Exploration of lattice Hamiltonians for functional and structural discovery via Gaussian Process-based Exploration-Exploitation
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by
Sergei V. Kalinin, Mani Valleti, Rama K. Vasudevan, Maxim Ziatdinov
2020
Abstract
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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