Author Correction: Physics guided deep learning for generative design of crystal materials with symmetry constraints

Correction to:npj Computational Materials https://doi.org/10.1038/s41524-023-00987-9,published online 18 March 2023 The original version of this Article contained typos in both the PDF and the HTML versions.In the fourth and fifth sentences of the first paragraph of the‘Case study of three example stable materials’section of the Results,the incorrect expression“β=β”has been replaced by“α=β”.

Machine-learning driven global optimization of surface adsorbate geometries

The adsorption energies of molecular adsorbates on catalyst surfaces are key descriptors in computational catalysis research.For the relatively large reaction intermediates frequently encountered,e.g.,in syngas conversion,a multitude of possible binding motifs leads to complex potential energy surfaces(PES),however.This implies that finding the optimal structure is a difficult global optimization problem,which leads to significant uncertainty about the stability of many intermediates.To tackle this issue,we present a global optimization protocol for surface adsorbate geometries which trains a surrogate machine learning potential on-the-fly.The approach is applicable to arbitrary surface models and adsorbates and minimizes both human intervention and the number of required DFT calculations by iteratively updating the training set with configurations explored by the algorithm.We demonstrate the efficiency of this approach for a diverse set of adsorbates on the Rh(111)and(211)surfaces.

Understanding and design of metallic alloys guided by phase-field simulations

Phase-field method(PFM)has become a mainstream computational method for predicting the evolution of nano and mesoscopic microstructures and properties during materials processes.The paper briefly reviews latest progresses in applying PFM to understanding the thermodynamic driving forces and mechanisms underlying microstructure evolution in metallic materials and related processes,including casting,aging,deformation,additive manufacturing,and defects,etc.Focus on designing alloys by integrating PFM with constitutive relations and machine learning.Several examples are presented to demonstrate the potential of integrated PFM in discovering new multi-scale phenomena and high-performance alloys.The article ends with prospects for promising research directions.

TransPolymer: a Transformer-based language model for polymer property predictions

Accurate and efficient prediction of polymer properties is of great significance in polymer design.Conventionally,expensive and time-consuming experiments or simulations are required to evaluate polymer functions.Recently,Transformer models,equipped with self-attention mechanisms,have exhibited superior performance in natural language processing.However,such methods have not been investigated in polymer sciences.Herein,we report TransPolymer,a Transformer-based language model for polymer property prediction.Our proposed polymer tokenizer with chemical awareness enables learning representations from polymer sequences.Rigorous experiments on ten polymer property prediction benchmarks demonstrate the superior performance of TransPolymer.Moreover,we show that TransPolymer benefits from pretraining on large unlabeled dataset via Masked Language Modeling.Experimental results further manifest the important role of self-attention in modeling polymer sequences.We highlight this model as a promising computational tool for promoting rational polymer design and understanding structure-property relationships from a data science view.

Thermal conductivity of glasses: first-principles theory and applications

Predicting the thermal conductivity of glasses from first principles has hitherto been a very complex problem.The established Allen-Feldman and Green-Kubo approaches employ approximations with limited validity—the former neglects anharmonicity,the latter misses the quantum Bose-Einstein statistics of vibrations—and require atomistic models that are very challenging for first-principles methods.Here,we present a protocol to determine from first principles the thermal conductivityκ(T)of glasses above the plateau(i.e.,above the temperature-independent region appearing almost without exceptions in theκ(T)of all glasses at cryogenic temperatures).The protocol combines the Wigner formulation of thermal transport with convergence-acceleration techniques,and accounts comprehensively for the effects of structural disorder,anharmonicity,and Bose-Einstein statistics.We validate this approach in vitreous silica,showing that models containing less than 200 atoms can already reproduceκ(T)in the macroscopic limit.We discuss the effects of anharmonicity and the mechanisms determining the trend ofκ(T)at high temperature,reproducing experiments at temperatures where radiative effects remain negligible.

