Surprisingly High Redundancy in Electronic Structure Data Across Materials Explained by Low Intrinsic Dimensionality

TL;DR

This paper uncovers significant redundancy in electronic structure datasets across materials, attributing it to low intrinsic dimensionality, and demonstrates effective data pruning strategies that maintain accuracy while greatly reducing dataset size and training time.

Contribution

It reveals the low-dimensional manifold structure of electronic data and introduces pruning methods that drastically reduce dataset size without sacrificing predictive accuracy.

Findings

Random pruning reduces dataset size with minimal accuracy loss.

Coverage-based pruning preserves accuracy using up to 100 times less data.

Electronic structure data lies on a low-dimensional, non-linear manifold.

Abstract

Machine learning (ML) models for electronic structure typically rely on large datasets generated by computationally expensive Kohn-Sham density functional theory calculations, as it is not known a priori which portions of the data are essential for accurate learning. Here, we reveal significant redundancies in electronic structure datasets across diverse material systems and attribute them to the low intrinsic dimensionality of the underlying data. We show that even random pruning can substantially reduce dataset size with minimal degradation in predictive accuracy. Moreover, a state-of-the-art coverage-based pruning strategy that samples data across all learning difficulties preserves chemical accuracy and model generalizability while using up to two orders of magnitude less data and reducing training time by a factor of three or more. We further demonstrate that the essential electronic structure information lies on a low-dimensional, non-linear manifold, providing a geometric explanation for the observed prunability. These observations are consistent with the predominance of local atomic environments in determining electronic properties, as suggested by nearsightedness arguments, and indicate that large-scale datasets may contain highly overlapping information. Our findings challenge the prevailing assumption that such extensive datasets are necessary for accurate ML-based electronic structure predictions and open a path toward identifying minimal, representative datasets for each material class.