Structural optimization of lead compounds is a crucial step in drug discovery.One optimization strategy is to modify the molecular structure of a scaffold to improve both its biological activities and absorption,distr...Structural optimization of lead compounds is a crucial step in drug discovery.One optimization strategy is to modify the molecular structure of a scaffold to improve both its biological activities and absorption,distribution,metabolism,excretion,and toxicity(ADMET)properties.One of the deep molecular generative model approaches preserves the scaffold while generating drug-like molecules,thereby accelerating the molecular optimization process.Deep molecular diffusion generative models simulate a gradual process that creates novel,chemically feasible molecules from noise.However,the existing models lack direct interatomic constraint features and struggle with capturing long-range dependencies in macromolecules,leading to challenges in modifying the scaffold-based molecular structures,and creates limitations in the stability and diversity of the generated molecules.To address these challenges,we propose a deep molecular diffusion generative model,the three-dimensional(3D)equivariant diffusion-driven molecular generation(3D-EDiffMG)model.The dual strong and weak atomic interaction force-based long-range dependency capturing equivariant encoder(dual-SWLEE)is introduced to encode both the bonding and non-bonding information based on strong and weak atomic interactions.Addi-tionally,a gate multilayer perceptron(gMLP)block with tiny attention is incorporated to explicitly model complex long-sequence feature interactions and long-range dependencies.The experimental results show that 3D-EDiffMG effectively generates unique,novel,stable,and diverse drug-like molecules,highlighting its potential for lead optimization and accelerating drug discovery.展开更多
In this paper versal unfolding theorem of multiparameter equivariant bifurcation problem with parameter symmetry is given. The necessary and sufficient condition that unfolding of multiparameter equivariant bifurcatio...In this paper versal unfolding theorem of multiparameter equivariant bifurcation problem with parameter symmetry is given. The necessary and sufficient condition that unfolding of multiparameter equivariant bifurcation problem with parameter symmetry factors through another is given. The corresponding results in [1]-[6] are generalized.展开更多
Let E be a compact Lie group, G a closed subgroup of E, and H a closed normal subgroup of G . For principal fibre bundle (E,p, E/G;G) and (E/H,p′,E/G;G/H), the relation between aut G(E) ...Let E be a compact Lie group, G a closed subgroup of E, and H a closed normal subgroup of G . For principal fibre bundle (E,p, E/G;G) and (E/H,p′,E/G;G/H), the relation between aut G(E) (resp. aut * G(E) ) and aut G/H (E/H) (resp.aut * G/H (E/H)) is investigated by using bundle map theory and transformation group theory. It will enable us to compute the group F G(E) (resp. E G(E)) while the group F G/H (E/H) is known.展开更多
For the unfolding of equivariant bifurcation problems with two types of state variables in the presence of parameter symmetry,the versal unfolding theorem with respect to left-right equivalence is obtained by using th...For the unfolding of equivariant bifurcation problems with two types of state variables in the presence of parameter symmetry,the versal unfolding theorem with respect to left-right equivalence is obtained by using the related methods and techniques in the singularity theory of smooth map-germs.The corresponding results in[4,9]can be considered as its special cases.A relationship between the versal unfolding w.r.t.left-right equivalence and the versal deformation w.r.t.contact equivalence is established.展开更多
Based on the left_right equivalent relation of smooth map_germs in singularity theory, the unfoldings of multiparameter equivariant bifurcation problems with respect to left_right equivalence are discussed. The state ...Based on the left_right equivalent relation of smooth map_germs in singularity theory, the unfoldings of multiparameter equivariant bifurcation problems with respect to left_right equivalence are discussed. The state variables of such an equivariant bifurcation problem were divided into two groups, in which the first can vary independently, while the others depend on the first in the varying process. By applying related methods and techniques in the unfolding theory of smooth map_germs, the necessary and sufficient condition for an unfolding of a multiparameter equivariant bifurcation problem with two groups of state variables to be versal is obtained.展开更多
