## Construction of ground-state preserving sparse lattice models for predictive materials simulations

## Abstract

First-principles based cluster expansion models are the dominant approach in *ab initio* thermodynamics of crystalline mixtures enabling the prediction of phase diagrams and novel ground states. However, despite recent advances, the construction of accurate models still requires a careful and time-consuming manual parameter tuning process for ground-state preservation, since this property is not guaranteed by default. In this paper, we present a systematic and mathematically sound method to obtain cluster expansion models that are guaranteed to preserve the ground states of their reference data. The method builds on the recently introduced compressive sensing paradigm for cluster expansion and employs quadratic programming to impose constraints on the model parameters. The robustness of our methodology is illustrated for two lithium transition metal oxides with relevance for Li-ion battery cathodes, i.e., Li _{2x}Fe _{2(1-x)}O _{2} and Li _{2x}Ti _{2(1-x)}O _{2}, for which the construction of cluster expansion models with compressive sensing alone has proven to be challenging. We demonstrate that our method not only guarantees ground-state preservation on the set of reference structures used for the model construction, but also show that out-of-sample ground-state preservation up to relatively large supercell size is achievable through a rapidly converging iterative refinement. This method provides amore »

- Authors:

- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Univ. of California, Berkeley, CA (United States)
- Chinese Academy of Sciences (CAS), Beijing (China)
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- 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)

- OSTI Identifier:
- 1476580

- Grant/Contract Number:
- AC02-05CH11231

- Resource Type:
- Accepted Manuscript

- Journal Name:
- npj Computational Materials

- Additional Journal Information:
- Journal Volume: 3; Journal Issue: 1; Related Information: © 2017 The Author(s).; Journal ID: ISSN 2057-3960

- Publisher:
- Nature Publishing Group

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE

### Citation Formats

```
Huang, Wenxuan, Urban, Alexander, Rong, Ziqin, Ding, Zhiwei, Luo, Chuan, and Ceder, Gerbrand. Construction of ground-state preserving sparse lattice models for predictive materials simulations. United States: N. p., 2017.
Web. doi:10.1038/s41524-017-0032-0.
```

```
Huang, Wenxuan, Urban, Alexander, Rong, Ziqin, Ding, Zhiwei, Luo, Chuan, & Ceder, Gerbrand. Construction of ground-state preserving sparse lattice models for predictive materials simulations. United States. doi:10.1038/s41524-017-0032-0.
```

```
Huang, Wenxuan, Urban, Alexander, Rong, Ziqin, Ding, Zhiwei, Luo, Chuan, and Ceder, Gerbrand. Mon .
"Construction of ground-state preserving sparse lattice models for predictive materials simulations". United States. doi:10.1038/s41524-017-0032-0. https://www.osti.gov/servlets/purl/1476580.
```

```
@article{osti_1476580,
```

title = {Construction of ground-state preserving sparse lattice models for predictive materials simulations},

author = {Huang, Wenxuan and Urban, Alexander and Rong, Ziqin and Ding, Zhiwei and Luo, Chuan and Ceder, Gerbrand},

abstractNote = {First-principles based cluster expansion models are the dominant approach in ab initio thermodynamics of crystalline mixtures enabling the prediction of phase diagrams and novel ground states. However, despite recent advances, the construction of accurate models still requires a careful and time-consuming manual parameter tuning process for ground-state preservation, since this property is not guaranteed by default. In this paper, we present a systematic and mathematically sound method to obtain cluster expansion models that are guaranteed to preserve the ground states of their reference data. The method builds on the recently introduced compressive sensing paradigm for cluster expansion and employs quadratic programming to impose constraints on the model parameters. The robustness of our methodology is illustrated for two lithium transition metal oxides with relevance for Li-ion battery cathodes, i.e., Li2xFe2(1-x)O2 and Li2xTi2(1-x)O2, for which the construction of cluster expansion models with compressive sensing alone has proven to be challenging. We demonstrate that our method not only guarantees ground-state preservation on the set of reference structures used for the model construction, but also show that out-of-sample ground-state preservation up to relatively large supercell size is achievable through a rapidly converging iterative refinement. This method provides a general tool for building robust, compressed and constrained physical models with predictive power.},

doi = {10.1038/s41524-017-0032-0},

journal = {npj Computational Materials},

number = 1,

volume = 3,

place = {United States},

year = {2017},

month = {8}

}

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