Topology,as a mathematical concept,has been introduced into condensed matter physics since the discovery of quantum Hall effect,which characterizes new physical scenario beyond the Landau theory.The topologically prot...Topology,as a mathematical concept,has been introduced into condensed matter physics since the discovery of quantum Hall effect,which characterizes new physical scenario beyond the Landau theory.The topologically protected physical quantities,such as the dissipationless quantum transport of edge/surface states as well as magnetic/dipole quasi-particles like skyrmions/bimerons,have attracted great research enthusiasms in the past decades.In recent years,another kind of topology in condensed matter was revealed in the magnetoelectric parameter space of multiferroics,which deepens our understanding of magnetoelectric physics.This topical review summarizes recent advances in this area,involving three types of type-Ⅱmultiferroics.With magnetism-induced ferroelectricity,topological behaviors can be manifested during the magnetoelectric switching processes driven by magnetic/electric fields,such as Roman-surface/Riemann-surface magnetoelectricity and magnetic crankshaft.These exotic topological magnetoelectric behaviors may be helpful to pursue energy-efficient and precise-control devices for spintronics and quantum computing.展开更多
Deployable Composite Thin-Walled Structures(DCTWS)are widely used in space applications due to their ability to compactly fold and self-deploy in orbit,enabled by cutouts.Cutout design is crucial for balancing structu...Deployable Composite Thin-Walled Structures(DCTWS)are widely used in space applications due to their ability to compactly fold and self-deploy in orbit,enabled by cutouts.Cutout design is crucial for balancing structural rigidity and flexibility,ensuring material integrity during large deformations,and providing adequate load-bearing capacity and stability once deployed.Most research has focused on optimizing cutout size and shape,while topology optimization offers a broader design space.However,the anisotropic properties of woven composite laminates,complex failure criteria,and multi-performance optimization needs have limited the exploration of topology optimization in this field.This work derives the sensitivities of bending stiffness,critical buckling load,and the failure index of woven composite materials with respect to element density,and formulates both single-objective and multi-objective topology optimization models using a linear weighted aggregation approach.The developed method was integrated with the commercial finite element software ABAQUS via a Python script,allowing efficient application to cutout design in various DCTWS configurations to maximize bending stiffness and critical buckling load under material failure constraints.Optimization of a classical tubular hinge resulted in improvements of 107.7%in bending stiffness and 420.5%in critical buckling load compared to level-set topology optimization results reported in the literature,validating the effectiveness of the approach.To facilitate future research and encourage the broader adoption of topology optimization techniques in DCTWS design,the source code for this work is made publicly available via a Git Hub link:https://github.com/jinhao-ok1/Topo-for-DCTWS.git.展开更多
Social bots are automated programs designed to spread rumors and misinformation,posing significant threats to online security.Existing research shows that the structure of a social network significantly affects the be...Social bots are automated programs designed to spread rumors and misinformation,posing significant threats to online security.Existing research shows that the structure of a social network significantly affects the behavioral patterns of social bots:a higher number of connected components weakens their collaborative capabilities,thereby reducing their proportion within the overall network.However,current social bot detection methods still make limited use of topological features.Furthermore,both graph neural network(GNN)-based methods that rely on local features and those that leverage global features suffer from their own limitations,and existing studies lack an effective fusion of multi-scale information.To address these issues,this paper proposes a topology-aware multi-scale social bot detection method,which jointly learns local and global representations through a co-training mechanism.At the local level,topological features are effectively embedded into node representations,enhancing expressiveness while alleviating the over-smoothing problem in GNNs.At the global level,a clustering attention mechanism is introduced to learn global node representations,mitigating the over-globalization problem.Experimental results demonstrate that our method effectively overcomes the limitations of single-scale approaches.Our code is publicly available at https://anonymous.4open.science/r/TopoMSG-2C41/(accessed on 27 October 2025).展开更多
The stress minimization multi-material topology optimization(MMTO)approach has recently attracted significant attention because of its applications in aerospace and mechanical engineering.Nonetheless,the stress minimi...The stress minimization multi-material topology optimization(MMTO)approach has recently attracted significant attention because of its applications in aerospace and mechanical engineering.Nonetheless,the stress minimization MMTO approach may result in stress surpassing the material's tolerance limit,potentially culminating in failure.This research proposes a novel way for imposing stress constraints on each material to regulate their respective stress levels.The fundamental concept is that each material possesses its own interpolation function for the stress model.The maximum von Mises stress for each material can be established with the definition of an upper limit,ensuring that the materials will perform safely and effectively.This aids topological structures in resisting failure and augmenting strength.A multi-physics system including thermoelastic and self-weight loads is concurrently examined alongside stress limitations.The global stress constraint utilizes the p-norm function,and the adjoint method is used to derive sensitivity.This work employs a three-field strategy utilizing density filtering and Heaviside projection functions to mitigate the artificial stress in low density.The technique is assessed through two-dimensional(2D)and three-dimensional(3D)examples,illustrating the influence of stress limits on the compliance minimization under heat and self-weight loads.The optimized results indicate a substantial decrease in the stress levels accompanied by a minor gain in compliance,while maintaining the stress within the specified range for all materials.展开更多
Based on the demands for crashworthiness and lightweight in the passive safety of transportation vehicles,metal-fiber reinforced polymer(FRP)hybrid thin-walled tubes(MFHTWTs)integrate the toughness,strength and lightw...Based on the demands for crashworthiness and lightweight in the passive safety of transportation vehicles,metal-fiber reinforced polymer(FRP)hybrid thin-walled tubes(MFHTWTs)integrate the toughness,strength and lightweight of two distinct material characteristics.MFHTWTs can achieve energy absorption through the coupling of material plastic deformation and fracture,demonstrating significant engineering value in passive safety.This review provides a comprehensive examination of the crashworthiness topology optimization of MFHTWTs,aiming to demonstrate that a deeply integrated approach combining topology and parameter opti-mization can realize an optimal design method for MFHTWTs,thereby maximizing the functional utilization of limited material.Firstly,the review highlights the crashworthiness topology optimization methods(CTOMs)based on thin-walled structures.With a particular focus on metal,the review discusses both the practical ap-plicability and limitations of CTOMs under crash conditions.Additionally,based on the methodology of the equivalent static load method(ESLM),the review emphasizes that topology optimization methods considering continuous fiber paths and multi-material interface connections are also applicable to the crashworthiness op-timization of MFHTWTs.Furthermore,to couple structural parameters and configuration characteristics,in-tegrated topology optimization methods,including parameter optimization,are proposed to provide a valuable reference for the global optimization of MFHTWTs.Thus,these methods can establish the mapping relationship between key parameters and the structural energy absorption capacity.展开更多
