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

## 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 themore »

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22), Materials Sciences & Engineering Division (SC-22.2)

- OSTI Identifier:
- 1477399

- Report Number(s):
- arXiv:1807.10753v1

Journal ID: ISSN 9999-0017; ark:/13030/qt56v9s5t4

- DOE Contract Number:
- AC02-05CH11231

- Resource Type:
- Journal Article

- Journal Name:
- arXiv.org Repository

- Additional Journal Information:
- Journal Volume: 2018; Journal ID: ISSN 9999-0017

- Publisher:
- Cornell University

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Huang, W, Urban, A, Xiao, P, Rong, Z, Das, H, Chen, T, Artrith, N, Toumar, A, and Ceder, G.
```*An L$_0$L$_1$-norm compressive sensing paradigm for the construction of sparse predictive lattice models using mixed integer quadratic programming*. United States: N. p., 2018.
Web.

```
Huang, W, Urban, A, Xiao, P, Rong, Z, Das, H, Chen, T, Artrith, N, Toumar, A, & Ceder, G.
```*An L$_0$L$_1$-norm compressive sensing paradigm for the construction of sparse predictive lattice models using mixed integer quadratic programming*. United States.

```
Huang, W, Urban, A, Xiao, P, Rong, Z, Das, H, Chen, T, Artrith, N, Toumar, A, and Ceder, G. Mon .
"An L$_0$L$_1$-norm compressive sensing paradigm for the construction of sparse predictive lattice models using mixed integer quadratic programming". United States.
```

```
@article{osti_1477399,
```

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

author = {Huang, W and Urban, A and Xiao, P and Rong, Z and Das, H and Chen, T and Artrith, N and Toumar, A and Ceder, G},

abstractNote = {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.},

doi = {},

journal = {arXiv.org Repository},

issn = {9999-0017},

number = ,

volume = 2018,

place = {United States},

year = {2018},

month = {7}

}