Associated with an immersion φ : S^3→ ■, we can define a canonical bundle endomorphism F : TS^3→ TS^3 by the pull back of the K?hler form of ■. In this article,related to F we study equivariant minimal immersions...Associated with an immersion φ : S^3→ ■, we can define a canonical bundle endomorphism F : TS^3→ TS^3 by the pull back of the K?hler form of ■. In this article,related to F we study equivariant minimal immersions from S^3 into ■ under the additional condition(?_XF)X = 0 for all X ∈ ker(F). As main result, we give a complete classification of such kinds of immersions. Moreover, we also construct a typical example of equivariant non-minimal immersion φ : S^3→ ■ satisfying(?_XF)X = 0 for all X ∈ ker(F), which is neither Lagrangian nor of CR type.展开更多
In this paper,we compute the first two equivariant heat kernel coeffcients of the Bochner Laplacian on differential forms.The first two equivariant heat kernel coeffcients of the Bochner Laplacian with torsion are als...In this paper,we compute the first two equivariant heat kernel coeffcients of the Bochner Laplacian on differential forms.The first two equivariant heat kernel coeffcients of the Bochner Laplacian with torsion are also given.We also study the equivariant heat kernel coeffcients of nonminimal operators on differential forms and get the equivariant Gilkey-Branson-Fulling formula.展开更多
Based on the contact equivalent relation of smooth map-germs in singularity theory, the stability of equivariant bifurcation problems with two types of state variables and their unfoldings in the presence of parameter...Based on the contact equivalent relation of smooth map-germs in singularity theory, the stability of equivariant bifurcation problems with two types of state variables and their unfoldings in the presence of parameter symmetry is discussed. Some basic results are obtained. Transversality condition is used to characterize the stability of equavariant bifurcation problems.展开更多
In addressing the challenge of motion artifacts in Positron Emission Tomography (PET) lung scans, our studyintroduces the Triple Equivariant Motion Transformer (TEMT), an innovative, unsupervised, deep-learningbasedfr...In addressing the challenge of motion artifacts in Positron Emission Tomography (PET) lung scans, our studyintroduces the Triple Equivariant Motion Transformer (TEMT), an innovative, unsupervised, deep-learningbasedframework for efficient respiratory motion correction in PET imaging. Unlike traditional techniques,which segment PET data into bins throughout a respiratory cycle and often face issues such as inefficiency andoveremphasis on certain artifacts, TEMT employs Convolutional Neural Networks (CNNs) for effective featureextraction and motion decomposition.TEMT’s unique approach involves transforming motion sequences into Liegroup domains to highlight fundamental motion patterns, coupled with employing competitive weighting forprecise target deformation field generation. Our empirical evaluations confirm TEMT’s superior performancein handling diverse PET lung datasets compared to existing image registration networks. Experimental resultsdemonstrate that TEMT achieved Dice indices of 91.40%, 85.41%, 79.78%, and 72.16% on simulated geometricphantom data, lung voxel phantom data, cardiopulmonary voxel phantom data, and clinical data, respectively. Tofacilitate further research and practical application, the TEMT framework, along with its implementation detailsand part of the simulation data, is made publicly accessible at https://github.com/yehaowei/temt.展开更多
Several equivalent formulations are given for equivariant coarse embedding into Hilbert space.Using these equivalent definitions,it is proved that for a metric space X and a Hilbert space H with proper and isometric g...Several equivalent formulations are given for equivariant coarse embedding into Hilbert space.Using these equivalent definitions,it is proved that for a metric space X and a Hilbert space H with proper and isometric group actions on both of them,if X is coarsely embeddable into H and the group is amenable,then the coarse embedding can be modified to be equivariant by using the invariant mean property of the amenable group.展开更多
The minimum risk equivariant estimator of a quantile of the common marginal distribution in a multivariate Lomax distribution with unknown location and scale parameters under Linex loss function is considered.
