Surrogate Functionals for Machine-Learned Orbital-Free Density Functional Theory

2026-04-22

AI Summary

This work proposes a purely data-driven orbital-free density functional theory (OF-DFT) framework that overcomes key limitations of traditional approaches, which rely on costly physical reference quantities and computationally expensive orthogonalization procedures. The method introduces a surrogate functional trained solely on ground-state electron densities as the supervisory signal, employing an enhanced gradient-descent loss and an adaptive sampling strategy to directly optimize the density toward the true ground state—without requiring orthogonalization or explicit physical fidelity constraints. Evaluated on the QM9 and QMugs benchmarks, the approach achieves density prediction accuracy on par with or exceeding that of current fully supervised models, while demonstrating substantially improved computational efficiency for large systems and superior scalability.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Computer Vision: Learning & Optimization for CV

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

We introduce surrogate functionals: machine-learned energy functionals for orbital-free density functional theory (OF-DFT) which are defined not by universal fidelity to a physical reference, but merely by the requirement that density optimization with a fixed procedure yields the true ground-state density. Helpfully, training surrogate functionals requires only ground-state densities, no energies or gradients away from the ground state. We here propose a gradient-descent-improvement loss that guarantees exponential convergence of the density to the ground state, and combine it with an adaptive sampling scheme that concentrates learning around the optimization trajectories actually visited during inference. On the QM9 and QMugs benchmarks, surrogate functionals achieve density errors competitive with or improving upon the state of the art for fully supervised machine-learned OF-DFT, while eliminating the need for the $O(N^3)$ orthononormalization step required by prior work, yielding improved runtime scaling for larger systems.

Problem

• orbital-free density functional theory
• machine learning
• surrogate functionals
• ground-state density
• energy functionals

Innovation

• surrogate functionals
• orbital-free DFT
• machine learning
• adaptive sampling
• density optimization