arXiv subjects

Vitaliy A Kurlin

Publications and source records attributed to Vitaliy A Kurlin.

4 recordsLinked to original sources

arXiv2026

Necessary conditions for benchmarking next-generation AI in materials discovery

Current AI predicts materials by speeding up energy minimisation and training on large databases. However, scaling data generation prevents manual analysis by domain experts. If novelty is evaluated by chemical compositions or traditional representations in Crystallographic Information Files, or standard structure matchers based on manually chosen thresholds, one can easily generate millions of ``new'' compositions or files without discovering truly novel materials. This paper uses a hierarchy of crystal invariants to continuously trace and quantify structural novelty based on the new mathematical definition of a crystal structure and asymptotic guarantees for invariant descriptors. The invariant-based analysis through cascade computations on a modest computer exposes the unexpected scale of duplication in the world's largest materials databases, shown here in the high-profile case of GNoME datasets. To prevent current ``embarrassment of over-prediction'', we propose necessary conditions for next-generation AI that should be automatically enforced before claiming any new materials.

cond-mat.mtrl-sci↗

arXiv2025

Geographic-style maps with a local novelty distance help navigate the materials space

With the advent of self-driving labs promising to synthesize large numbers of new materials, new automated tools are required for checking potential duplicates in existing structural databases before a material can be claimed as novel. To avoid duplication, we rigorously define the novelty metric of any periodic material as the smallest distance to its nearest neighbor among already known materials. Using ultra-fast structural invariants, all such nearest neighbors can be found within seconds on a typical computer even if a given crystal is disguised by changing a unit cell, perturbing atoms, or replacing chemical elements. This real-time novelty check is demonstrated by finding near-duplicates of the 43 materials produced by Berkeley's A-lab in the world's largest collections of inorganic structures, the Inorganic Crystal Structure Database and the Materials Project. To help future self-driving labs successfully identify novel materials, we propose navigation maps of the materials space where any new structure can be quickly located by its invariant descriptors similar to a geographic location on Earth.

cond-mat.mtrl-sci↗

arXiv2025

Geometric Data Science

This book introduces the new research area of Geometric Data Science, where data can represent any real objects through geometric measurements. The first part of the book focuses on finite point sets. The most important result is a complete and continuous classification of all finite clouds of unordered points under rigid motion in any Euclidean space. The key challenge was to avoid the exponential complexity arising from permutations of the given unordered points. For a fixed dimension of the ambient Euclidean space, the times of all algorithms for the resulting invariants and distance metrics depend polynomially on the number of points. The second part of the book advances a similar classification in the much more difficult case of periodic point sets, which model all periodic crystals at the atomic scale. The most significant result is the hierarchy of invariants from the ultra-fast to complete ones. The key challenge was to resolve the discontinuity of crystal representations that break down under almost any noise. Experimental validation on all major materials databases confirmed the Crystal Isometry Principle: any real periodic crystal has a unique location in a common moduli space of all periodic structures under rigid motion. The resulting moduli space contains all known and not yet discovered periodic crystals and hence continuously extends Mendeleev's table to the full crystal universe.

math.MG↗

arXiv2025

Higher-order, generically complete, continuous, and polynomial-time isometry invariants of periodic sets

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 skewed ground-truth because past comparisons relied on unstable 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 invariants that distinguish all known counter-examples to the completeness of past descriptors and detect thousands of (near-)duplicates in large high-profile databases of crystals within two days on a modest desktop computer.

cs.CG↗