1. Introduction. Throughout this note, G is a finite group, M is a compact connected smooth on-dimensional manifold with or without boundary M, and G acts smoothly on M. We follow the standard notations ([B], [tD]). T...1. Introduction. Throughout this note, G is a finite group, M is a compact connected smooth on-dimensional manifold with or without boundary M, and G acts smoothly on M. We follow the standard notations ([B], [tD]). The isotropy subgroup of a point展开更多
In modern computational materials,machine learning has shown the capability to predict interatomic potentials,thereby supporting and accelerating conventional molecular dynamics(MD)simulations.However,existing models ...In modern computational materials,machine learning has shown the capability to predict interatomic potentials,thereby supporting and accelerating conventional molecular dynamics(MD)simulations.However,existing models typically sacrifice either accuracy or efficiency.Moreover,efficient models are highly demanded for offering simulating systems on a considerably larger scale at reduced computational costs.Here,we introduce an efficient equivariant graph neural network(E^(2)GNN)that can enable accurate and efficient interatomic potential and force predictions for molecules and crystals.Rather than relying on higher-order representations,E^(2)GNN employs a scalar-vector dual representation to encode equivariant features.By learning geometric symmetry information,our model remains efficient while ensuring prediction accuracy and robustness through the equivariance.Our results show that E^(2)GNN consistently outperforms the prediction performance of the representative baselines and achieves significant efficiency across diverse datasets,which include catalysts,molecules,and organic isomers.Furthermore,we conductMDsimulations using the E^(2)GNN force field across solid,liquid,and gas systems.It is found that E^(2)GNN can achieve the accuracy of ab initio MD across all examined systems.展开更多
The piezoelectric materials enable the mutual conversion between mechanical and electrical energy,which drive a multi-billion dollar industry through their applications as sensors,actuators,and energy harvesters.The t...The piezoelectric materials enable the mutual conversion between mechanical and electrical energy,which drive a multi-billion dollar industry through their applications as sensors,actuators,and energy harvesters.The third-rank piezoelectric tensor is the core matrices for piezoelectric materials and their devices.However,the high costs of obtaining full piezoelectric tensor data through either experimental or computational methods make a significant challenge.Here,we propose an equivariant attention tensor graph neural network(EATGNN)that can identify crystal symmetry and remain independent of the reference frame,ultimately enabling the accurate prediction of the complete third-rank piezoelectric tensor.Especially,we perform an irreducible decomposition of the piezoelectric tensor into four irreducible representations to efficiently reserve the symmetry under group transformation operations.Our results further demonstrate that this model performs well in both bulk and twodimensional materials.Finally,combining EATGNN with first-principles calculations,we discovered several potential high-performance piezoelectric materials.展开更多
We introduce finite group action for associative algebras equipped with a derivation(that is,AssDer pairs)and equivariant cohomology for such algebraic object.Next,we discuss equivariant deformation theory and study i...We introduce finite group action for associative algebras equipped with a derivation(that is,AssDer pairs)and equivariant cohomology for such algebraic object.Next,we discuss equivariant deformation theory and study its relation with the equivariant cohomology.展开更多
In this paper,we propose a new numerical scheme for the coupled Stokes-Darcy model with the Beavers-Joseph-Saffman interface condition.We use the weak Galerkin method to discretize the Stokes equation and the mixed fi...In this paper,we propose a new numerical scheme for the coupled Stokes-Darcy model with the Beavers-Joseph-Saffman interface condition.We use the weak Galerkin method to discretize the Stokes equation and the mixed finite element method to discretize the Darcy equation.A discrete inf-sup condition is proved and the optimal error estimates are also derived.Numerical experiments validate the theoretical analysis.展开更多
Fast and accurate spectral prediction plays a crucial role in molecular design within fields such as pharmaceutical and materials science.Nevertheless,predicting molecular spectra typically requires quantum chemistry ...Fast and accurate spectral prediction plays a crucial role in molecular design within fields such as pharmaceutical and materials science.Nevertheless,predicting molecular spectra typically requires quantum chemistry calculations,posing significant challenges for fast predictions and highthroughput screening.In this paper,we propose an equivariant,fast,and robust model,named EnviroDetaNet,which integrates molecular environment information.EnviroDetaNet employs an E(3)-equivariant message-passing neural network combining intrinsic atomic properties,spatial features,and environmental information,allowing it tocomprehensively capture both local and global molecular information.Compared to state-of-the-art machine learning models,EnviroDetaNet excels in various predictive tasks and maintains high accuracy even with a 50%reduction in training data,demonstrating strong generalization capabilities.Ablation studies confirm that molecular environment information is crucial for improving model stability and accuracy.EnviroDetaNet also shows outstanding performance in spectral predictions for complex molecular systems,making it a powerful tool for accelerating molecular discovery.展开更多
