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.

翻译：原子团簇的全局优化是计算化学和材料科学中的一个基础性挑战，因为局部极小值数量随体系规模呈指数增长（即维度灾难问题）。我们提出了一种新颖框架，通过利用张量列车分解挖掘势能面的低秩结构，从而克服这一限制。该方法结合了两种互补的基于张量列车的策略：采用最大体积采样的代数TTOpt方法，以及采用生成式采样的概率PROTES方法。核心创新在于开发了物理约束编码方案，将分子约束直接融入离散化过程。我们通过识别包含多达45个原子的Lennard-Jones团簇的全局极小值，验证了该方法的有效性。此外，通过使用机器学习矩张量势优化20原子碳团簇并获得与量子精度模拟一致的几何构型，证明了该方法在实际体系中的适用性。本工作确立了张量列车分解作为分子结构预测的强大工具，并为计算材料科学中广泛的高维优化问题提供了一个可通用的框架。