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

2026-01-26

AI Summary

This work addresses the curse of dimensionality in global optimization of atomic clusters, where the number of local minima on the potential energy surface grows exponentially with system size. The authors propose a physics-informed Tensor Train (TT) decomposition method that integrates molecular symmetries and bond-length priors into a discrete encoding scheme, enabling, for the first time, a synergistic model combining physical constraints with low-rank tensor structure. By coupling TT-based algebraic optimization (TTOpt), probabilistic generative sampling (PROTES), and a machine-learned interatomic potential (Moment Tensor Potential), the approach efficiently explores high-dimensional configuration spaces. The method successfully identifies the global minimum of a 45-atom Lennard-Jones cluster and reproduces quantum-accuracy results for a 20-atom carbon cluster, significantly enhancing both scalability and accuracy in large-scale cluster optimization.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

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.

Problem

• global optimization
• atomic clusters
• potential energy surface
• curse of dimensionality
• molecular structure prediction

Innovation

• Tensor Train decomposition
• global optimization
• atomic clusters
• physically-constrained encoding
• potential energy surface