The paper introduces a tensor algebra, ∗_G, that enforces exact symmetry in machine‑learned models of molecular and crystal responses. By applying this algebra to the Orb‑v3 force field, the authors demonstrate that many models incorrectly alter a crystal’s space group during relaxation, and they show how projections derived from ∗_G can correct these errors without retraining. The method yields reference‑free error bounds and symmetry‑preserving low‑rank approximations, reducing space‑group changes to at most 2%.
By Paulina Hoyos, Shashanka Ubaru, Dongsung Huh, Vasileios Kalantzis, Kenneth L. Clarkson, Misha Kilmer, Haim Avron, Lior Horesh
arXiv:2607. 07127v1 Announce Type: cross Abstract: Lattice field theory is the workhorse of non-perturbative physics, used to simulate phenomena from the strong nuclear force to critical phenomena in materials.
By Tobias G\"obel, Julian R. Ebelt, Zier Mensch, Mathis Gerdes, Miranda C. N. Cheng
NucleoNet is a neural‑network variational Monte Carlo ansatz that treats electrons and nuclei as a unified particle set, allowing a single model to be optimized across multiple geometries. The approach uses a shared electron–nucleus backbone to evolve one‑particle and two‑particle representations, with nuclear streams learning representations that condition orbital construction while antisymmetry is enforced only by electronic determinants. On small‑molecule benchmarks, NucleoNet matches the accuracy of established neural‑wavefunction baselines with far fewer parameters and successfully describes dissociation curves and minimum‑energy paths for several systems, demonstrating that a compact wavefunction can capture molecular geometries with a single set of parameters.
By Qiao Gao, Yang Huang, Enze Hou, Yuzhi Liu, Jingrun Chen, Han Wang
arXiv:2606. 06866v1 Announce Type: new Abstract: The prediction of masses of atomic nuclei using machine learning can complement theoretical models and advance the exploration of poorly known domains of the nuclear chart.
By Ziyuan Li, Paulo S. A. Freitas, John W. Clark, Babette Dellen
The paper introduces UniTB, a universal, E(3)-equivariant Hamiltonian framework that blends density‑functional tight‑binding priors with deep learning to predict electronic structures efficiently. UniTB corrects a prior Hamiltonian via a mixture‑of‑experts network and a charge‑equilibration head, ensuring physical downstream properties and suppressing spurious states. Trained on over 29,000 crystals, UniTB achieves sub‑meV accuracy, matches DFT predictions for amorphous Ge‑Sb‑Te, and enables rapid screening of more than 16,000 materials for industrial applications.
By Mingkang Liu, Zhanghao Zhouyin, Guanghui Wang, Daye Zheng, Lei Shen, Qiangqiang Gu
The article reviews recent progress in applying machine learning to high‑energy nuclear physics, highlighting a shift from basic pattern recognition to physics‑integrated workflows. It covers calibrated Bayesian extraction of QCD matter properties, equation‑of‑state inference from heavy‑ion and neutron‑star data, generative event modeling, neural unfolding of weak signals, differentiable inverse solvers, gauge‑equivariant lattice‑field samplers, and holographic QCD reconstructions. The focus is on how ML models incorporate physical constraints—symmetries, conservation laws, causality, thermodynamic stability, and topology—and how uncertainty quantification and validation ensure reliable physics conclusions.
By Xun Chen, Weiyao Ke, Yu-Gang Ma, Long-Gang Pang, Kai Zhou