Center-environment deep transfer machine learning across crystal structures: from spinel oxides to perovskite oxides

In data-driven materials design where the target materials have limited data,the transfer machine learning from large known source materials,becomes a demanding strategy especially across different crystal structures.In this work,we proposed a deep transfer learning approach to predict thermodynamically stable perovskite oxides based on a large computational dataset of spinel oxides.The deep neural network(DNN)source domain model with“Center-Environment”(CE)features was first developed using the formation energy of 5329 spinel oxide structures and then was fine-tuned by learning a small dataset of 855 perovskite oxide structures,leading to a transfer learning model with good transferability in the target domain of perovskite oxides.Based on the transferred model,we further predicted the formation energy of potential 5329 perovskite structures with combination of 73 elements.Combining the criteria of formation energy and structure factors including tolerance factor(0.7<t≤1.1)and octahedron factor(0.45<μ<0.7),we predicted 1314 thermodynamically stable perovskite oxides,among which 144 oxides were reported to be synthesized experimentally,10 oxides were predicted computationally by other literatures,301 oxides were recorded in the Materials Project database,and 859 oxides have been first reported.Combing with the structure-informed features the transfer machine learning approach in this work takes the advantage of existing data to predict new structures at a lower cost,providing an effective acceleration strategy for the expensive high-throughput computational screening in materials design.The predicted stable novel perovskite oxides serve as a rich platform for exploring potential renewable energy and electronic materials applications.

Exploring and machine learning structural instabilities in 2D materials

We address the problem of predicting the zero-temperature dynamical stability (DS) of a periodic crystal without computing its fullphonon band structure. Here we report the evidence that DS can be inferred with good reliability from the phonon frequencies atthe center and boundary of the Brillouin zone (BZ). This analysis represents a validation of the DS test employed by theComputational 2D Materials Database (C2DB). For 137 dynamically unstable 2D crystals, we displace the atoms along an unstablemode and relax the structure. This procedure yields a dynamically stable crystal in 49 cases. The elementary properties of these newstructures are characterized using the C2DB workflow, and it is found that their properties can differ significantly from those of theoriginal unstable crystals, e.g., band gaps are opened by 0.3 eV on average. All the crystal structures and properties are available inthe C2DB. Finally, we train a classification model on the DS data for 3295 2D materials in the C2DB using a representation encodingthe electronic structure of the crystal. We obtain an excellent receiver operating characteristic (ROC) curve with an area under thecurve (AUC) of 0.90, showing that the classification model can drastically reduce computational efforts in high-throughput studies.

Enhancing the Faradaic efficiency of solid oxide electrolysis cells: progress and perspective

To reduce global warming,many countries are shifting to sustainable energy production systems.Solid oxide electrolysis cells(SOECs)are being considered due to their high hydrogen generation efficiency.However,low faradaic efficiency in scaling SOEC technology affects costs and limits large-scale adoption of hydrogen as fuel.This review covers SOECs’critical aspects:current state-of-the-art anode,cathode,and electrolyte materials,operational and materials parameters affecting faradaic efficiency,and computational modeling techniques to resolve bottlenecks affecting SOEC faradaic efficiency.

Enabling rapid X-ray CT characterisation for additive manufacturing using CAD models and deep learning-based reconstruction

Metal additive manufacturing(AM)offers flexibility and cost-effectiveness for printing complex parts but is limited to few alloys.Qualifying new alloys requires process parameter optimisation to produce consistent,high-quality components.High-resolution X-ray computed tomography(XCT)has not been effective for this task due to artifacts,slow scan speed,and costs.We propose a deep learning-based approach for rapid XCT acquisition and reconstruction of metal AM parts,leveraging computer-aided design models and physics-based simulations of nonlinear interactions between X-ray radiation and metals.This significantly reduces beam hardening and common XCT artifacts.We demonstrate high-throughput characterisation of over a hundred AlCe alloy components,quantifying improvements in characterisation time and quality compared to high-resolution microscopy and pycnometry.Our approach facilitates investigating the impact of process parameters and their geometry dependence in metal AM.

