An L$_0$L$_1$-norm compressive sensing paradigm for the construction of sparse predictive lattice models using mixed integer quadratic programming

TL;DR

This paper introduces a robust L0L1-norm compressive sensing method using mixed-integer quadratic programming to construct sparser, more predictive lattice models for crystalline materials, overcoming limitations of traditional L1-norm approaches.

Contribution

The paper develops a new L0L1-norm compressive sensing approach with MIQP implementation, enabling more robust and sparser lattice models for materials science applications.

Findings

Produces sparser lattice models that are at least as predictive as L1-based models.

Successfully applied to four transition-metal oxides relevant for battery cathodes.

Enhances the applicability of compressive sensing in materials modeling.

Abstract

First-principles based lattice models allow the modeling of ab initio thermodynamics of crystalline mixtures for applications such as the construction of phase diagrams and the identification of ground state atomic orderings. The recent development of compressive sensing approaches for the construction of lattice models has further enabled the systematic construction of sparse physical models without the need for human intuition other than requiring the compactness of effective cluster interactions. However, conventional compressive sensing based on L1-norm regularization is strictly only applicable to certain classes of optimization problems and is otherwise not guaranteed to generate optimally sparse and transferable results, so that the method can only be applied to some materials science applications. In this paper, we illustrate a more robust L0L1-norm compressive-sensing method that removes the limitations of conventional compressive sensing and generally results in sparser lattice models that are at least as predictive as those obtained from L1-norm compressive sensing. Apart from the theory, a practical implementation based on state-of-the-art mixed-integer quadratic programming (MIQP) is proposed. The robustness of our methodology is illustrated for four different transition-metal oxides with relevance as battery cathode materials: Li2xTi2(1-x)O2, Li2xNi2yO2, MgxCr2O4, and NaxCrO2. This method provides a practical and robust approach for the construction of sparser and more predictive lattice models, improving on the compressive sensing paradigm and making it applicable to a much broader range of applications.