Excess biological fluids around skin wounds can lead to infections and impede the healing process.Researchers have exten-sively studied dressings with varying water contents for wound care.However,hydrophilic and hydr...Excess biological fluids around skin wounds can lead to infections and impede the healing process.Researchers have exten-sively studied dressings with varying water contents for wound care.However,hydrophilic and hydrophobic-hydrophilic dressings often face challenges such as slow fluid transfer and excessive retention.This study introduces an innovative approach involving the use of superhydrophobic–hydrophobic–hydrophilic dual-gradient electrospun nanofibers to form a 3D biomimetic nanofiber scaffold(3D BNSF).The 3D BNSF is composed of hydrophobic polycaprolactone and thermo-plastic polyurethane,along with antibacterial,superhydrophobic nano-chitin particles.In vitro and in vivo experiments have demonstrated that this scaffold exhibits excellent antibacterial properties and compatibility with cells,facilitating complete wound healing and regeneration.This study offers a new perspective on the targeted acceleration of wound healing,with the potential to become an alternative strategy for clinical applications.展开更多
Density-functional theory with extended Hubbard functionals(DFT+U+V)provides a robust framework to accurately describe complex materials containing transition-metal or rare-earth elements.It does so by mitigating self...Density-functional theory with extended Hubbard functionals(DFT+U+V)provides a robust framework to accurately describe complex materials containing transition-metal or rare-earth elements.It does so by mitigating self-interaction errors inherent to semi-local functionals which are particularly pronounced in systems with partially-filled d and f electronic states.However,achieving accuracy in this approach hinges upon the accurate determination of the on-site U and inter-site V Hubbard parameters.In practice,these are obtained either by semi-empirical tuning,requiring prior knowledge,or,more correctly,by using predictive but expensive first-principles calculations.Here,we present a machine learning model based on equivariant neural networks which uses atomic occupation matrices as descriptors,directly capturing the electronic structure,local chemical environment,and oxidation states of the system at hand.We target here the prediction of Hubbard parameters computed self-consistently with iterative linear-response calculations,as implemented in density-functional perturbation theory(DFPT),and structural relaxations.Remarkably,when trained on data from 12 materials spanning various crystal structures and compositions,our model achieves mean absolute relative errors of 3%and 5%for Hubbard U and V parameters,respectively.By circumventing computationally expensive DFT or DFPT self-consistent protocols,our model significantly expedites the prediction of Hubbard parameters with negligible computational overhead,while approaching the accuracy of DFPT.Moreover,owing to its robust transferability,the model facilitates accelerated materials discovery and design via high-throughput calculations,with relevance for various technological applications.展开更多
Graph Neural Network(GNN)potentials relying on chemical locality offer near-quantum mechanical accuracy at significantly reduced computational costs.Message-passing GNNs model interactions beyond their immediate neigh...Graph Neural Network(GNN)potentials relying on chemical locality offer near-quantum mechanical accuracy at significantly reduced computational costs.Message-passing GNNs model interactions beyond their immediate neighborhood by propagating local information between neighboring particles while remaining effectively local.However,locality precludes modeling long-range effects critical to many real-world systems,such as charge transfer,electrostatic interactions,and dispersion effects.In this work,we propose the Charge Equilibration Layer for Long-range Interactions(CELLI)to address the challenge of efficiently modeling non-local interactions.This novel architecture generalizes the classical charge equilibration(Qeq)method to a model-agnostic building block for modern equivariant GNN potentials.Therefore,CELLI extends the capability of GNNs to model longrange interactions while providing high interpretability through explicitly modeled charges.On benchmark systems,CELLI achieves state-of-the-art results for strictly local models.CELLI generalizes to diverse datasets and large structureswhile providing high computational efficiency and robust predictions.展开更多
基金supported by the National Key R&D Program of China(Grant No.:2023YFF1205102)the National Natural Science Foundation of China(Grant Nos.:82273856,22077143,and 21977127)the Science Foundation of Guangzhou,China(No.:2Grant024A04J2172).
