A Schrodinger eigenvalue problem is solved for the 219 quantum simple harmonic oscillator using a finite element discretization of real space within which elements are adaptively spatially refined. We compare two comp...A Schrodinger eigenvalue problem is solved for the 219 quantum simple harmonic oscillator using a finite element discretization of real space within which elements are adaptively spatially refined. We compare two competing methods of adaptively discretizing the real-space grid on which computations are performed without modifying the standard polynomial basis-set traditionally used in finite element interpolations; namely, （i） an application of the Kelly error estimator, and （ii） a refinement based on the local potential level. When the performance of these methods are compared to standard uniform global refinement, we find that they significantly improve the total time spent in the eigensolver.展开更多
Accelerated design of hard-coating materials requires state-of-the-art computational tools,which include data-driven techniques,building databases,and training machine learning models.We develop a heavily automated hi...Accelerated design of hard-coating materials requires state-of-the-art computational tools,which include data-driven techniques,building databases,and training machine learning models.We develop a heavily automated high-throughput workflow to build a database of industrially relevant hard-coating materials,such as binary and ternary nitrides.We use the high-throughput toolkit to automate the density functional theory calculation workflow.We present results,including elastic constants that are a key parameter determining mechanical properties of hard-coatings,for X_(1−x)Y_(x)N ternary nitrides,where X,Y∈{Al,Ti,Zr,Hf}and fraction x=0,1/4,1/2,3/4,1.We also explore ways for machine learning to support and complement the designed databases.We find that the crystal graph convolutional neural network trained on ordered lattices has sufficient accuracy for the disordered nitrides,suggesting that existing databases provide important data for predicting mechanical properties of qualitatively different types of materials,in our case disordered hard-coating alloys.展开更多
基金Developed under the Auspices of the Development Projects N N519 402837 and R15 012 03Founded by the Polish Ministry of Science and Higher Education
文摘A Schrodinger eigenvalue problem is solved for the 219 quantum simple harmonic oscillator using a finite element discretization of real space within which elements are adaptively spatially refined. We compare two competing methods of adaptively discretizing the real-space grid on which computations are performed without modifying the standard polynomial basis-set traditionally used in finite element interpolations; namely, （i） an application of the Kelly error estimator, and （ii） a refinement based on the local potential level. When the performance of these methods are compared to standard uniform global refinement, we find that they significantly improve the total time spent in the eigensolver.
基金The authors gratefully acknowledge financial support from the Competence Center Functional Nanoscale Materials(FunMat-II)(Vinnova Grant No.2016-05156)Support from the Knut and Alice Wallenberg Foundation(Wallenberg Scholar Grant No.KAW-2018.0194)+3 种基金the Swedish Government Strategic Research Areas in Materials Science on Functional Materials at Linköping University(Faculty Grant SFO-Mat-LiU No.200900971)SeRC is gratefully acknowledged.Theoretical analysis of results of first-principles calculations was supported by the Russian Science Foundation(Project No.18-12-00492)R.A.acknowledges support from the Swedish Research Council(VR)Grant No.2020-05402 and the Swedish e-Science Centre(SeRC)The computations were enabled by resources provided by the Swedish National Infrastructure for Computing(SNIC),partially funded by the Swedish Research Council through grant agreement no.2018-05973。
文摘Accelerated design of hard-coating materials requires state-of-the-art computational tools,which include data-driven techniques,building databases,and training machine learning models.We develop a heavily automated high-throughput workflow to build a database of industrially relevant hard-coating materials,such as binary and ternary nitrides.We use the high-throughput toolkit to automate the density functional theory calculation workflow.We present results,including elastic constants that are a key parameter determining mechanical properties of hard-coatings,for X_(1−x)Y_(x)N ternary nitrides,where X,Y∈{Al,Ti,Zr,Hf}and fraction x=0,1/4,1/2,3/4,1.We also explore ways for machine learning to support and complement the designed databases.We find that the crystal graph convolutional neural network trained on ordered lattices has sufficient accuracy for the disordered nitrides,suggesting that existing databases provide important data for predicting mechanical properties of qualitatively different types of materials,in our case disordered hard-coating alloys.