The moving morphable component(MMC)topology optimization method,as a typical explicit topology optimization method,has been widely concerned.In the MMC topology optimization framework,the surrogate material model is m...The moving morphable component(MMC)topology optimization method,as a typical explicit topology optimization method,has been widely concerned.In the MMC topology optimization framework,the surrogate material model is mainly used for finite element analysis at present,and the effectiveness of the surrogate material model has been fully confirmed.However,there are some accuracy problems when dealing with boundary elements using the surrogate material model,which will affect the topology optimization results.In this study,a boundary element reconstruction(BER)model is proposed based on the surrogate material model under the MMC topology optimization framework to improve the accuracy of topology optimization.The proposed BER model can reconstruct the boundary elements by refining the local meshes and obtaining new nodes in boundary elements.Then the density of boundary elements is recalculated using the new node information,which is more accurate than the original model.Based on the new density of boundary elements,the material properties and volume information of the boundary elements are updated.Compared with other finite element analysis methods,the BER model is simple and feasible and can improve computational accuracy.Finally,the effectiveness and superiority of the proposed method are verified by comparing it with the optimization results of the original surrogate material model through several numerical examples.展开更多
Accurate estimation of photovoltaic(PV)parameters is essential for optimizing solar module perfor-mance and enhancing resource efficiency in renewable energy systems.This study presents a process innovation by introdu...Accurate estimation of photovoltaic(PV)parameters is essential for optimizing solar module perfor-mance and enhancing resource efficiency in renewable energy systems.This study presents a process innovation by introducing,for the first time,the Triangulation Topology Aggregation Optimizer(TTAO)integrated with parallel computing to address PV parameter estimation challenges.The effectiveness and robustness of TTAO are rigorously evaluated using two standard benchmark datasets(KC200GT and R.T.C.France solar cells)and a real-world dataset(Poly70W solar module)under single-,double-,and triple-diode configurations.Results show that TTAO consistently achieves superior accuracy by producing the lowest RMSE values and faster convergence compared to state-of-the-art metaheuristic algorithms.In addition,the integration of parallel computing significantly enhances computational efficiency,reducing execution time by up to 85%without compromising accuracy.Validation using real-world data further demonstrates TTAO’s adaptability and practical relevance in renewable energy systems,effectively bridging the gap between theoretical modeling and real-world implementation for PV system monitoring and optimization,contributing to climate mitigation through improved solar energy performance.展开更多
The event-triggered mechanism serves as an effective discontinuous control strategy for addressing the consensus tracking problem in multiagent systems(MASs).This approach optimizes energy consumption by updating the ...The event-triggered mechanism serves as an effective discontinuous control strategy for addressing the consensus tracking problem in multiagent systems(MASs).This approach optimizes energy consumption by updating the controller only when some observed errors exceed a predefined threshold.Considering the influence of noise on agent dynamics in complex control environments,this study investigates an event-triggered control scheme for stochastic MASs,where noise is modeled as Brownian motion.Furthermore,the communication topology of the stochastic MASs is assumed to exhibit a Markovian switching mechanism.Analytical criteria are derived to guarantee consensus tracking in the mean square sense,and a numerical example is provided to validate the effectiveness of the proposed control methods.展开更多
Forced imbibition,the invasion of a wetting fluid into porous rocks,plays an important role in the effective exploitation of hydrocarbon resources and the geological sequestration of carbon dioxide.However,the interfa...Forced imbibition,the invasion of a wetting fluid into porous rocks,plays an important role in the effective exploitation of hydrocarbon resources and the geological sequestration of carbon dioxide.However,the interface dynamics influenced by complex topology commonly leads to non-wetting fluid trapping.Particularly,the underlying mechanisms under viscously unfavorable conditions remain unclear.This study employs a direct numerical simulation method to simulate forced imbibition through the reconstructed digital rocks of sandstone.The interface dynamics and fluid–fluid interactions are investigated through transient simulations,while the pore topology metrics are introduced to analyze the impact on steady-state residual fluid distribution obtained by a pseudo-transient scheme.The results show that the cooperative pore-filling process promoted by corner flow is dominant at low capillary numbers.This leads to unstable inlet pressure,mass flow,and interface curvature,which correspond to complicated interface dynamics and higher residual fluid saturation.During forced imbibition,the interface curvature gradually increases,with the pore-filling mechanisms involving the cooperation of main terminal meniscus movement and arc menisci filling.Complex topology with small diameter pores may result in the destabilization of interface curvature.The residual fluid saturation is negatively correlated with porosity and pore throat size,and positively correlated with tortuosity and aspect ratio.A large mean coordination number characterizing global connectivity promotes imbibition.However,high connectivity characterized by the standardized Euler number corresponding to small pores is associated with a high probability of non-wetting fluid trapping.展开更多
Heat dissipation performance is critical to the design of high-end equipment,such as integrated chips and high-precision machine tools.Owing to the advantages of artificial intelligence in solving complex tasks involv...Heat dissipation performance is critical to the design of high-end equipment,such as integrated chips and high-precision machine tools.Owing to the advantages of artificial intelligence in solving complex tasks involving a large number of variables,researchers have exploited deep learning to expedite the optimization of material properties,such as the heat dissipation of solid isotropic materials with penalization(SIMP).However,because the approach is limited by discrete datasets and labeled training forms,ensuring the continuous adaptation of the condition domain and maintaining the stability of the design structure remain major challenges in the current intelligent design methodology for thermally conductive structures.In this study,we propose an innovative intelligent design fram-ework integrating Conditional Deep Convolutional Generative Adversarial Networks(CDCGAN)with SIMP,capable of creating topology structures that meet prescribed thermal conduction performance.This proposed design strategy significantly reduces the computational time required to solve symmetric and random heat sink problems compared with existing design approaches and is approximately 98%faster than standard SIMP methods and 55.5%faster than conventional deep-learning-based methods.In addition,we benchmarked the design performance of the proposed framework against theoretical structural designs via experimental measurements.We observed a 50.1%reduction in the average temperature and a 28.2%reduction in the highest temperature in our designed topology compared with those theoretical structure designs.展开更多