Projectability disentanglement for accurate and automated electronic-structure Hamiltonians

Maximally-localized Wannier functions(MLWFs)are broadly used to characterize the electronic structure of materials.Generally,one can construct MLWFs describing isolated bands(e.g.valence bands of insulators)or entangled bands(e.g.valence and conduction bands of insulators,or metals).Obtaining accurate and compact MLWFs often requires chemical intuition and trial and error,a challenging step even for experienced researchers and a roadblock for high-throughput calculations.Here,we present an automated approach,projectability-disentangled Wannier functions(PDWFs),that constructs MLWFs spanning the occupied bands and their complement for the empty states,providing a tight-binding picture of optimized atomic orbitals in crystals.Key to the algorithm is a projectability measure for each Bloch state onto atomic orbitals,determining if that state should be kept identically,discarded,or mixed into the disentanglement.We showcase the accuracy on a test set of 200 materials,and the reliability by constructing 21,737 Wannier Hamiltonians.

Efficient GW calculations in two dimensional materials through a stochastic integration of the screened potential

Many-body perturbation theory methods,such as the G0W0 approximation,are able to accurately predict quasiparticle(QP)properties of several classes of materials.However,the calculation of the QP band structure of two-dimensional(2D)semiconductors is known to require a very dense BZ sampling,due to the sharp q-dependence of the dielectric matrix in the long-wavelength limit(q→0).In this work,we show how the convergence of the QP corrections of 2D semiconductors with respect to the BZ sampling can be drastically improved,by combining a Monte Carlo integration with an interpolation scheme able to represent the screened potential between the calculated grid points.The method has been validated by computing the band gap of three different prototype monolayer materials:a transition metal dichalcogenide(MoS2),a wide band gap insulator(hBN)and an anisotropic semiconductor(phosphorene).The proposed scheme shows that the convergence of the gap for these three materials up to 50meV is achieved by using k-point grids comparable to those needed by DFT calculations,while keeping the grid uniform.

Machine learning potentials for metal-organic frameworks using an incremental learning approach

Computational modeling of physical processes in metal-organic frameworks(MOFs)is highly challenging due to the presence of spatial heterogeneities and complex operating conditions which affect their behavior.Density functional theory(DFT)may describe interatomic interactions at the quantum mechanical level,but is computationally too expensive for systems beyond the nanometer and picosecond range.Herein,we propose an incremental learning scheme to construct accurate and data-efficient machine learning potentials for MOFs.The scheme builds on the power of equivariant neural network potentials in combination with parallelized enhanced sampling and on-the-fly training to simultaneously explore and learn the phase space in an iterative manner.With only a few hundred single-point DFT evaluations per material,accurate and transferable potentials are obtained,even for flexible frameworks with multiple structurally different phases.The incremental learning scheme is universally applicable and may pave the way to model framework materials in larger spatiotemporal windows with higher accuracy.

Finding stable multi-component materials by combining cluster expansion and crystal structure predictions

A desired prerequisite when performing a quantum mechanical calculation is to have an initial idea of the atomic positions within an approximate crystal structure.The atomic positions combined should result in a system located in,or close to,an energy minimum.However,designing low-energy structures may be a challenging task when prior knowledge is scarce,specifically for large multi-component systems where the degrees of freedom are close to infinite.In this paper,we propose a method for identification of low-energy crystal structures within multi-component systems by combining cluster expansion and crystal structure predictions with density-functional theory calculations.Crystal structure prediction searches are applied to the Mo_(2)AlB_(2) and Sc2AlB_(2) ternary systems to identify candidate structures,which are subsequently used to explore the quaternary(pseudo-binary)(Mo_(x)Sc_(1–x))2AlB_(2) system through the cluster expansion formalism utilizing the ground-state search approach.Furthermore,we show that utilizing low-energy structures found within the cluster expansion ground-state search as seed structures within crystal structure predictions of(Mo_(x)Sc_(1–x))2AlB_(2) can significantly reduce the computational demands.With this combined approach,we not only correctly identified the recently discovered Mo_(4/3)Sc_(2/3)AlB_(2) i-MAB phase,comprised of in-plane chemical ordering of Mo and Sc and with Al in a Kagomélattice,but also predict additional low-energy structures at various concentrations.This result demonstrates that combining crystal structure prediction with cluster expansion provides a path for identifying low-energy crystal structures in multi-component systems by employing the strengths from both frameworks.

