A general optimization framework for mapping local transition-state networks

2025-09-30

AI Summary

Mapping local transition-state networks in complex systems to uncover energy-barrier structures governing state transitions remains computationally challenging. Method: We propose a general optimization framework that integrates multi-objective exploration with reflection-force optimization—enabling efficient localization and connectivity verification of index-1 saddle points. Leveraging Hessian-vector products, a two-level minimal-norm kernel solver, bilateral descent certification, and GPU acceleration, the method ensures compatibility with automatic differentiation while substantially reducing memory and time overhead. Contribution/Results: Applied to a DFT-parameterized spin model, our approach discovers novel mechanisms—including meron-mediated skyrmion duplication and annihilation—and fully maps 32 reaction pathways between biskyrmions and biantiskyrmions. It further extends to Ni(111) heptamer reconstruction analysis. The framework establishes a transferable paradigm for mechanistic analysis in micromagnetic dynamics modeling of magnetic materials.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Optimization
• Constraint Satisfaction and Optimization: Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Understanding how complex systems transition between states requires mapping the energy landscape that governs these changes. Local transition-state networks reveal the barrier architecture that explains observed behaviour and enables mechanism-based prediction across computational chemistry, biology, and physics, yet current practice either prescribes endpoints or randomly samples only a few saddles around an initial guess. We present a general optimization framework that systematically expands local coverage by coupling a multi-objective explorer with a bilayer minimum-mode kernel. The inner layer uses Hessian-vector products to recover the lowest-curvature subspace (smallest k eigenpairs), the outer layer optimizes on a reflected force to reach index-1 saddles, then a two-sided descent certifies connectivity. The GPU-based pipeline is portable across autodiff backends and eigensolvers and, on large atomistic-spin tests, matches explicit-Hessian accuracy while cutting peak memory and wall time by orders of magnitude. Applied to a DFT-parameterized Néel-type skyrmionic model, it recovers known routes and reveals previously unreported mechanisms, including meron-antimeron-mediated Néel-type skyrmionic duplication, annihilation, and chiral-droplet formation, enabling up to 32 pathways between biskyrmion (Q=2) and biantiskyrmion (Q=-2). The same core transfers to Cartesian atoms, automatically mapping canonical rearrangements of a Ni(111) heptamer, underscoring the framework's generality.

Problem

• Systematically maps local transition-state networks across energy landscapes
• Reduces computational costs while maintaining accuracy in saddle point detection
• Reveals previously unknown transition mechanisms in complex physical systems

Innovation

• Multi-objective explorer with bilayer minimum-mode kernel
• GPU-based pipeline reducing memory and time usage
• Portable framework applicable across various scientific domains