This paper presents a deep learning-based topology optimization method for the joint design of material layout and fiber orientation in continuous fiber-reinforced composite structure(CFRCS).The proposed method mainly...This paper presents a deep learning-based topology optimization method for the joint design of material layout and fiber orientation in continuous fiber-reinforced composite structure(CFRCS).The proposed method mainly includes three steps:(1)a ResUNet-involved generative and adversarial network(ResUNet-GAN)is developed to establish the end-to-end mapping from structural design parameters to fiber-reinforced composite optimized structure,and a fiber orientation chromatogram is presented to represent continuous fiber angles;(2)to avoid the local optimum problem,the independent continuous mapping method(ICM method)considering the improved principal stress orientation interpolated continuous fiber angle optimization(PSO-CFAO)strategy is utilized to construct CFRCS topology optimization dataset;(3)the well-trained ResUNet-GAN is deployed to design the optimal structural material distribution together with the corresponding continuous fiber orientations.Numerical simulations for benchmark structure verify that the proposed method greatly improves the design efficiency of CFRCS along with high design accuracy.Furthermore,the CFRCS topology configuration designed by ResUNet-GAN is fabricated by additive manufacturing.Compression experiments of the specimens show that both the stiffness structure and peak load of the CFRCS topology configuration designed by the proposed method have significantly enhanced.The proposed deep learning-based topology optimization method will provide great flexibility in CFRCS for engineering applications.展开更多
Metalens technology has been applied extensively in miniaturized and integrated infrared imaging systems.However,due to the high phase dispersion of unit structures,metalens often exhibits chromatic aberration,making ...Metalens technology has been applied extensively in miniaturized and integrated infrared imaging systems.However,due to the high phase dispersion of unit structures,metalens often exhibits chromatic aberration,making broadband achromatic infrared imaging challenging to achieve.In this paper,six different unit structures based on chalcogenide glass are constructed,and their phase-dispersion parameters are analyzed to establish a database.On this basis,using chromatic aberration compensation and parameterized adjoint topology optimization,a broadband achromatic metalens with a numerical aperture of 0.5 is designed by arranging these six unit structures in the far-infrared band.Simulation results show that the metalens achieves near diffraction-limited focusing within the operating wavelength range of 9−11μm,demonstrating the good performance of achromatic aberration with flat focusing efficiency of 54%−58%across all wavelengths.展开更多
We demonstrate that the sliding motion between two layers of the newly discovered ferroelectric and topologically trivial bismuth(Bi)monolayer[Nature 61767(2023)]can induce a sequence of topological phase transitions,...We demonstrate that the sliding motion between two layers of the newly discovered ferroelectric and topologically trivial bismuth(Bi)monolayer[Nature 61767(2023)]can induce a sequence of topological phase transitions,alternating between Z_(2)trivial and nontrivial states.The lateral shift,while preserving spatial symmetry,can switch the quantum spin Hall state on and of.The sliding-induced changes in out-of-plane atomic buckling,which are directly coupled to in-plane ferroelectricity,are shown to signifcantly modulate the band gap and drive the topological phase transitions.We map out the topological phase diagram and in-plane ferroelectricity with respect to sliding displacements.With appropriate sliding,the bismuth bilayer can transition into a nontrivial polar metal,exhibiting a pronounced shift current response arising from interband geometric quantities of electronic bands.Moreover,bilayer Bi supports a sliding-tunable nonlinear anomalous Hall response resulting from the geometric Berry curvature dipole.Confgurations that are Z_(2)nontrivial can generate drastically different transverse currents orthogonal to the external electric feld,as both the direction and magnitude of the Berry curvature dipole at the Fermi level are highly sensitive to the sliding displacement.Our results suggest that bilayer bismuth,with its ability to generate multiple types of geometric currents,ofers a versatile platform for power-efcient“Berry slidetronics”for multistate memory applications integrating both band topology and ferroelectricity.展开更多
Objective To configure the complex traditional Chinese medicine(TCM)prescription using digit topology circle and to derive digit topology circle.Methods The basic digit topology circles were constructed.Different digi...Objective To configure the complex traditional Chinese medicine(TCM)prescription using digit topology circle and to derive digit topology circle.Methods The basic digit topology circles were constructed.Different digit topology circles were derived using basic digit topology circle,the character strings,and the digit groups.Different digit topology circles with ternary Chinese medicine were derived by adding ternary Chinese medicine into digit topology circles.The valuable TCM prescriptions were configured using the derived digit topology circles.Results Nine simple basic digit topology circles were constructed from the character strings.Multiple digit topology circles and some digit topology circles with ternary Chinese medicine were derived using basic digit topology circles,the character strings,and the digit groups.Four complex TCM prescriptions were configured using four derived digit topology circles digit topology circles,respectively.Conclusion The digit topology circles can be used to configure some existing TCM prescriptions and many novel TCM prescriptions.It has been verified that some existing TCM prescriptions have been used successfully to treat patients with diseases.Some novel valuable TCM prescriptions configured by digit topology circles may be used to treat patients with diseases.展开更多
The development of chassis active safety control technology has improved vehicle stability under extreme conditions.However,its cross-system and multi-functional characteristics make the controller difficult to achiev...The development of chassis active safety control technology has improved vehicle stability under extreme conditions.However,its cross-system and multi-functional characteristics make the controller difficult to achieve cooperative goals.In addition,the chassis system,which has high complexity,numerous subsystems,and strong coupling,will also lead to low computing efficiency and poor control effect of the controller.Therefore,this paper proposes a scenario-driven hybrid distributed model predictive control algorithm with variable control topology.This algorithm divides multiple stability regions based on the vehicle’s β−γ phase plane,forming a mapping relationship between the control structure and the vehicle’s state.A control input fusion mechanism within the transition domain is designed to mitigate the problems of system state oscillation and control input jitter caused by switching control structures.Then,a distributed state-space equation with state coupling and input coupling characteristics is constructed,and a weighted local agent cost function in quadratic programming is derived.Through cost coupling,local agents can coordinate global performance goals.Finally,through Simulink/CarSim joint simulation and hardware-in-the-loop(HIL)test,the proposed algorithm is validated to improve vehicle stability while ensuring trajectory tracking accuracy and has good applicability for multi-objective coordinated control.This paper combines the advantages of distributed MPC and decentralized MPC,achieving a balance between approximating the global optimal results and the solution’s efficiency.展开更多
The unfilled skutterudite family has recently gained attention as a potential platform for hosting Dirac states. In this study, we systematically investigate the transport properties of IrSb_(3) single crystals. Magne...The unfilled skutterudite family has recently gained attention as a potential platform for hosting Dirac states. In this study, we systematically investigate the transport properties of IrSb_(3) single crystals. Magnetoresistance measurements exhibit prominent Shubnikov–de Haas oscillations and negative magnetoresistance at low temperatures. Quantum oscillation analysis extracts a nontrivial Berry phase and confirms a three-dimensional Fermi surface. Additionally, density functional theory calculations indicate the presence of nontrivial topological bands and surface states, suggesting that IrSb_(3) is a topological semimetal. These findings contribute to the growing family of topological materials and provide a platform for further exploration of quantum transport phenomena.展开更多