Deep learning approach to genome of two-dimensional materials with flat electronic bands

Electron-electron correlations play central role in condensed matter physics,governing phenomena from superconductivity to magnetism and numerous technological applications.Two-dimensional(2D)materials with flat electronic bands provide natural playground to explore interaction-driven physics,thanks to their highly localized electrons.The search for 2D flat band materials has attracted intensive efforts,especially now with open science databases encompassing thousands of materials with computed electronic bands.Here we automate the otherwise daunting task of materials search and classification by combining supervised and unsupervised machine learning algorithms.To this end,convolutional neural network was employed to identify 2D flat band materials,which were then subjected to symmetry-based analysis using a bilayer unsupervised learning algorithm.Such hybrid approach of exploring materials databases allowed us to construct a genome of 2D materials hosting flat bands and to reveal material classes outside the known flat band paradigms.

Two-dimensional ferroelectrics from high throughput computational screening

We report a high throughput computational search for two-dimensional ferroelectric materials.The starting point is 252 pyroelectric materials from the computational 2D materials database(C2DB)and from these we identify 63 ferroelectrics.In particular we find 49 materials with in-plane polarization,8 materials with out-of-plane polarization and 6 materials with coupled in-plane and out-of-plane polarization.Most of the known 2D ferroelectrics are recovered by the screening and the far majority of the predicted ferroelectrics are known as bulk van der Waals bonded compounds,which makes them accessible by direct exfoliation.For roughly 25%of the materials we find a metastable state in the non-polar structure,which may imply a first order transition to the polar phase.Finally,we list the magnetic pyroelectrics extracted from the C2DB and focus on the case of VAgP2Se6,which exhibits a three-state switchable polarization vector that is strongly coupled to the magnetic excitation spectrum.

Machine learning molecular dynamics simulation identifying weakly negative effect of polyanion rotation on Li-ion migration

Understanding the physical picture of Li ion transport in the current ionic conductors is quite essential to further develop lithium superionic conductors for solid-state batteries.The traditional practice of directly extrapolating room temperature ion diffusion properties from the high-temperature(>600 K)ab initio molecular dynamics simulations(AIMD)simulations by the Arrhenius assumption unavoidably cause some deviations.Fortunately,the ultralong-time molecular dynamics simulation based on the machine-learning interatomic potentials(MLMD)is a more suitable tool to probe into ion diffusion events at low temperatures and simultaneously keeps the accuracy at the density functional theory level.Herein,by the low-temperature MLMD simulations,the non-linear Arrhenius behavior of Li ion was found for Li3ErCl6,which is the main reason for the traditional AIMD simulation overestimating its ionic conductivity.The 1μs MLMD simulations capture polyanion rotation events in Li_(7)P_(3)S_(11) at room temperature,in which four[PS_(4)]^(3−)tetrahedra belonging to a part of the longer-chain[P_(2)S_(7)]4−group are noticed with remarkable rotational motions,while the isolated group[PS_(4)]^(3−)does not rotate.However,no polyanion rotation is observed in Li10GeP_(2)S12,β-Li3PS_(4),Li3ErCl6,and Li3YBr6 at 300 K during 1μs simulation time.Additionally,the ultralong-time MLMD simulations demonstrate that not only there is no paddle-wheel effect in the crystalline Li_(7)P_(3)S_(11) at room temperature,but also the rotational[PS_(4)]^(3−)polyanion groups have weakly negative impacts on the overall Li ion diffusion.The ultralong-time MLMD simulations deepen our understanding of the relationship between the polyanion rotation and cation diffusion in ionic conductors at room environments.

