通过基于高斯过程的探索来探索用于功能和结构发现的格点哈密顿算子
Exploration of lattice Hamiltonians for functional and structural discovery via Gaussian Process-based Exploration-Exploitation
摘要：
从简单晶格到复杂量子哈密顿量的统计物理模型是现代物理学的支柱之一，它允许几十年的科学发现，并提供了一个通用的框架来理解从合金到受挫和相分离材料到量子系统的广泛现象。传统上，探索对应于多维参数空间的哈密顿相图进行了基本的物理原理，解析近似，和广泛的数值模拟的组合。然而，复杂多维参数空间的探索受制于经典的维度问题，并且集中在低维流形上的感兴趣的行为可能仍未被发现。在这里，我们证明了探索和探索-利用与高斯过程建模和贝叶斯优化的组合允许有效地探索晶格哈密顿的参数空间，并有效地映射特定宏观功能或局部结构最大化的区域。我们认为，这种方法是通用的，可以进一步扩展远远超出晶格哈密顿有效地探索更复杂的非晶格和动态模型的参数空间。
英文摘要：
Statistical physics models ranging from simple lattice to complex quantum Hamiltonians are one of the mainstays of modern physics, that have allowed both decades of scientific discovery and provided a universal framework to understand a broad range of phenomena from alloying to frustrated and phase-separated materials to quantum systems. Traditionally, exploration of the phase diagrams corresponding to multidimensional parameter spaces of Hamiltonians was performed using a combination of basic physical principles, analytical approximations, and extensive numerical modeling. However, exploration of complex multidimensional parameter spaces is subject to the classic dimensionality problem, and the behaviors of interest concentrated on low dimensional manifolds can remain undiscovered. Here, we demonstrate that a combination of exploration and exploration-exploitation with Gaussian process modeling and Bayesian optimization allows effective exploration of the parameter space for lattice Hamiltonians, and effectively maps the regions at which specific macroscopic functionalities or local structures are maximized. We argue that this approach is general and can be further extended well beyond the lattice Hamiltonians to effectively explore parameter space of more complex off-lattice and dynamic models.
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