[Paper Review] Atomistic Global Optimization X: A Python package for optimization of atomistic structures

Mads-Peter Verner Christiansen, Nikolaj Rønne+1 more|arXiv (Cornell University)|Apr 4, 2022

Machine Learning in Materials Science91 references37 citations

TL;DR

This paper introduces AGOX, a modular Python framework for global optimization of atomistic structures, enabling efficient implementation and experimentation with diverse algorithms—from random search to machine learning-augmented methods like GOFEE. It integrates with ASE and supports on-the-fly surrogate models using Gaussian process regression, significantly accelerating structure searches across complex systems like clusters, surfaces, and graphene-embedded nitrides.

ABSTRACT

Modelling and understanding properties of materials from first principles require knowledge of the underlying atomistic structure. This entails knowing the individual identity and position of all involved atoms. Obtaining such information for macro-molecules, nano-particles, clusters, and for the surface, interface, and bulk phases of amorphous and solid materials represents a difficult high dimensional global optimization problem. The rise of machine learning techniques in materials science has, however, led to many compelling developments that may speed up such structure searches. The complexity of the new methods have established the necessity for an efficient way of experimenting with and assembling them into global optimization algorithms. In this paper we introduce the Atomistic Global Optimization X (AGOX) framework and code, as a customizable approach to building efficient global optimization algorithms. A modular way of expressing global optimization algorithms is described and modern programming practices are used to enable that modularity in the freely available AGOX python package. Two examples of global optimization problems are analyzed: One that is computationally inexpensive which is used to showcase that AGOX enables the expression of multiple global optimization algorithms. As the other example, AGOX is used for solving a complex atomistic optimization problem for a metal-nitride nano-cluster embedded in a graphene sheet as described at the density functional theory (DFT) level.

Motivation & Objective

• To develop a flexible, extensible framework for implementing and testing global optimization algorithms in atomistic systems.
• To address the growing complexity of modern optimization methods, especially those incorporating machine learning, by enabling rapid prototyping and experimentation.
• To streamline the integration of first-principles calculations and surrogate models within a single, user-friendly codebase.
• To support diverse optimization strategies—from basin-hopping to evolutionary algorithms and ML-accelerated methods—across a range of materials systems.
• To provide a scalable, parallelizable solution that leverages modern programming practices and interoperability with electronic structure codes.

Proposed method

• AGOX is built on a modular architecture with data-type modules (e.g., environment, population) and action-type modules (e.g., generate, optimize, evaluate) to compose global optimization workflows.
• It supports multiple optimization strategies, including random structure search (RSS), basin-hopping (BH), evolutionary algorithms (EA), and GOFEE, which uses a surrogate potential to reduce expensive DFT evaluations.
• The framework employs Gaussian Process Regression (GPR) with a double Gaussian kernel for surrogate energy landscape modeling, enabling uncertainty-aware optimization via the lower-confidence-bound (LCB) acquisition function.
• Structural fingerprints based on radial and angular components (Oganov-Valle features) are used as input to the GPR model, with parameters set to σ = 0.2 Å, l1 = 1.0 Å, l2 = 0.1 Å, β = 0.01, and Rθ = 4 Å.
• Spectral clustering via graph Laplacian eigenvalues is used to identify topologically distinct structures, enabling robust clustering independent of minor bond length variations.
• The framework integrates with ASE and supports parallelization via methods like parallel tempering, enabling efficient use of HPC resources.

Experimental results

Research questions

• RQ1 How can a modular, composable framework be designed to support diverse global optimization algorithms for atomistic systems?
• RQ2 To what extent can machine learning surrogate models, particularly GPR with LCB acquisition, reduce computational cost in global optimization of complex materials?
• RQ3 How does AGOX enable surgical algorithmic modifications to improve efficiency, as demonstrated in tin-oxide surface reconstructions?
• RQ4 Can AGOX effectively scale to large, computationally demanding systems such as metal-nitride clusters in graphene with spin polarization?
• RQ5 How does spectral clustering of atomic graphs improve the identification of unique, non-redundant structures in optimization outputs?

Key findings

• AGOX successfully implements and benchmarks multiple global optimization methods, including RSS, BH, EA, and GOFEE, on diverse systems such as supported clusters, surface reconstructions, and large carbon clusters.
• The GOFEE method with LCB acquisition reduced the number of expensive DFT evaluations by prioritizing promising candidates based on predicted energy and uncertainty.
• In the tin-oxide surface case, AGOX enabled direct comparison of standard basin-hopping and a machine learning-enhanced variant, demonstrating reduced computational cost with the latter.
• Parallel tempering was successfully applied in AGOX to accelerate convergence for a 2D carbon cluster, showing effective use of parallel computing resources.
• Spectral clustering based on Laplacian eigenvalues effectively grouped structurally similar configurations, enabling robust identification of unique structures without sensitivity to minor bond-length variations.
• The framework achieved full reproducibility and ease of use, with AGOX v1.1.0 released under GNU GPLv3 and documentation available at https://agox.gitlab.io/agox, supporting community adoption and extension.