Global Optimization of Atomic Clusters via Physically-Constrained Tensor Train Decomposition

• URL: http://arxiv.org/abs/2601.18592v1
• Date: Mon, 26 Jan 2026 15:38:20 GMT
• Title: Global Optimization of Atomic Clusters via Physically-Constrained Tensor Train Decomposition
• Authors: Konstantin Sozykin, Nikita Rybin, Andrei Chertkov, Anh-Huy Phan, Ivan Oseledets, Alexander Shapeev, Ivan Novikov, Gleb Ryzhakov,
• Abstract summary: We introduce a novel framework that overcomes the limitation by exploiting the low-rank structure of potential energy surfaces.<n>We demonstrate the efficacy of our method by identifying global minima of Lennard-Jones clusters containing up to 45 atoms.<n>We establish its practical applicability to real-world systems by optimizing 20-atom carbon clusters using a machine-learned Moment Potential.
• Score: 37.69102815774395
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: The global optimization of atomic clusters represents a fundamental challenge in computational chemistry and materials science due to the exponential growth of local minima with system size (i.e., the curse of dimensionality). We introduce a novel framework that overcomes this limitation by exploiting the low-rank structure of potential energy surfaces through Tensor Train (TT) decomposition. Our approach combines two complementary TT-based strategies: the algebraic TTOpt method, which utilizes maximum volume sampling, and the probabilistic PROTES method, which employs generative sampling. A key innovation is the development of physically-constrained encoding schemes that incorporate molecular constraints directly into the discretization process. We demonstrate the efficacy of our method by identifying global minima of Lennard-Jones clusters containing up to 45 atoms. Furthermore, we establish its practical applicability to real-world systems by optimizing 20-atom carbon clusters using a machine-learned Moment Tensor Potential, achieving geometries consistent with quantum-accurate simulations. This work establishes TT-decomposition as a powerful tool for molecular structure prediction and provides a general framework adaptable to a wide range of high-dimensional optimization problems in computational material science.

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