文摘Structural optimization of lead compounds is a crucial step in drug discovery.One optimization strategy is to modify the molecular structure of a scaffold to improve both its biological activities and absorption,distribution,metabolism,excretion,and toxicity(ADMET)properties.One of the deep molecular generative model approaches preserves the scaffold while generating drug-like molecules,thereby accelerating the molecular optimization process.Deep molecular diffusion generative models simulate a gradual process that creates novel,chemically feasible molecules from noise.However,the existing models lack direct interatomic constraint features and struggle with capturing long-range dependencies in macromolecules,leading to challenges in modifying the scaffold-based molecular structures,and creates limitations in the stability and diversity of the generated molecules.To address these challenges,we propose a deep molecular diffusion generative model,the three-dimensional(3D)equivariant diffusion-driven molecular generation(3D-EDiffMG)model.The dual strong and weak atomic interaction force-based long-range dependency capturing equivariant encoder(dual-SWLEE)is introduced to encode both the bonding and non-bonding information based on strong and weak atomic interactions.Addi-tionally,a gate multilayer perceptron(gMLP)block with tiny attention is incorporated to explicitly model complex long-sequence feature interactions and long-range dependencies.The experimental results show that 3D-EDiffMG effectively generates unique,novel,stable,and diverse drug-like molecules,highlighting its potential for lead optimization and accelerating drug discovery.
基金This work is supported by NNSF of China(10271023) and Hunan Provincial Natural Science Foundation of China(04JJ3072).
文摘In this paper versal unfolding theorem of multiparameter equivariant bifurcation problem with parameter symmetry is given. The necessary and sufficient condition that unfolding of multiparameter equivariant bifurcation problem with parameter symmetry factors through another is given. The corresponding results in [1]-[6] are generalized.
文摘Let E be a compact Lie group, G a closed subgroup of E, and H a closed normal subgroup of G . For principal fibre bundle (E,p, E/G;G) and (E/H,p′,E/G;G/H), the relation between aut G(E) (resp. aut * G(E) ) and aut G/H (E/H) (resp.aut * G/H (E/H)) is investigated by using bundle map theory and transformation group theory. It will enable us to compute the group F G(E) (resp. E G(E)) while the group F G/H (E/H) is known.
文摘For the unfolding of equivariant bifurcation problems with two types of state variables in the presence of parameter symmetry,the versal unfolding theorem with respect to left-right equivalence is obtained by using the related methods and techniques in the singularity theory of smooth map-germs.The corresponding results in[4,9]can be considered as its special cases.A relationship between the versal unfolding w.r.t.left-right equivalence and the versal deformation w.r.t.contact equivalence is established.
文摘Based on the left_right equivalent relation of smooth map_germs in singularity theory, the unfoldings of multiparameter equivariant bifurcation problems with respect to left_right equivalence are discussed. The state variables of such an equivariant bifurcation problem were divided into two groups, in which the first can vary independently, while the others depend on the first in the varying process. By applying related methods and techniques in the unfolding theory of smooth map_germs, the necessary and sufficient condition for an unfolding of a multiparameter equivariant bifurcation problem with two groups of state variables to be versal is obtained.
文摘Associated with an immersion φ : S^3→ ■, we can define a canonical bundle endomorphism F : TS^3→ TS^3 by the pull back of the K?hler form of ■. In this article,related to F we study equivariant minimal immersions from S^3 into ■ under the additional condition(?_XF)X = 0 for all X ∈ ker(F). As main result, we give a complete classification of such kinds of immersions. Moreover, we also construct a typical example of equivariant non-minimal immersion φ : S^3→ ■ satisfying(?_XF)X = 0 for all X ∈ ker(F), which is neither Lagrangian nor of CR type.
