer bond orders) at coupled-cluster accuracy across nine main-group elements, including the under-served phosphorus, sulfur, and chlorine chemistries. The model is trained on a new in-house dataset of multi-property labels computed at the CCSD(T) level for all nine elements. On a held-out test set, it reduces the error of every property by a factor of 3.8 to 230 relative to semi-local, hybrid, and double-hybrid DFT (referenced to composite CCSD(T)/cc-pVTZ; Methods), while adding only ~25 ms wall time per molecule, delivering coupled-cluster-quality predictions at the cost of a single DFT calculation. Critically, deriving every property from a predicted Hamiltonian rather than pooling per-atom features builds the correct size-scaling into the model architecture: on pi-conjugated oligothiophenes it matches finite-field CCSD polarizability and the EOM-CCSD optical gap to ~2% at the largest sizes where those references remain affordable (44 and 37 atoms, where a single CCSD field point already costs ~500x the model's entire inference) and extrapolates the corrected trends to 58-atom chains, a regime where pooling-based architectures fail by construction. Accurate extrapolation is therefore set by the model's inductive bias rather than by the training data.
While machine learning interatomic potentials (MLiPs) have matured to revolutionize material science, deep learning models for electronic structure are just beginning to emerge and restricted, almost exclusively, to non-orthogonal basis Hamiltonians. We introduce G(Wa)NN, the first deep-learning model capable of generating the electronic Hamiltonian of solid-state systems in an orthogonal Wannier basis. G(Wa)NN is trained on an unprecedented, diverse dataset of more than 111K Wannier Hamiltonians (150M+ hopping matrices) spanning 69 elements. The combination of optimized inference and linear-scaling methods for orthogonal Hamiltonians unlock transport simulations at massive scales (10K+ atoms). Crucially, the framework supports local finetuning, allowing users to adapt the base model to custom Wannier Hamiltonian datasets. To seamlessly translate these predictions into physical observables, we introduce Tailwater, a Python package providing an API interface to G(Wa)NN alongside a high performance post-processing library. Tailwater enables automated projection of the predicted Hamiltonian into an arbitrary low-energy subspace-directly mirroring familiar Wannier90 workflows-and includes a suite of Kernel Polynomial Method (KPM) functions that exploit the orthogonal basis to achieve strict linear scaling for spectral observables. The Tailwater ecosystem, with the G(Wa)NN model at its core, aims to help bridge the gap between deep learning and macro-scale quantum transport simulations.
Machine-learning-based nonlocal density functional approximations have demonstrated substantial potential in advancing the applicability of electronic density functional theory. However, most existing approaches rely on handcrafted local or nonlocal descriptors, which limits their scalability in modeling long-range electronic responses. In this work, we propose a novel exchange-correlation functional approximation model-GTAttn-XC, which introduces a learnable attention mechanism to enable unsupervised modeling of long-range electronic responses. By coupling a multiscale real-space grid graph representation with attention operators, the proposed method achieves a unified description of local accuracy and nonlocal interactions, while avoiding the computational overhead associated with explicit high-order correlation terms. Evaluations on multiple benchmark datasets, including MGCDB84, demonstrate that the model consistently delivers high accuracy across a range of tasks, such as weak interactions, reaction energies, barrier heights, and thermochemical energies. These results establish a new technical pathway toward high-accuracy nonlocal exchange-correlation approximations.
Xin Wang, Jianzhou Feng, Hao Zhang et al.· Journal of Chemical Physics· 0 citations
Mandala is a modular software framework for learning block-sparse electronic-structure matrices with E(3)-equivariant graph neural networks that connects electronic-structure learning and observable-guided modeling while retaining a representation tied to quantum-mechanical operators rather than only scalar or vector targets as in MLIPs.
B. Brzoza, Wiktoria Szopa, Z. Elabid et al.· 0 citations
Rem3Di is introduced, a representation-learning framework that repurposes latent features from atomistic foundation models as transferable molecular descriptors for property prediction and virtual screening and provides a route from simulation-trained atomistic representations to transferable, chirality-aware molecular representations for chemical machine learning.
Steffen Wedig, Felix Burton, Rokas Elijošius et al.· 0 citations
Foundation machine-learning interatomic potentials (MLIPs) enable atomistic simulations at substantially lower computational cost than first-principles methods, but their reliability across structural geometries remains insufficiently understood. Here, we construct a density-functional-theory dataset of ZrO2 configurations spanning bulk, slab, particle, neck, and atomically thin wire environments motivated by an experimentally observed ZrO2 desintering process involving neck thinning and atomic wire formation. We first benchmark 26 pretrained MLIPs and observe pronounced geometry-dependent degradation in zero-shot predictions. Without any training, after only reference-energy alignment, the best zero-shot model (ORB-V3) reaches energy and force root-mean-square errors of 6 meV/atom and 197.3 meV/{\AA}, respectively, with the largest force errors in neck and wire configurations. We then compare zero-shot inference, fine-tuning, and training from scratch strategies. Fine-tuning yields lower energy and force errors than training from scratch, while both require comparable wall-clock time. Geometry-specific fine-tuning improves in-domain accuracy but frequently produces negative transfer to other structural classes, whereas mixed-geometry fine-tuning reduces cross-geometry errors. Evaluations of elastic and vibrational properties, surface energies, and neck dynamics further show that rankings based on average energy and force errors do not universally predict property-level behavior. These results demonstrate that geometry-diverse target data and independent physical validations are necessary when adapting foundation MLIPs to low-coordination (ionic) nanostructures.
P. Zanineli, B. Focassio, G. R. Schleder· 0 citations