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., 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.
Highlights
First-principles density functional theory (DFT) calculations have established themselves as a routine and reliable tool in computational materials science research[1,2,3,4] and have enabled important advancements in materials discovery.[1, 2, 5] implementations with increasing numerical efficiency and growing computational power have made it possible to simulate ever larger structures with DFT, the method’s intrinsic scaling with the number of electrons prevents applications that require large structures and intensive sampling
Approximate energy models fitted to DFT reference data, such as cluster expansion (CE) lattice models[6,7,8,9] or machine learning regression,[10, 11] can overcome these limitations by constructing computationally more efficient models with accuracies that are close to DFT for a chosen structural and chemical space
We propose a robust and efficient scheme to construct ground-state preserving CE models based on compressive sensing[17, 19] and quadratic programming.[20]
Summary
Wenxuan Huang[1], Alexander Urban 2, Ziqin Rong[1], Zhiwei Ding 1, Chuan Luo[3] and Gerbrand Ceder[1,2,4]. The method builds on the recently introduced compressive sensing paradigm for cluster expansion and employs quadratic programming to impose constraints on the model parameters. We demonstrate that our method guarantees ground-state preservation on the set of reference structures used for the model construction, and 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
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