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 a general tool for building robust, compressed and constrained physical models with predictive power. 1, 2, 5 Although 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 (thousands of atoms) and intensive sampling (millions of configurations). Approximate energy models fitted to DFT reference data, such as cluster expansion (CE) lattice models 6-9 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. One prototypical application for approximate energy models is the prediction of ordered ground states based on an underlying lattice topology.

Revealing the Atomic Origin of Heterogeneous Li‐Ion Diffusion by Probing Na

“…As shown in Figure h and the lattice model inset, the strain from the particular edge dislocation can reach 20% at the dislocation core. Such highly strained lattice could act as a high speed pipe for ion diffusion according to the literature report that expanded lattice can significantly increase ion transport kinetics . It is also consistent with the dislocation mediated fast ion migration observed in other materials .…”

Robust data-driven approach for predicting the configurational energy of high entropy alloys

“…Due to expensive time costs in experimental research, computational simulations, typically first-principles calculations are playing an increasingly central role in the investigation of various properties of HEAs [11,12,13].First-principles density functional theory (DFT) methods have established as a powerful and reliable tool in computational material science and have enabled critical advancements in materials properties and performance discovery [14,15]. With the increasing numerical efficiency and growing computing power (parallel and GPU computing), it is still difficult to address the challenge of DFT calculations in relatively large supercells (thousands of atoms) and intensive sampling (huge number of configurations) [16]. To characterize the orderdisorder phase transition, a straightforward way is to combine the DFT method with Monte Carlo simulations.…”

“…Testing performance comparison between ensemble sampling strategy and sampling drawn from only single supercell. Blue, orange and green bars: testing results using 150 data only from one specific supercell(16,32, 64 for NbMoTaW and 20, 40, 80 for NbMoTaWV and NbMoTaWTi respectively). Red bar: testing results using an ensemble of 150 data that consists of three 50 data drawn from each supercell.…”

“…Total 150 data randomly drawn from each smaller supercells(16,32, 64 for NbMoTaW and 20, 40, 80 for NbMoTaWV and NbMoTaWTi) are selected as the training dataset. The ensemble sampling strategy performs an ensemble of dataset which is achieved by randomly drawn 50 data using Latin hypercube sampling[54] from each of three supercells.…”

Machine-learning the configurational energy of multicomponent crystalline solids

“…55 Recently, methods have also been developed to determine the ground states of a cluster expansion 56 and to impose constraints as part of the regression step to ensure that the cluster expansion predicts ground states correctly. 57 Here, we build on the cluster expansion approach, but relax the constraint of linearity and leverage advanced machine learning tools such as neural networks and Gaussian process regressions to represent crystal properties that depend on alloy configuration in terms of symmetry invariant descriptors of order. As descriptors, we use site-centric correlation functions, which are related to the correlation functions introduced by Sanchez and De Fontaine 58,59 and are at the core of the cluster expansion approach.…”