Physics aligned models improve predictions of electronic ground states
Physics-Aligned Electronic Ground-State Learning Improves Generalization
Machine Learning
Summary
Predicting the behavior of molecules and materials accurately and quickly is hard because standard methods either take too long or don’t handle new, unseen molecules well. The authors propose new machine learning models that respect the physics of how electrons arrange themselves in molecules, improving prediction accuracy and speed. These models better generalize to larger or different molecules, and can self-check their own predictions to avoid big mistakes. They also show the models can adapt to chemical reactions without needing additional labeled data.
What this means in practice
- •For computational chemists: Use physics-aligned models to speed up electronic structure calculations with improved accuracy for larger molecular systems beyond existing data.
- •For materials simulation engineers: Integrate these aligned learning models to predict forces and energies efficiently for reactive chemical simulations relevant to material design.
Authors
Eike S. Eberhard, Xaver Kainz, Viktor Kotsev, Abdulrahman Aldossary, Stephan Günnemann
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.