论文标题
$ \ ell_0 \ ell_2 $ -norm正规化回归模型，用于在多组件系统中构建强大群集扩展
An $\ell_0\ell_2$-norm regularized regression model for construction of robust cluster expansions in multicomponent systems
论文作者
论文摘要
我们将$ \ ell_0 \ ell_2 $ -norm正则化和层次结构限制引入线性回归，以构建群集扩展，以描述材料中的构型障碍。该方法是通过混合整数二次编程（MIQP）实现的。 $ \ ell_2 $ -norm正则化用于抑制固有的数据噪声，而$ \ ell_0 $ -norm用于惩罚解决方案中的非零元素的数量。簇之间的层次结构关系施加了相关的物理，并且自然而然地由MIQP范式包含。因此，可以很好地优化稀疏性和群集层次结构，以获得具有改进的物理含义的稳健，融合和有效的群集相互作用。 We demonstrate the effectiveness of $\ell_0\ell_2$-norm regularization in two high-component disordered rocksalt cathode material systems, where we compare the cross-validation and convergence speed, reproduction of phase diagrams, voltage profiles, and Li-occupancy energies with those of the conventional $\ell_1$-norm regularized cluster expansion model.
We introduce the $\ell_0\ell_2$-norm regularization and hierarchy constraints into linear regression for the construction of cluster expansion to describe configurational disorder in materials. The approach is implemented through mixed integer quadratic programming (MIQP). The $\ell_2$-norm regularization is used to suppress intrinsic data noise, while $\ell_0$-norm is used to penalize the number of non-zero elements in the solution. The hierarchy relation between clusters imposes relevant physics and is naturally included by the MIQP paradigm. As such, sparseness and cluster hierarchy can be well optimized to obtain a robust, converged, and effective cluster interactions with improved physical meaning. We demonstrate the effectiveness of $\ell_0\ell_2$-norm regularization in two high-component disordered rocksalt cathode material systems, where we compare the cross-validation and convergence speed, reproduction of phase diagrams, voltage profiles, and Li-occupancy energies with those of the conventional $\ell_1$-norm regularized cluster expansion model.