This study presents an extension of multiscale topology optimization by integrating both yield stress and local/global buckling considerations into the design process.Building upon established multiscale methodologies...This study presents an extension of multiscale topology optimization by integrating both yield stress and local/global buckling considerations into the design process.Building upon established multiscale methodologies,we develop a new framework incorporating yield stress limits either as constraints or objectives alongside previously established local and global buckling constraints.This approach significantly refines the optimization process,ensuring that the resulting designs meet mechanical performance criteria and adhere to critical material yield constraints.First,we establish local density-dependent von Mises yield surfaces based on local yield estimates from homogenization-based analysis to predict the local yield limits of the homogenized materials.Then,these local yield-based load factors are combined with local and global buckling criteria to obtain topology optimized designs that consider yield and buckling failure on all levels.This integration is crucial for the practical application of optimized structures in real-world scenarios,where material yield and stability behavior critically influence structural integrity and durability.Numerical examples demonstrate how optimized designs depend on the stiffness to yield ratio of the considered building material.Despite the foundational assumption of the separation of scales,the de-homogenized structures,even at relatively coarse length scales,exhibit a remarkably high degree of agreement with the corresponding homogenized predictions.展开更多
Pursuing new two-dimensional(2D)materials has been a hot topic in materials science,driven by their potential for diverse applications.Recent research has unveiled stable planar hypercoordinate motifs with unconventio...Pursuing new two-dimensional(2D)materials has been a hot topic in materials science,driven by their potential for diverse applications.Recent research has unveiled stable planar hypercoordinate motifs with unconventional geometric arrangements and bonding patterns that facilitate the synthesis of new 2D materials with diverse applications.Among these,yet the design of 2D transition metal systems featuring planar pentacoordinate boron(ppB)is particularly intriguing.Here we address this gap by proposing a novel family of transition metal boride monolayers(MBenes)composed of ppB and heptacoordinate M motifs.The novelty of our MBenes stems from their distinct atomic arrangements and bonding configurations,setting them apart from traditional 2D materials.High-throughput calculations identified 10 stable MBenes(with the stoichiometry of MB,M=Cr,Fe,Co,Ni,Cu,Mo,Pd,Ag,Pt,Au)with exceptional thermodynamic,dynamic,thermal,and mechanical stabilities attributed to strong BB covalent bonds and MB ionic interactions.Notably,five of these MBenes(M=Ni,Pd,Pt,Ag,Au)hold high promise as topological superconducting materials with superconducting transition temperatures of 2.4-5.2 K.This discovery not only enriches the family of topological superconducting materials but also opens new avenues for quantum device development.Meanwhile,FeB monolayer exhibits robust ferromagnetic properties with a high Curie temperature of~750 K,which is particularly significant for spintronics applications.In addition,NiB and CuB MBenes demonstrate extremely low sodium diffusion barriers(about 30 and 90 meV)and high sodium storage capacities(788 and 734 mAh g1,respectively),making them promising anode materials for sodium-ion batteries(SIBs).This study expands the selection of electrode materials for SIBs and mitigates some existing limitations in battery technology.Overall,these findings underscore the multifunctional potential of MBenes,positioning them as transformative materials for quantum computing,spintronics,and energy storage applications.展开更多
As primary load-bearing components extensively utilized in engineering applications,beam structures necessitate the design of their microstructural configurations to achieve lightweight objectives while satisfying div...As primary load-bearing components extensively utilized in engineering applications,beam structures necessitate the design of their microstructural configurations to achieve lightweight objectives while satisfying diverse mechanical performance requirements.Combining topology optimization with fully coupled homogenization beam theory,we provide a highly efficient design tool to access desirable periodic microstructures for beams.The present optimization framework comprehensively takes into account for key deformation modes,including tension,bending,torsion,and shear deformation,all within a unified formulation.Several numerical results prove that our method can be used to handle kinds of microstructure design for beam-like structures,e.g.,extreme tension(compression)-torsion stiffness,maximization of minimum critical buckling load,and minimization of structural compliance.When optimizing microstructures for macroscopic performance,we emphasize investigating the influence of shear stiffness on the optimized results.The novel chiral beam-like structures are fabricated and tested.The experimental results indicate that the optimized tension(compression)-torsion structure has excellent buffer characteristics,as compared with the traditional square tube.This proposed optimization framework can be further extended to other physical problems of Timoshenko beams.展开更多
A data-driven model ofmultiple variable cutting(M-VCUT)level set-based substructure is proposed for the topology optimization of lattice structures.TheM-VCUTlevel setmethod is used to represent substructures,enriching...A data-driven model ofmultiple variable cutting(M-VCUT)level set-based substructure is proposed for the topology optimization of lattice structures.TheM-VCUTlevel setmethod is used to represent substructures,enriching their diversity of configuration while ensuring connectivity.To construct the data-driven model of substructure,a database is prepared by sampling the space of substructures spanned by several substructure prototypes.Then,for each substructure in this database,the stiffness matrix is condensed so that its degrees of freedomare reduced.Thereafter,the data-drivenmodel of substructures is constructed through interpolationwith compactly supported radial basis function(CS-RBF).The inputs of the data-driven model are the design variables of topology optimization,and the outputs are the condensed stiffness matrix and volume of substructures.During the optimization,this data-driven model is used,thus avoiding repeated static condensation that would requiremuch computation time.Several numerical examples are provided to verify the proposed method.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12325401,12274069,123B2053)。
文摘Topology,as a mathematical concept,has been introduced into condensed matter physics since the discovery of quantum Hall effect,which characterizes new physical scenario beyond the Landau theory.The topologically protected physical quantities,such as the dissipationless quantum transport of edge/surface states as well as magnetic/dipole quasi-particles like skyrmions/bimerons,have attracted great research enthusiasms in the past decades.In recent years,another kind of topology in condensed matter was revealed in the magnetoelectric parameter space of multiferroics,which deepens our understanding of magnetoelectric physics.This topical review summarizes recent advances in this area,involving three types of type-Ⅱmultiferroics.With magnetism-induced ferroelectricity,topological behaviors can be manifested during the magnetoelectric switching processes driven by magnetic/electric fields,such as Roman-surface/Riemann-surface magnetoelectricity and magnetic crankshaft.These exotic topological magnetoelectric behaviors may be helpful to pursue energy-efficient and precise-control devices for spintronics and quantum computing.
