Concurrent learning scheme for crystal structure prediction

Crystal structure prediction (CSP) and machine learning potential (MLP) are two fundamental methods for modern computational material discovery. While the former aims at efficient sampling of the potential energy surface (PES) for discovering new materials, the latter focuses on reproducing the PES to accelerate various atomic simulation tasks. In this work, we combine the two methods within a concurrent learning framework in an effort to generate efficient MLP models for accelerating CSP. The proposed scheme explores the PES through the swarm-intelligence calypso method, labels the most representative structures with quantum mechanical calculations, and learns the PES through a deep potential (DP) model. The process proceeds in an iterative, computationally efficient, and automated manner, leading to the collection of a most compact reference training set from which the resulting DP model is proven particularly suitable for accelerating calypso structure prediction. The scheme has been systematically benchmarked on binary magnesium-aluminium (Mg-Al) alloys and ternary lithium-lanthanum-hydrogen (Li-La-H) superhydrides, demonstrating its efficiency and reliability in DP model construction and calypso structure prediction. The proposed scheme represents a promising routine to perform the structure prediction of large or multicomponent systems.

Figure 1

Workflow of a concurrent learning scheme for construction of a DP model. The scheme produces DP models by iterative configuration sampling, quantum mechanical calculation, and model retraining/updating.

Figure 2

(a) The model deviation distribution for Mg-Al structures during the calypso-based dpgen iterations. Gray horizonal dashed lines denote the lower and upper bounds of trust level, ${\sigma }_{lo}$ and ${\sigma }_{hi}$. The green dotted line denotes the percentage of accurate structure in each iteration. (b) The formation energy of Mg-Al compounds with respect to decomposition into Mg and Al. Data points are colored according to the absolute value of the difference between the energy above the hull calculated by DP and DFT ($\mathrm{\Delta }{E}_{\text{ebh}}=|E_{\text{ebh}}^{\text{DFT}}-E_{\text{ebh}}^{\text{DP}}|$). (c) Comparison of the energy calculated by DP and DFT for low-lying local minimum structures uncovered by structure searches. The solid black line and dashed line represent $y=x$ and $y=x\pm 0.05$, respectively.

Figure 3

The structures and phonon-dispersion curves calculated by DP and DFT for (a) $P\text{−}62m-{\mathrm{Mg}}_2\mathrm{Al}$ and (b) $Im\text{−}3m\text{−}{\mathrm{Mg}}_3{\mathrm{Al}}_{13}$. Green and gray balls denote Mg and Al atoms, respectively.

Figure 4

(a) The model deviation distribution for Mg-Al structures during the calypso-based dpgen iterations. Gray horizonal dashed lines denote the lower and upper bounds of the trust level, ${\sigma }_{lo}$ and ${\sigma }_{hi}$. The green dotted line denotes the percentage of accurate structure in each iteration. (b) The formation energy of Li-La-H compounds with respect to decomposition into Li, La, and H. Data points are colored according to enthalpy above the hull calculated by DFT. (c) Crystal structure of predicted $Cmcm-{\mathrm{Li}}_2{\mathrm{La}}_2{\mathrm{H}}_{23}$, which consists of two types of La@${\mathrm{H}}_{28}$ hydrogen cage and one type of Li@${\mathrm{H}}_{18}$ hydrogen cage.