arXiv AI
Oct 5

Equivariant Flow Matching for Electron Density Prediction

The paper introduces OrbFlow, an SE(3)-equivariant generative model that predicts Gaussian-type orbital coefficients for electron density using flow matching. By training with a two-phase trajectory curriculum, OrbFlow improves accuracy on QM9 and MD benchmarks, reducing density errors significantly compared to previous models. The predicted densities also accelerate self-consistent field procedures, cutting iterations by up to 68% and accurately reproducing dipole and quadrupole moments without additional SCF calculations.

By Chenxing Liang, Chengdong Wang, Yuchao Lin, Xiaofeng Qian, Shuiwang Ji
arXiv Machine Learning
Oct 8

Physics-Aligned Electronic Ground-State Learning Improves Generalization

The paper introduces Physics‑Aligned Electronic Ground‑State Models (GSMs) that sit between machine‑learned interatomic potentials and Kohn‑Sham density functional theory in terms of computational cost and accuracy. By aligning GSM learning objectives with KS‑DFT equations and enforcing physical constraints, the authors develop new training techniques—OrthoNormal‑Loss (ON‑Loss), Grassmann Restricted Occupied‑Orbital Training (GROOT), and Residual Optimal‑gauge Conditioning‑aware KS‑Eq. Training (ROCKET)—which dramatically reduce energy and force errors in size‑extrapolation tests from QM9 to QM40. The models also achieve near‑chemical‑accuracy predictions on reactive chemistry benchmarks and demonstrate efficient label‑free self‑consistency fine‑tuning. whyItMatters":"The work advances the cost‑accuracy frontier for electronic structure predictions, enabling more reliable out‑of‑distribution generalization in drug and material discovery."

By Eike S. Eberhard, Xaver Kainz, Viktor Kotsev, Abdulrahman Aldossary, Stephan G\"unnemann
arXiv Statistics ML
Sep 28

Multivariate conformal uncertainty propagation in multitask atomistic simulation: Successes and pitfalls

The paper explores multivariate conformal uncertainty propagation for multitask atomistic simulations, introducing methods such as Bonferroni‑corrected hyperrectangles, hyperellipsoidal sets based on Mahalanobis distance, and custom loss functions within conformal risk control. It applies these techniques to calibrate predictions of energies, forces, and stresses, then propagates the resulting uncertainty sets to downstream quantities like elastic constants and vacancy formation energies. The study emphasizes how incorporating correlation predictions can capture symmetries and error cancellation, and discusses the interaction between computational protocols and conformal guarantees.

By Katharine Fisher, Michael Herbst, James Kermode, Youssef Marzouk