A general optimization framework for mapping local transition-state networks
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912618124410880 |
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| author | Xu, Qichen Delin, Anna |
| author_facet | Xu, Qichen Delin, Anna |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_26269 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A general optimization framework for mapping local transition-state networks Xu, Qichen Delin, Anna Computational Physics Materials Science Neural and Evolutionary Computing 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. |
| title | A general optimization framework for mapping local transition-state networks |
| topic | Computational Physics Materials Science Neural and Evolutionary Computing |
| url | https://arxiv.org/abs/2509.26269 |