UC Berkeley

We introduce ℓ0ℓ2-norm regularization and hierarchy constraints into linear regression for the construction of cluster expansions to describe configurational disorder in materials. The approach is implemented through mixed integer quadratic programming (MIQP). The ℓ2-norm regularization is used to suppress intrinsic data noise, while the ℓ0-norm is used to penalize the number of nonzero 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 set of effective cluster interactions with improved physical meaning. We demonstrate the effectiveness of ℓ0ℓ2-norm regularization in two high-component disordered rocksalt cathode material systems, where we compare the cross-validation, convergence speed, and the reproduction of phase diagrams, voltage profiles, and Li-occupancy energies with those of the conventional ℓ1-norm regularized cluster expansion models.