基金supported by the National Natural Science Foundation of China(No.12202295)the International(Regional)Cooperation and Exchange Projects of the National Natural Science Foundation of China(No.W2421002)+2 种基金the Sichuan Science and Technology Program(No.2025ZNSFSC0845)Zhejiang Provincial Natural Science Foundation of China(No.ZCLZ24A0201)the Fundamental Research Funds for the Provincial Universities of Zhejiang(No.GK249909299001-004)。
文摘Deployable Composite Thin-Walled Structures(DCTWS)are widely used in space applications due to their ability to compactly fold and self-deploy in orbit,enabled by cutouts.Cutout design is crucial for balancing structural rigidity and flexibility,ensuring material integrity during large deformations,and providing adequate load-bearing capacity and stability once deployed.Most research has focused on optimizing cutout size and shape,while topology optimization offers a broader design space.However,the anisotropic properties of woven composite laminates,complex failure criteria,and multi-performance optimization needs have limited the exploration of topology optimization in this field.This work derives the sensitivities of bending stiffness,critical buckling load,and the failure index of woven composite materials with respect to element density,and formulates both single-objective and multi-objective topology optimization models using a linear weighted aggregation approach.The developed method was integrated with the commercial finite element software ABAQUS via a Python script,allowing efficient application to cutout design in various DCTWS configurations to maximize bending stiffness and critical buckling load under material failure constraints.Optimization of a classical tubular hinge resulted in improvements of 107.7%in bending stiffness and 420.5%in critical buckling load compared to level-set topology optimization results reported in the literature,validating the effectiveness of the approach.To facilitate future research and encourage the broader adoption of topology optimization techniques in DCTWS design,the source code for this work is made publicly available via a Git Hub link:https://github.com/jinhao-ok1/Topo-for-DCTWS.git.
基金supported by“the Fundamental Research Funds for the Central Universities”(Grant No.CUCAI2511).
文摘Social bots are automated programs designed to spread rumors and misinformation,posing significant threats to online security.Existing research shows that the structure of a social network significantly affects the behavioral patterns of social bots:a higher number of connected components weakens their collaborative capabilities,thereby reducing their proportion within the overall network.However,current social bot detection methods still make limited use of topological features.Furthermore,both graph neural network(GNN)-based methods that rely on local features and those that leverage global features suffer from their own limitations,and existing studies lack an effective fusion of multi-scale information.To address these issues,this paper proposes a topology-aware multi-scale social bot detection method,which jointly learns local and global representations through a co-training mechanism.At the local level,topological features are effectively embedded into node representations,enhancing expressiveness while alleviating the over-smoothing problem in GNNs.At the global level,a clustering attention mechanism is introduced to learn global node representations,mitigating the over-globalization problem.Experimental results demonstrate that our method effectively overcomes the limitations of single-scale approaches.Our code is publicly available at https://anonymous.4open.science/r/TopoMSG-2C41/(accessed on 27 October 2025).
基金Project supported by the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(No.RS-2025-02303676)。
文摘The stress minimization multi-material topology optimization(MMTO)approach has recently attracted significant attention because of its applications in aerospace and mechanical engineering.Nonetheless,the stress minimization MMTO approach may result in stress surpassing the material's tolerance limit,potentially culminating in failure.This research proposes a novel way for imposing stress constraints on each material to regulate their respective stress levels.The fundamental concept is that each material possesses its own interpolation function for the stress model.The maximum von Mises stress for each material can be established with the definition of an upper limit,ensuring that the materials will perform safely and effectively.This aids topological structures in resisting failure and augmenting strength.A multi-physics system including thermoelastic and self-weight loads is concurrently examined alongside stress limitations.The global stress constraint utilizes the p-norm function,and the adjoint method is used to derive sensitivity.This work employs a three-field strategy utilizing density filtering and Heaviside projection functions to mitigate the artificial stress in low density.The technique is assessed through two-dimensional(2D)and three-dimensional(3D)examples,illustrating the influence of stress limits on the compliance minimization under heat and self-weight loads.The optimized results indicate a substantial decrease in the stress levels accompanied by a minor gain in compliance,while maintaining the stress within the specified range for all materials.
基金Supported by National Natural Science Foundation of China(Grant Nos.52202431,52172353).
文摘Based on the demands for crashworthiness and lightweight in the passive safety of transportation vehicles,metal-fiber reinforced polymer(FRP)hybrid thin-walled tubes(MFHTWTs)integrate the toughness,strength and lightweight of two distinct material characteristics.MFHTWTs can achieve energy absorption through the coupling of material plastic deformation and fracture,demonstrating significant engineering value in passive safety.This review provides a comprehensive examination of the crashworthiness topology optimization of MFHTWTs,aiming to demonstrate that a deeply integrated approach combining topology and parameter opti-mization can realize an optimal design method for MFHTWTs,thereby maximizing the functional utilization of limited material.Firstly,the review highlights the crashworthiness topology optimization methods(CTOMs)based on thin-walled structures.With a particular focus on metal,the review discusses both the practical ap-plicability and limitations of CTOMs under crash conditions.Additionally,based on the methodology of the equivalent static load method(ESLM),the review emphasizes that topology optimization methods considering continuous fiber paths and multi-material interface connections are also applicable to the crashworthiness op-timization of MFHTWTs.Furthermore,to couple structural parameters and configuration characteristics,in-tegrated topology optimization methods,including parameter optimization,are proposed to provide a valuable reference for the global optimization of MFHTWTs.Thus,these methods can establish the mapping relationship between key parameters and the structural energy absorption capacity.
