Physics-Aligned Electronic Ground-State Learning Improves Generalization

2026-10-07

AI Summary

This study addresses the limited out-of-distribution generalization of machine learning interatomic potentials and their inherent trade-off between computational cost and accuracy by proposing a physics-aligned electronic ground-state descriptor model. Methodologically, Kohn-Sham density functional theory constraints are embedded into the learning architecture, and three techniques—ON-Loss, GROOT, and ROCKET—are introduced to eliminate unphysical degrees of freedom and enable label-free self-consistent fine-tuning. Experimental results demonstrate that energy and force prediction errors are reduced by over 95%, achieving a mean absolute error of 0.07 mHa on the QMugs dataset, with reaction chemistry errors falling below chemical accuracy thresholds. These improvements significantly enhance the cross-scale generalization performance of the model.

Abstract

Machine-learned interatomic potentials (MLIPs) excel at in-distribution tasks, accelerating drug and material development, yet they struggle to generalize out-of-distribution. We propose to push the cost-accuracy Pareto frontier by designing observable-agnostic electronic ground-state descriptor models (GSMs) with computational costs situated between MLIPs and Kohn-Sham density functional theory (KS-DFT). We align the learning objectives and architectures of GSMs with the governing equations of KS-DFT by enforcing physical constraints and removing optimization pressure on unphysical or irrelevant degrees of freedom. In our size-extrapolation experiments from QM9 to QM40, our combined contributions OrthoNormal-Loss (ON-Loss) and Grassmann Restricted Occupied-Orbital Training (GROOT) reach a 79.1% energy and 83.4% force mean absolute error (MAE) reduction over previous state-of-the-art density GSMs. For Hamiltonian GSMs, ON-Loss and Residual Optimal-gauge Conditioning-aware KS-Eq. Training (ROCKET) together reduce the energy and force MAEs of the strongest baseline by 99.8% and 95.9%, respectively. Using a self-consistency rejection criterion, we filter out extrapolation errors on QMugs, rejecting fewer than 0.4% of predictions while reaching an energy MAE of 0.07 mHa. Finally, we demonstrate the efficiency of label-free self-consistency fine-tuning, and transfer GSMs to reactive chemistry in Transition1x, reaching energy errors below chemical accuracy.

Problem

• Machine-learned interatomic potentials
• Out-of-distribution generalization
• Electronic ground-state learning
• Size extrapolation

Innovation

• Electronic Ground-State Descriptor Models
• Physics-Aligned Learning
• Out-of-Distribution Generalization
• Self-Consistency Fine-Tuning
• Kohn-Sham Density Functional Theory