基于相干和冗余的多组分氧化物组态能的稀疏展开
Sparse expansions of multicomponent oxide configuration energy using coherency & redundancy
摘要：
压缩传感已成为一种被广泛接受的范式，用于构建高维集团膨胀模型用于统计力学研究的原子配置在复杂的多组分晶体材料。然而，由于物理系统无法访问某些配置，因此难以获得用于压缩感测的最小相干性测量以保证模型参数的准确估计所需的严格采样要求，并且在某些情况下不可能满足。然而，能量对原子配置的依赖性仍然可以在没有这些严格要求的情况下通过使用压缩感测来充分地学习，所述压缩感测通过使用被称为帧的冗余函数集的相干测量来进行。我们开发了一个特定的框架，从工会的所有占用为基础的集群扩展基集。我们说明了如何使用这个高度冗余的框架产生稀疏扩展的配置能量的复杂氧化物材料的竞争力，往往超过预测精度和稀疏性的模型从标准的集群扩展。
英文摘要：
Compressed sensing has become a widely accepted paradigm to construct high dimensional cluster expansion models used for statistical mechanical studies of atomic configuration in complex multicomponent crystalline materials. However, strict sampling requirements necessary to obtain minimal coherence measurements for compressed sensing to guarantee accurate estimation of model parameters are difficult and in some cases impossible to satisfy due to the inability of physical systems to access certain configurations. Nevertheless, the dependence of energy on atomic configuration can still be adequately learned without these strict requirements by using compressed sensing by way of coherent measurements using redundant function sets known as frames. We develop a particular frame constructed from the union of all occupancy-based cluster expansion basis sets. We illustrate how using this highly redundant frame yields sparse expansions of the configuration energy of complex oxide materials that are competitive and often surpass the prediction accuracy and sparsity of models obtained from standard cluster expansions.
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