基金supported by the Science and Technology Research Project of Henan Province(242102241055)the Industry-University-Research Collaborative Innovation Base on Automobile Lightweight of“Science and Technology Innovation in Central Plains”(2024KCZY315)the Opening Fund of State Key Laboratory of Structural Analysis,Optimization and CAE Software for Industrial Equipment(GZ2024A03-ZZU).
文摘The moving morphable component(MMC)topology optimization method,as a typical explicit topology optimization method,has been widely concerned.In the MMC topology optimization framework,the surrogate material model is mainly used for finite element analysis at present,and the effectiveness of the surrogate material model has been fully confirmed.However,there are some accuracy problems when dealing with boundary elements using the surrogate material model,which will affect the topology optimization results.In this study,a boundary element reconstruction(BER)model is proposed based on the surrogate material model under the MMC topology optimization framework to improve the accuracy of topology optimization.The proposed BER model can reconstruct the boundary elements by refining the local meshes and obtaining new nodes in boundary elements.Then the density of boundary elements is recalculated using the new node information,which is more accurate than the original model.Based on the new density of boundary elements,the material properties and volume information of the boundary elements are updated.Compared with other finite element analysis methods,the BER model is simple and feasible and can improve computational accuracy.Finally,the effectiveness and superiority of the proposed method are verified by comparing it with the optimization results of the original surrogate material model through several numerical examples.
基金funded by the Malaysian Ministry of Higher Education through the Fundamental Research Grant Scheme(FRGS/1/2024/ICT02/UCSI/02/1).
文摘Accurate estimation of photovoltaic(PV)parameters is essential for optimizing solar module perfor-mance and enhancing resource efficiency in renewable energy systems.This study presents a process innovation by introducing,for the first time,the Triangulation Topology Aggregation Optimizer(TTAO)integrated with parallel computing to address PV parameter estimation challenges.The effectiveness and robustness of TTAO are rigorously evaluated using two standard benchmark datasets(KC200GT and R.T.C.France solar cells)and a real-world dataset(Poly70W solar module)under single-,double-,and triple-diode configurations.Results show that TTAO consistently achieves superior accuracy by producing the lowest RMSE values and faster convergence compared to state-of-the-art metaheuristic algorithms.In addition,the integration of parallel computing significantly enhances computational efficiency,reducing execution time by up to 85%without compromising accuracy.Validation using real-world data further demonstrates TTAO’s adaptability and practical relevance in renewable energy systems,effectively bridging the gap between theoretical modeling and real-world implementation for PV system monitoring and optimization,contributing to climate mitigation through improved solar energy performance.
文摘The event-triggered mechanism serves as an effective discontinuous control strategy for addressing the consensus tracking problem in multiagent systems(MASs).This approach optimizes energy consumption by updating the controller only when some observed errors exceed a predefined threshold.Considering the influence of noise on agent dynamics in complex control environments,this study investigates an event-triggered control scheme for stochastic MASs,where noise is modeled as Brownian motion.Furthermore,the communication topology of the stochastic MASs is assumed to exhibit a Markovian switching mechanism.Analytical criteria are derived to guarantee consensus tracking in the mean square sense,and a numerical example is provided to validate the effectiveness of the proposed control methods.
基金supported by the National Natural Science Foundation of China(Grant Nos.42172159 and 42302143)the Postdoctora Fellowship Program of the China Postdoctoral Science Foundation(CPSF)(Grant No.GZB20230864).
文摘Forced imbibition,the invasion of a wetting fluid into porous rocks,plays an important role in the effective exploitation of hydrocarbon resources and the geological sequestration of carbon dioxide.However,the interface dynamics influenced by complex topology commonly leads to non-wetting fluid trapping.Particularly,the underlying mechanisms under viscously unfavorable conditions remain unclear.This study employs a direct numerical simulation method to simulate forced imbibition through the reconstructed digital rocks of sandstone.The interface dynamics and fluid–fluid interactions are investigated through transient simulations,while the pore topology metrics are introduced to analyze the impact on steady-state residual fluid distribution obtained by a pseudo-transient scheme.The results show that the cooperative pore-filling process promoted by corner flow is dominant at low capillary numbers.This leads to unstable inlet pressure,mass flow,and interface curvature,which correspond to complicated interface dynamics and higher residual fluid saturation.During forced imbibition,the interface curvature gradually increases,with the pore-filling mechanisms involving the cooperation of main terminal meniscus movement and arc menisci filling.Complex topology with small diameter pores may result in the destabilization of interface curvature.The residual fluid saturation is negatively correlated with porosity and pore throat size,and positively correlated with tortuosity and aspect ratio.A large mean coordination number characterizing global connectivity promotes imbibition.However,high connectivity characterized by the standardized Euler number corresponding to small pores is associated with a high probability of non-wetting fluid trapping.
基金Supported by National Natural Science Foundation of China(Grant Nos.52222508 and 52335011)。
文摘Heat dissipation performance is critical to the design of high-end equipment,such as integrated chips and high-precision machine tools.Owing to the advantages of artificial intelligence in solving complex tasks involving a large number of variables,researchers have exploited deep learning to expedite the optimization of material properties,such as the heat dissipation of solid isotropic materials with penalization(SIMP).However,because the approach is limited by discrete datasets and labeled training forms,ensuring the continuous adaptation of the condition domain and maintaining the stability of the design structure remain major challenges in the current intelligent design methodology for thermally conductive structures.In this study,we propose an innovative intelligent design fram-ework integrating Conditional Deep Convolutional Generative Adversarial Networks(CDCGAN)with SIMP,capable of creating topology structures that meet prescribed thermal conduction performance.This proposed design strategy significantly reduces the computational time required to solve symmetric and random heat sink problems compared with existing design approaches and is approximately 98%faster than standard SIMP methods and 55.5%faster than conventional deep-learning-based methods.In addition,we benchmarked the design performance of the proposed framework against theoretical structural designs via experimental measurements.We observed a 50.1%reduction in the average temperature and a 28.2%reduction in the highest temperature in our designed topology compared with those theoretical structure designs.
基金supported by the National Natural Science Foundation of China(Grant No.11872080)Beijing Natural Science Foundation(Grant No.3192005).
