Towards continuous machine learning on periodic crystals by ultra-fast invariants

Daniel Eric Widdowson, Vitaliy Kurlin

Keywords: scientific integrity, periodic crystal, isometry invariant, continuous metric

TL;DR: This paper proposes a new continuous approach to all data (including periodic crystals) that have ambiguous representations

Abstract:

Periodic point sets model all solid crystalline materials (crystals) whose atoms can be considered zero-sized points with or without atomic types.

This paper addresses the fundamental problem of checking whether claimed crystals are novel, not noisy perturbations of known materials obtained by unrealistic atomic replacements. Such near-duplicates have already skewed ground truth because past comparisons relied on discontinuous cells and symmetries.

The proposed Lipschitz continuity under noise is a new essential requirement for machine learning on any data objects that have ambiguous representations and live in continuous spaces.

For periodic point sets under isometry (any distance-preserving transformation), we designed the invariants that distinguish all known counter-examples to the completeness of past descriptors and detect thousands of (near-)duplicates in the world's five largest databases in a few minutes on a modest desktop computer.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Submission Number: 11960