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1. Formation energy prediction of crystalline compounds using deep convolutional network learning on voxel image representation

   https://doi.org/10.1038/s43246-023-00433-9  

   Davariashtiyani, Ali; Kadkhodaei, Sara (December 2023, Communications Materials)

   Abstract Emerging machine-learned models have enabled efficient and accurate prediction of compound formation energy, with the most prevalent models relying on graph structures for representing crystalline materials. Here, we introduce an alternative approach based on sparse voxel images of crystals. By developing a sophisticated network architecture, we showcase the ability to learn the underlying features of structural and chemical arrangements in inorganic compounds from visual image representations, subsequently correlating these features with the compounds’ formation energy. Our model achieves accurate formation energy prediction by utilizing skip connections in a deep convolutional network and incorporating augmentation of rotated crystal samples during training, performing on par with state-of-the-art methods. By adopting visual images as an alternative representation for crystal compounds and harnessing the capabilities of deep convolutional networks, this study extends the frontier of machine learning for accelerated materials discovery and optimization. In a comprehensive evaluation, we analyse the predicted convex hulls for 3115 binary systems and introduce error metrics beyond formation energy error. This evaluation offers valuable insights into the impact of formation energy error on the performance of the predicted convex hulls. 

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2. Topological representations of crystalline compounds for the machine-learning prediction of materials properties

   https://doi.org/10.1038/s41524-021-00493-w  

   Jiang, Yi; Chen, Dong; Chen, Xin; Li, Tangyi; Wei, Guo-Wei; Pan, Feng (December 2021, npj Computational Materials)

   null (Ed.)

   Abstract Accurate theoretical predictions of desired properties of materials play an important role in materials research and development. Machine learning (ML) can accelerate the materials design by building a model from input data. For complex datasets, such as those of crystalline compounds, a vital issue is how to construct low-dimensional representations for input crystal structures with chemical insights. In this work, we introduce an algebraic topology-based method, called atom-specific persistent homology (ASPH), as a unique representation of crystal structures. The ASPH can capture both pairwise and many-body interactions and reveal the topology-property relationship of a group of atoms at various scales. Combined with composition-based attributes, ASPH-based ML model provides a highly accurate prediction of the formation energy calculated by density functional theory (DFT). After training with more than 30,000 different structure types and compositions, our model achieves a mean absolute error of 61 meV/atom in cross-validation, which outperforms previous work such as Voronoi tessellations and Coulomb matrix method using the same ML algorithm and datasets. Our results indicate that the proposed topology-based method provides a powerful computational tool for predicting materials properties compared to previous works. 

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3. Predicting synthesizability of crystalline materials via deep learning

   https://doi.org/10.1038/s43246-021-00219-x  

   Davariashtiyani, Ali; Kadkhodaie, Zahra; Kadkhodaei, Sara (December 2021, Communications Materials)

   Abstract Predicting the synthesizability of hypothetical crystals is challenging because of the wide range of parameters that govern materials synthesis. Yet, exploring the exponentially large space of novel crystals for any future application demands an accurate predictive capability for synthesis likelihood to avoid a haphazard trial-and-error. Typically, benchmarks of synthesizability are defined based on the energy of crystal structures. Here, we take an alternative approach to select features of synthesizability from the latent information embedded in crystalline materials. We represent the atomic structure of crystalline materials by three-dimensional pixel-wise images that are color-coded by their chemical attributes. The image representation of crystals enables the use of a convolutional encoder to learn the features of synthesizability hidden in structural and chemical arrangements of crystalline materials. Based on the presented model, we can accurately classify materials into synthesizable crystals versus crystal anomalies across a broad range of crystal structure types and chemical compositions. We illustrate the usefulness of the model by predicting the synthesizability of hypothetical crystals for battery electrode and thermoelectric applications. 

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4. Machine learned interatomic potentials for ternary carbides trained on the AFLOW database

   https://doi.org/10.1038/s41524-024-01321-7  

   Roberts, Josiah; Rijal, Biswas; Divilov, Simon; Maria, Jon-Paul; Fahrenholtz, William G; Wolfe, Douglas E; Brenner, Donald W; Curtarolo, Stefano; Zurek, Eva (December 2024, npj Computational Materials)

   Abstract Large-density functional theory (DFT) databases are a treasure trove of energies, forces, and stresses that can be used to train machine-learned interatomic potentials for atomistic modeling. Herein, we employ structural relaxations from the AFLOW database to train moment tensor potentials (MTPs) for four carbide systems: CHfTa, CHfZr, CMoW, and CTaTi. The resulting MTPs are used to relax ~6300 random symmetric structures, and are subsequently improved via active learning to generate robust potentials (RP) that can relax a wide variety of structures, and accurate potentials (AP) designed for the relaxation of low-energy systems. This protocol is shown to yield convex hulls that are indistinguishable from those predicted by AFLOW for the CHfTa, CHfZr, and CTaTi systems, and in the case of the CMoW system to predict thermodynamically stable structures that are not found within AFLOW, highlighting the potential of the employed protocol within crystal structure prediction. Relaxation of over three hundred (Mo_1−xW_x)C stoichiometry crystals first with the RP then with the AP yields formation enthalpies that are in excellent agreement with those obtained via DFT. 

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5. Enhancing material property prediction with ensemble deep graph convolutional networks

   https://doi.org/10.3389/fmats.2024.1474609  

   Rahman, Chowdhury_Mohammad Abid; Bhandari, Ghadendra; Nasrabadi, Nasser M; Romero, Aldo H; Gyawali, Prashnna K (October 2024, Frontiers in Materials)

   Machine learning (ML) models have emerged as powerful tools for accelerating materials discovery and design by enabling accurate predictions of properties from compositional and structural data. These capabilities are vital for developing advanced technologies across fields such as energy, electronics, and biomedicine, potentially reducing the time and resources needed for new material exploration and promoting rapid innovation cycles. Recent efforts have focused on employing advanced ML algorithms, including deep learning-based graph neural networks, for property prediction. Additionally, ensemble models have proven to enhance the generalizability and robustness of ML and Deep Learning (DL). However, the use of such ensemble strategies in deep graph networks for material property prediction remains underexplored. Our research provides an in-depth evaluation of ensemble strategies in deep learning-based graph neural network, specifically targeting material property prediction tasks. By testing the Crystal Graph Convolutional Neural Network (CGCNN) and its multitask version, MT-CGCNN, we demonstrated that ensemble techniques, especially prediction averaging, substantially improve precision beyond traditional metrics for key properties like formation energy per atom $\left(\mathrm{\Delta }{E}^f\right)$, band gap $\left(E_g\right)$, density $\left(\rho \right)$, equivalent reaction energy per atom $\left(E_{\mathit{rxn,atom}}\right)$, energy per atom $\left(E_{\mathit{atom}}\right)$and atomic density $\left({\rho }_{\mathit{atom}}\right)$in 33,990 stable inorganic materials. These findings support the broader application of ensemble methods to enhance predictive accuracy in the field. 

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