文摘This paper presents a deep learning-based topology optimization method for the joint design of material layout and fiber orientation in continuous fiber-reinforced composite structure(CFRCS).The proposed method mainly includes three steps:(1)a ResUNet-involved generative and adversarial network(ResUNet-GAN)is developed to establish the end-to-end mapping from structural design parameters to fiber-reinforced composite optimized structure,and a fiber orientation chromatogram is presented to represent continuous fiber angles;(2)to avoid the local optimum problem,the independent continuous mapping method(ICM method)considering the improved principal stress orientation interpolated continuous fiber angle optimization(PSO-CFAO)strategy is utilized to construct CFRCS topology optimization dataset;(3)the well-trained ResUNet-GAN is deployed to design the optimal structural material distribution together with the corresponding continuous fiber orientations.Numerical simulations for benchmark structure verify that the proposed method greatly improves the design efficiency of CFRCS along with high design accuracy.Furthermore,the CFRCS topology configuration designed by ResUNet-GAN is fabricated by additive manufacturing.Compression experiments of the specimens show that both the stiffness structure and peak load of the CFRCS topology configuration designed by the proposed method have significantly enhanced.The proposed deep learning-based topology optimization method will provide great flexibility in CFRCS for engineering applications.
文摘Metalens technology has been applied extensively in miniaturized and integrated infrared imaging systems.However,due to the high phase dispersion of unit structures,metalens often exhibits chromatic aberration,making broadband achromatic infrared imaging challenging to achieve.In this paper,six different unit structures based on chalcogenide glass are constructed,and their phase-dispersion parameters are analyzed to establish a database.On this basis,using chromatic aberration compensation and parameterized adjoint topology optimization,a broadband achromatic metalens with a numerical aperture of 0.5 is designed by arranging these six unit structures in the far-infrared band.Simulation results show that the metalens achieves near diffraction-limited focusing within the operating wavelength range of 9−11μm,demonstrating the good performance of achromatic aberration with flat focusing efficiency of 54%−58%across all wavelengths.
基金the supports from Westlake Education Foundationthe support provided by the National Natural Science Foundation of China(Grant No.12304049)。
文摘We demonstrate that the sliding motion between two layers of the newly discovered ferroelectric and topologically trivial bismuth(Bi)monolayer[Nature 61767(2023)]can induce a sequence of topological phase transitions,alternating between Z_(2)trivial and nontrivial states.The lateral shift,while preserving spatial symmetry,can switch the quantum spin Hall state on and of.The sliding-induced changes in out-of-plane atomic buckling,which are directly coupled to in-plane ferroelectricity,are shown to signifcantly modulate the band gap and drive the topological phase transitions.We map out the topological phase diagram and in-plane ferroelectricity with respect to sliding displacements.With appropriate sliding,the bismuth bilayer can transition into a nontrivial polar metal,exhibiting a pronounced shift current response arising from interband geometric quantities of electronic bands.Moreover,bilayer Bi supports a sliding-tunable nonlinear anomalous Hall response resulting from the geometric Berry curvature dipole.Confgurations that are Z_(2)nontrivial can generate drastically different transverse currents orthogonal to the external electric feld,as both the direction and magnitude of the Berry curvature dipole at the Fermi level are highly sensitive to the sliding displacement.Our results suggest that bilayer bismuth,with its ability to generate multiple types of geometric currents,ofers a versatile platform for power-efcient“Berry slidetronics”for multistate memory applications integrating both band topology and ferroelectricity.
基金National Natural Science Foundation of China(91748125)National Administration of Traditional Chinese Medicine’s National Inheritance Studio Construction Project for Famous Veteran Traditional Chinese Medicine Experts([2022]75)。
文摘Objective To configure the complex traditional Chinese medicine(TCM)prescription using digit topology circle and to derive digit topology circle.Methods The basic digit topology circles were constructed.Different digit topology circles were derived using basic digit topology circle,the character strings,and the digit groups.Different digit topology circles with ternary Chinese medicine were derived by adding ternary Chinese medicine into digit topology circles.The valuable TCM prescriptions were configured using the derived digit topology circles.Results Nine simple basic digit topology circles were constructed from the character strings.Multiple digit topology circles and some digit topology circles with ternary Chinese medicine were derived using basic digit topology circles,the character strings,and the digit groups.Four complex TCM prescriptions were configured using four derived digit topology circles digit topology circles,respectively.Conclusion The digit topology circles can be used to configure some existing TCM prescriptions and many novel TCM prescriptions.It has been verified that some existing TCM prescriptions have been used successfully to treat patients with diseases.Some novel valuable TCM prescriptions configured by digit topology circles may be used to treat patients with diseases.
基金Supported by National Natural Science Foundation of China(Grant Nos.52225212,52272418,U22A20100)National Key Research and Development Program of China(Grant No.2022YFB2503302).
文摘The development of chassis active safety control technology has improved vehicle stability under extreme conditions.However,its cross-system and multi-functional characteristics make the controller difficult to achieve cooperative goals.In addition,the chassis system,which has high complexity,numerous subsystems,and strong coupling,will also lead to low computing efficiency and poor control effect of the controller.Therefore,this paper proposes a scenario-driven hybrid distributed model predictive control algorithm with variable control topology.This algorithm divides multiple stability regions based on the vehicle’s β−γ phase plane,forming a mapping relationship between the control structure and the vehicle’s state.A control input fusion mechanism within the transition domain is designed to mitigate the problems of system state oscillation and control input jitter caused by switching control structures.Then,a distributed state-space equation with state coupling and input coupling characteristics is constructed,and a weighted local agent cost function in quadratic programming is derived.Through cost coupling,local agents can coordinate global performance goals.Finally,through Simulink/CarSim joint simulation and hardware-in-the-loop(HIL)test,the proposed algorithm is validated to improve vehicle stability while ensuring trajectory tracking accuracy and has good applicability for multi-objective coordinated control.This paper combines the advantages of distributed MPC and decentralized MPC,achieving a balance between approximating the global optimal results and the solution’s efficiency.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 12474052, U2032214, and 11904002)the HFIPS Director’s Fund (Grant No. YZJJQY202304)+3 种基金the Youth Innovation Promotion Association of CAS (Grant No. 2021117)Anhui Provincial Major S&T Project (Grant No. s202305a12020005)supported by the Basic Research Program of the Chinese Academy of Sciences Based on Major Scientific Infrastructures (Grant No. JZHKYPT-2021-08)the High Magnetic Field Laboratory of Anhui Province under Contract No. AHHM-FX-2020-02。
文摘The unfilled skutterudite family has recently gained attention as a potential platform for hosting Dirac states. In this study, we systematically investigate the transport properties of IrSb_(3) single crystals. Magnetoresistance measurements exhibit prominent Shubnikov–de Haas oscillations and negative magnetoresistance at low temperatures. Quantum oscillation analysis extracts a nontrivial Berry phase and confirms a three-dimensional Fermi surface. Additionally, density functional theory calculations indicate the presence of nontrivial topological bands and surface states, suggesting that IrSb_(3) is a topological semimetal. These findings contribute to the growing family of topological materials and provide a platform for further exploration of quantum transport phenomena.