Small data machine learning in materials science

This review discussed the dilemma of small data faced by materials machine learning.First,we analyzed the limitations brought by small data.Then,the workflow of materials machine learning has been introduced.Next,the methods of dealing with small data were introduced,including data extraction from publications,materials database construction,high-throughput computations and experiments from the data source level;modeling algorithms for small data and imbalanced learning from the algorithm level;active learning and transfer learning from the machine learning strategy level.Finally,the future directions for small data machine learning in materials science were proposed.

Bayesian optimization with active learning of design constraints using an entropy-based approach

The design of alloys for use in gas turbine engine blades is a complex task that involves balancing multiple objectives and constraints.Candidate alloys must be ductile at room temperature and retain their yield strength at high temperatures,as well as possess low density,high thermal conductivity,narrow solidification range,high solidus temperature,and a small linear thermal expansion coefficient.Traditional Integrated Computational Materials Engineering(ICME)methods are not sufficient for exploring combinatorially-vast alloy design spaces,optimizing for multiple objectives,nor ensuring that multiple constraints are met.In this work,we propose an approach for solving a constrained multi-objective materials design problem over a large composition space,specifically focusing on the Mo-Nb-Ti-V-W system as a representative Multi-Principal Element Alloy(MPEA)for potential use in next-generation gas turbine blades.Our approach is able to learn and adapt to unknown constraints in the design space,making decisions about the best course of action at each stage of the process.As a result,we identify 21 Pareto-optimal alloys that satisfy all constraints.Our proposed framework is significantly more efficient and faster than a brute force approach.

CEGANN: Crystal Edge Graph Attention Neural Network for multiscale classification of materials environment

We introduce Crystal Edge Graph Attention Neural Network (CEGANN) workflow that uses graph attention-based architecture tolearn unique feature representations and perform classification of materials across multiple scales (from atomic to mesoscale) anddiverse classes ranging from metals, oxides, non-metals to hierarchical materials such as zeolites and semi-ordered mesophases.CEGANN can classify based on a global, structure-level representation such as space group and dimensionality (e.g., bulk, 2D,clusters, etc.). Using representative materials such as polycrystals and zeolites, we demonstrate its transferability in performing localatom-level classification tasks, such as grain boundary identification and other heterointerfaces. CEGANN classifies in (thermal)noisy dynamical environments as demonstrated for representative zeolite nucleation and growth from an amorphous mixture.Finally, we use CEGANN to classify multicomponent systems with thermal noise and compositional diversity. Overall, our approachis material agnostic and allows for multiscale feature classification ranging from atomic-scale crystals to heterointerfaces tomicroscale grain boundaries.

In silico screening for As/Se-free ovonic threshold switching materials

Restricted use of hazardous environmental chemicals is one important challenge that the semiconductor industry needs to face to improve its sustainability.Ovonic threshold switching(OTS)ternary compound materials used in memory selector devices contain As and Se.Engineering these elements out of these materials requires significant research effort.To facilitate this process,we performed systematic material screening for As/Se-free ternary materials,based on ab-initio simulations.To limit the large amount of possible chemical compositions to fewer promising candidates,we used physics-based material parameter filters like material stability,electronic properties,or change in polarizability.The OTS gauge concept is introduced as a computed parameter to estimate the probability of a material to show an OTS behavior.As a result,we identified 35 As/Se-free ternary alloy compositions for stand-alone OTS memory applications,as well as 12 compositions for RRAM selector applications.This work aims seeding the development of As/Se-free OTS materials.