基金supported by NSFC(10801027)Fok Ying Tong Education Foundation(121003)
文摘In this paper,we compute the first two equivariant heat kernel coeffcients of the Bochner Laplacian on differential forms.The first two equivariant heat kernel coeffcients of the Bochner Laplacian with torsion are also given.We also study the equivariant heat kernel coeffcients of nonminimal operators on differential forms and get the equivariant Gilkey-Branson-Fulling formula.
基金Project supported by the National Natural Science Foundation of China(No.10671002)the Natural Science Foundation of Hunan Province of China(No.04JJ3072)the Science Foundation of the Education Department of Hunan Province of China(No.04C383)
文摘Based on the contact equivalent relation of smooth map-germs in singularity theory, the stability of equivariant bifurcation problems with two types of state variables and their unfoldings in the presence of parameter symmetry is discussed. Some basic results are obtained. Transversality condition is used to characterize the stability of equavariant bifurcation problems.
基金the National Natural Science Foundation of China(No.82160347)Yunnan Provincial Science and Technology Department(No.202102AE090031)Yunnan Key Laboratory of Smart City in Cyberspace Security(No.202105AG070010).
文摘In addressing the challenge of motion artifacts in Positron Emission Tomography (PET) lung scans, our studyintroduces the Triple Equivariant Motion Transformer (TEMT), an innovative, unsupervised, deep-learningbasedframework for efficient respiratory motion correction in PET imaging. Unlike traditional techniques,which segment PET data into bins throughout a respiratory cycle and often face issues such as inefficiency andoveremphasis on certain artifacts, TEMT employs Convolutional Neural Networks (CNNs) for effective featureextraction and motion decomposition.TEMT’s unique approach involves transforming motion sequences into Liegroup domains to highlight fundamental motion patterns, coupled with employing competitive weighting forprecise target deformation field generation. Our empirical evaluations confirm TEMT’s superior performancein handling diverse PET lung datasets compared to existing image registration networks. Experimental resultsdemonstrate that TEMT achieved Dice indices of 91.40%, 85.41%, 79.78%, and 72.16% on simulated geometricphantom data, lung voxel phantom data, cardiopulmonary voxel phantom data, and clinical data, respectively. Tofacilitate further research and practical application, the TEMT framework, along with its implementation detailsand part of the simulation data, is made publicly accessible at https://github.com/yehaowei/temt.
基金Supported by National Natural Science Foundation of China(11871342)。
文摘Several equivalent formulations are given for equivariant coarse embedding into Hilbert space.Using these equivalent definitions,it is proved that for a metric space X and a Hilbert space H with proper and isometric group actions on both of them,if X is coarsely embeddable into H and the group is amenable,then the coarse embedding can be modified to be equivariant by using the invariant mean property of the amenable group.
文摘The minimum risk equivariant estimator of a quantile of the common marginal distribution in a multivariate Lomax distribution with unknown location and scale parameters under Linex loss function is considered.
文摘1. Introduction. Throughout this note, G is a finite group, M is a compact connected smooth on-dimensional manifold with or without boundary M, and G acts smoothly on M. We follow the standard notations ([B], [tD]). The isotropy subgroup of a point
基金supported by the National Natural Science Foundation of China(Grant No.62176272)Research and Development Program of Guangzhou Science and Technology Bureau(No.2023B01J1016)+2 种基金Key-Area Research and Development Program of Guangdong Province(No.2020B1111100001)Singapore MOE Tier 1(No.A-8001194-00-00)Singapore MOE Tier 2(No.A-8001872-00-00).
文摘In modern computational materials,machine learning has shown the capability to predict interatomic potentials,thereby supporting and accelerating conventional molecular dynamics(MD)simulations.However,existing models typically sacrifice either accuracy or efficiency.Moreover,efficient models are highly demanded for offering simulating systems on a considerably larger scale at reduced computational costs.Here,we introduce an efficient equivariant graph neural network(E^(2)GNN)that can enable accurate and efficient interatomic potential and force predictions for molecules and crystals.Rather than relying on higher-order representations,E^(2)GNN employs a scalar-vector dual representation to encode equivariant features.By learning geometric symmetry information,our model remains efficient while ensuring prediction accuracy and robustness through the equivariance.Our results show that E^(2)GNN consistently outperforms the prediction performance of the representative baselines and achieves significant efficiency across diverse datasets,which include catalysts,molecules,and organic isomers.Furthermore,we conductMDsimulations using the E^(2)GNN force field across solid,liquid,and gas systems.It is found that E^(2)GNN can achieve the accuracy of ab initio MD across all examined systems.