基金supported by Villum Fonden through the Villum Investigator Project“AMSTRAD”(Grant No.VIL54487).
文摘This study presents an extension of multiscale topology optimization by integrating both yield stress and local/global buckling considerations into the design process.Building upon established multiscale methodologies,we develop a new framework incorporating yield stress limits either as constraints or objectives alongside previously established local and global buckling constraints.This approach significantly refines the optimization process,ensuring that the resulting designs meet mechanical performance criteria and adhere to critical material yield constraints.First,we establish local density-dependent von Mises yield surfaces based on local yield estimates from homogenization-based analysis to predict the local yield limits of the homogenized materials.Then,these local yield-based load factors are combined with local and global buckling criteria to obtain topology optimized designs that consider yield and buckling failure on all levels.This integration is crucial for the practical application of optimized structures in real-world scenarios,where material yield and stability behavior critically influence structural integrity and durability.Numerical examples demonstrate how optimized designs depend on the stiffness to yield ratio of the considered building material.Despite the foundational assumption of the separation of scales,the de-homogenized structures,even at relatively coarse length scales,exhibit a remarkably high degree of agreement with the corresponding homogenized predictions.
基金supported by Research Foundation for Advanced Talents of Inner Mongolia Normal University(2025YJRC005)the National Natural Science Foundation of China(12364038)+5 种基金the“Grassland Talents”project of the Inner Mongolia Autonomous Region(12000-12102613)the Young Science and Technology Talents Cultivation Project of Inner Mongolia University(21200-5223708)the Industrial Technology Innovation Projects of Inner Mongolia Academy of Science and Technology of China(2023JSYD01002)Science and Technology Plan Projects of Inner Mongolia Autonomous Region of China(2023KYPT0012)Key Project Funding from the Inner Mongolia Autonomous Region Natural Science Foundation(2023ZD27)High Level Introduction of Talent Research Start-up Fund(5909002405).
文摘Pursuing new two-dimensional(2D)materials has been a hot topic in materials science,driven by their potential for diverse applications.Recent research has unveiled stable planar hypercoordinate motifs with unconventional geometric arrangements and bonding patterns that facilitate the synthesis of new 2D materials with diverse applications.Among these,yet the design of 2D transition metal systems featuring planar pentacoordinate boron(ppB)is particularly intriguing.Here we address this gap by proposing a novel family of transition metal boride monolayers(MBenes)composed of ppB and heptacoordinate M motifs.The novelty of our MBenes stems from their distinct atomic arrangements and bonding configurations,setting them apart from traditional 2D materials.High-throughput calculations identified 10 stable MBenes(with the stoichiometry of MB,M=Cr,Fe,Co,Ni,Cu,Mo,Pd,Ag,Pt,Au)with exceptional thermodynamic,dynamic,thermal,and mechanical stabilities attributed to strong BB covalent bonds and MB ionic interactions.Notably,five of these MBenes(M=Ni,Pd,Pt,Ag,Au)hold high promise as topological superconducting materials with superconducting transition temperatures of 2.4-5.2 K.This discovery not only enriches the family of topological superconducting materials but also opens new avenues for quantum device development.Meanwhile,FeB monolayer exhibits robust ferromagnetic properties with a high Curie temperature of~750 K,which is particularly significant for spintronics applications.In addition,NiB and CuB MBenes demonstrate extremely low sodium diffusion barriers(about 30 and 90 meV)and high sodium storage capacities(788 and 734 mAh g1,respectively),making them promising anode materials for sodium-ion batteries(SIBs).This study expands the selection of electrode materials for SIBs and mitigates some existing limitations in battery technology.Overall,these findings underscore the multifunctional potential of MBenes,positioning them as transformative materials for quantum computing,spintronics,and energy storage applications.
基金supported by the National Natural Science Foundation of China(grant number 11902015)the Open Fund of Deceleration and Landing Laboratory of the Fifth Academy of Aerospace Science and Technology Group(grant number EDL19092138)the Ministry of Education Chunhui Plan(HZKY20220014).
文摘As primary load-bearing components extensively utilized in engineering applications,beam structures necessitate the design of their microstructural configurations to achieve lightweight objectives while satisfying diverse mechanical performance requirements.Combining topology optimization with fully coupled homogenization beam theory,we provide a highly efficient design tool to access desirable periodic microstructures for beams.The present optimization framework comprehensively takes into account for key deformation modes,including tension,bending,torsion,and shear deformation,all within a unified formulation.Several numerical results prove that our method can be used to handle kinds of microstructure design for beam-like structures,e.g.,extreme tension(compression)-torsion stiffness,maximization of minimum critical buckling load,and minimization of structural compliance.When optimizing microstructures for macroscopic performance,we emphasize investigating the influence of shear stiffness on the optimized results.The novel chiral beam-like structures are fabricated and tested.The experimental results indicate that the optimized tension(compression)-torsion structure has excellent buffer characteristics,as compared with the traditional square tube.This proposed optimization framework can be further extended to other physical problems of Timoshenko beams.
基金supported by the National Natural Science Foundation of China(Grant No.12272144).
文摘A data-driven model ofmultiple variable cutting(M-VCUT)level set-based substructure is proposed for the topology optimization of lattice structures.TheM-VCUTlevel setmethod is used to represent substructures,enriching their diversity of configuration while ensuring connectivity.To construct the data-driven model of substructure,a database is prepared by sampling the space of substructures spanned by several substructure prototypes.Then,for each substructure in this database,the stiffness matrix is condensed so that its degrees of freedomare reduced.Thereafter,the data-drivenmodel of substructures is constructed through interpolationwith compactly supported radial basis function(CS-RBF).The inputs of the data-driven model are the design variables of topology optimization,and the outputs are the condensed stiffness matrix and volume of substructures.During the optimization,this data-driven model is used,thus avoiding repeated static condensation that would requiremuch computation time.Several numerical examples are provided to verify the proposed method.
