arXiv:2506. 09398v4 Announce Type: replace Abstract: We consider the task of predicting Hamiltonian matrices to accelerate electronic structure calculations, which plays an important role in physics, chemistry, and materials science.
The paper introduces MEHnet-MG, an equivariant neural network that predicts a one‑electron Hamiltonian from a single inexpensive B3LYP/def2‑SVP calculation and uses it to compute a wide range of molecular properties—energy, optical gap, dipole, quadrupole, polarizability, Mulliken charges, and Mayer bond orders—at coupled‑cluster accuracy for nine main‑group elements, including phosphorus, sulfur, and chlorine. Trained on a new CCSD(T) dataset, the model reduces property errors by factors ranging from 3.8 to 230 compared to various DFT methods while adding only ~25 ms per molecule. Importantly, by deriving properties from a predicted Hamiltonian rather than pooling atomic features, the architecture naturally incorporates correct size‑scaling, enabling accurate extrapolation to large π‑conjugated systems (up to 58 atoms) where traditional pooling‑based models fail.
arXiv:2608.28853v1 Announce Type: cross Abstract: Equivariant graph neural networks provide a principled way to model geometric systems, but efficient first-order architectures remain limited in how...
arXiv:2604. 20308v2 Announce Type: replace Abstract: Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (directions, gradients), yet many tasks require matrix-valued representations that capture relationships between directions-such as how atomic orientations covary in a molecule.
arXiv:2607. 01408v1 Announce Type: cross Abstract: $\mathrm{E}(3)$-equivariant networks are promising for 3D atomistic system modeling, yet their scalability is limited by the $O(L^6)$ complexity of the Clebsch-Gordan Tensor Product (CGTP).
arXiv:2607. 05736v1 Announce Type: new Abstract: Molecular property prediction often relies on isolated data modalities, where continuous 3D graph neural networks (GNNs) struggle to efficiently capture long-range topological dependencies and exact macroscopic heuristics.
The paper presents a neural operator that learns the Kohn–Sham map, directly predicting electron density from the Kohn–Sham potential without orbital diagonalization. Using a domain‑invariant SE(3)‑equivariant Fourier neural operator trained on 8,504 molecules and solids, the model achieves quasi‑linear scaling self‑consistent field (SCF) convergence across diverse systems—including organic molecules, insulators, and metals—while reproducing Kohn–Sham DFT accuracy for densities, spectra, and structural observables. This enables large‑scale simulations, such as magnesium dislocation densities with 82,500 valence electrons, on a single GPU.
arXiv:2609. 21085v1 Announce Type: cross Abstract: Gaussian processes (GPs) provide principled probabilistic predictions while encoding prior knowledge, including equivariances.
arXiv:2606. 30961v1 Announce Type: cross Abstract: Advances in deep learning architectures and representations have enabled ML-driven chemical property prediction, but state-of-the-art (SOTA) models have remained largely confined to independent codebases and lack support for diverse chemical species.
arXiv:2606. 28911v1 Announce Type: new Abstract: Machine-learned (ML) operator models can be trained to predict density functional theory (DFT) Hamiltonian/density matrices at significantly reduced computational cost, thus extending electronic-structure calculations to previously unfeasible scales.
arXiv:2607. 19083v1 Announce Type: new Abstract: Equivariant graph neural networks provide a powerful modeling language for three-dimensional scientific data, but their reuse is often limited by implementations tied to specific tasks, outputs, and training regimes.
MAELLE is a mechanistic reaction prediction framework that models chemical reactions as discrete flow matching over graph-structured electron occupation vectors. It formulates the reactant-to-product mapping as a Continuous-time Markov Chain on electron sites and uses Optimal Transport to generate mechanistically interpretable edit trajectories without elementary step annotations. The method achieves competitive accuracy on the USPTO-480K benchmark, remains robust in out-of-distribution scenarios, and can recover mechanistic pathways that align with known chemistry and predict side products.