基金supported by the National Key R&D Program of China(2019YFE0112000)the Zhejiang Provincial Natural Science Foundation of China(LR21A040001,LDT23F04014F01)the National Natural Science Foundation of China(No.11974307).
文摘The piezoelectric materials enable the mutual conversion between mechanical and electrical energy,which drive a multi-billion dollar industry through their applications as sensors,actuators,and energy harvesters.The third-rank piezoelectric tensor is the core matrices for piezoelectric materials and their devices.However,the high costs of obtaining full piezoelectric tensor data through either experimental or computational methods make a significant challenge.Here,we propose an equivariant attention tensor graph neural network(EATGNN)that can identify crystal symmetry and remain independent of the reference frame,ultimately enabling the accurate prediction of the complete third-rank piezoelectric tensor.Especially,we perform an irreducible decomposition of the piezoelectric tensor into four irreducible representations to efficiently reserve the symmetry under group transformation operations.Our results further demonstrate that this model performs well in both bulk and twodimensional materials.Finally,combining EATGNN with first-principles calculations,we discovered several potential high-performance piezoelectric materials.
基金supported by the Guangdong Basic and Applied Basic Research Foundation(Grant No.2022A1515012176)by the Shenzhen Institute of Information Technology(Grant No.2023djpigyb05).
文摘We introduce finite group action for associative algebras equipped with a derivation(that is,AssDer pairs)and equivariant cohomology for such algebraic object.Next,we discuss equivariant deformation theory and study its relation with the equivariant cohomology.
基金Science and Technology Commission of Shanghai Municipality(STCSM)(Grant No.18dz2271000)Natural Science Foundation of Shanghai(Grant No.20ZR1416700)National Natural Science Foundation of China(Grant No.11931007)。
文摘In this paper,we propose a new numerical scheme for the coupled Stokes-Darcy model with the Beavers-Joseph-Saffman interface condition.We use the weak Galerkin method to discretize the Stokes equation and the mixed finite element method to discretize the Darcy equation.A discrete inf-sup condition is proved and the optimal error estimates are also derived.Numerical experiments validate the theoretical analysis.
基金supported by the National Key R&D Program of China(Grant No.2023YFF1204903)the National Natural Science Foundation of China(Grants No.22222303,22173032,21933010,22250710136,22333006)the Artificial Intelligence-Driven Reform of Scientific Research Paradigms:Empowerment Program for Discipline Advancement(Grants No.2024AI01009),Y.W.acknowledges support from the Schmidt Science Fellowship,in partnership with the Rhodes Trust,and the Simons Center for Computational Physical Chemistry at New York University,We sincerely thank the High-Performance Computing(HPC)resources supported by New York University and NYU Abu Dhabi.
文摘Fast and accurate spectral prediction plays a crucial role in molecular design within fields such as pharmaceutical and materials science.Nevertheless,predicting molecular spectra typically requires quantum chemistry calculations,posing significant challenges for fast predictions and highthroughput screening.In this paper,we propose an equivariant,fast,and robust model,named EnviroDetaNet,which integrates molecular environment information.EnviroDetaNet employs an E(3)-equivariant message-passing neural network combining intrinsic atomic properties,spatial features,and environmental information,allowing it tocomprehensively capture both local and global molecular information.Compared to state-of-the-art machine learning models,EnviroDetaNet excels in various predictive tasks and maintains high accuracy even with a 50%reduction in training data,demonstrating strong generalization capabilities.Ablation studies confirm that molecular environment information is crucial for improving model stability and accuracy.EnviroDetaNet also shows outstanding performance in spectral predictions for complex molecular systems,making it a powerful tool for accelerating molecular discovery.
