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.

中文翻译：

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通过基于高斯过程的探索-利用，探索格子哈密顿量以进行功能和结构发现

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，它支持了数十年的科学发现，并提供了一个通用框架来理解从合金化到挫败和相分离材料到量子系统。传统上，与哈密顿量的多维参数空间对应的相图的探索是使用基本物理原理、解析近似和广泛的数值建模的组合来进行的。然而，复杂的多维参数空间的探索受制于经典的维数问题，并且集中在低维流形上的兴趣行为可能仍未被发现。这里，我们证明了探索和探索开发与高斯过程建模和贝叶斯优化的结合可以有效探索格子哈密顿量的参数空间，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，可以进一步扩展到格子哈密顿量之外，以有效探索更复杂的非格子和动态模型的参数空间。