基金supported by the National Natural Science Foundation of China(22278225)National Key Research and Development Program of China(2018YFC1602800)+1 种基金China Postdoctoral Science Foundation(2022M712180)Natural Science Foundation of Fujian Province(2022J02021).
文摘Excess biological fluids around skin wounds can lead to infections and impede the healing process.Researchers have exten-sively studied dressings with varying water contents for wound care.However,hydrophilic and hydrophobic-hydrophilic dressings often face challenges such as slow fluid transfer and excessive retention.This study introduces an innovative approach involving the use of superhydrophobic–hydrophobic–hydrophilic dual-gradient electrospun nanofibers to form a 3D biomimetic nanofiber scaffold(3D BNSF).The 3D BNSF is composed of hydrophobic polycaprolactone and thermo-plastic polyurethane,along with antibacterial,superhydrophobic nano-chitin particles.In vitro and in vivo experiments have demonstrated that this scaffold exhibits excellent antibacterial properties and compatibility with cells,facilitating complete wound healing and regeneration.This study offers a new perspective on the targeted acceleration of wound healing,with the potential to become an alternative strategy for clinical applications.
基金support by the NCCR MARVEL,a National Centre of Competence in Research,funded by the Swiss National Science Foundation(Grant number 205602)supported by a grant from the Swiss National Supercomputing Centre(CSCS)under project ID s1073(Piz Daint)and ID 465000416(LUMI-G)supported by MIAI@Grenoble Alpes,(ANR-19-P3IA-0003).
文摘Density-functional theory with extended Hubbard functionals(DFT+U+V)provides a robust framework to accurately describe complex materials containing transition-metal or rare-earth elements.It does so by mitigating self-interaction errors inherent to semi-local functionals which are particularly pronounced in systems with partially-filled d and f electronic states.However,achieving accuracy in this approach hinges upon the accurate determination of the on-site U and inter-site V Hubbard parameters.In practice,these are obtained either by semi-empirical tuning,requiring prior knowledge,or,more correctly,by using predictive but expensive first-principles calculations.Here,we present a machine learning model based on equivariant neural networks which uses atomic occupation matrices as descriptors,directly capturing the electronic structure,local chemical environment,and oxidation states of the system at hand.We target here the prediction of Hubbard parameters computed self-consistently with iterative linear-response calculations,as implemented in density-functional perturbation theory(DFPT),and structural relaxations.Remarkably,when trained on data from 12 materials spanning various crystal structures and compositions,our model achieves mean absolute relative errors of 3%and 5%for Hubbard U and V parameters,respectively.By circumventing computationally expensive DFT or DFPT self-consistent protocols,our model significantly expedites the prediction of Hubbard parameters with negligible computational overhead,while approaching the accuracy of DFPT.Moreover,owing to its robust transferability,the model facilitates accelerated materials discovery and design via high-throughput calculations,with relevance for various technological applications.
基金Funded by the European Union. Views and opinions expressed are, however, those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive AgencyNeither the European Union nor the granting authority can be held responsible for them. This work was funded by the ERC (StG SupraModel) - 101077842the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 534045056 and 561190767.
文摘Graph Neural Network(GNN)potentials relying on chemical locality offer near-quantum mechanical accuracy at significantly reduced computational costs.Message-passing GNNs model interactions beyond their immediate neighborhood by propagating local information between neighboring particles while remaining effectively local.However,locality precludes modeling long-range effects critical to many real-world systems,such as charge transfer,electrostatic interactions,and dispersion effects.In this work,we propose the Charge Equilibration Layer for Long-range Interactions(CELLI)to address the challenge of efficiently modeling non-local interactions.This novel architecture generalizes the classical charge equilibration(Qeq)method to a model-agnostic building block for modern equivariant GNN potentials.Therefore,CELLI extends the capability of GNNs to model longrange interactions while providing high interpretability through explicitly modeled charges.On benchmark systems,CELLI achieves state-of-the-art results for strictly local models.CELLI generalizes to diverse datasets and large structureswhile providing high computational efficiency and robust predictions.
