Recent progress in topology optimization(TO)has seen a growing integration of machine learning to accelerate computation.Among these,online learning stands out as a promising strategy for large-scale TO tasks,as it el...Recent progress in topology optimization(TO)has seen a growing integration of machine learning to accelerate computation.Among these,online learning stands out as a promising strategy for large-scale TO tasks,as it eliminates the need for pre-collected training datasets by updating surrogate models dynamically using intermediate optimization data.Stress-constrained lightweight design is an important class of problem with broad engineering relevance.Most existing frameworks use pixel or voxel-based representations and employ the finite element method(FEM)for analysis.The limited continuity across finite elements often compromises the accuracy of stress evaluation.To overcome this limitation,isogeometric analysis is employed as it enables smooth representation of structures and thus more accurate stress computation.However,the complexity of the stress-constrained design problem together with the isogeometric representation results in a large computational cost.This work proposes a multi-grid,single-mesh online learning framework for isogeometric topology optimization(ITO),leveraging the Fourier Neural Operator(FNO)as a surrogate model.Operating entirely within the isogeometric analysis setting,the framework provides smooth geometry representation and precise stress computation,without requiring traditional mesh generation.A localized training approach is employed to enhance scalability,while a multi-grid decomposition scheme incorporates global structural context into local predictions to boost FNO accuracy.By learning the mapping from spatial features to sensitivity fields,the framework enables efficient single-resolution optimization,avoiding the computational burden of two-resolution simulations.The proposed method is validated through 2D stress-constrained design examples,and the effect of key parameters is studied.展开更多
Although full waveform inversion in the frequency domain can overcome the local minima problem in the time direction, such problem still exists in the space direction because of the media subsurface complexity. Based ...Although full waveform inversion in the frequency domain can overcome the local minima problem in the time direction, such problem still exists in the space direction because of the media subsurface complexity. Based on the optimal steep descent methods, we present an algorithm which combines the preconditioned bi-conjugated gradient stable method and the multi-grid method to compute the wave propagation and the gradient space. The multiple scale prosperity of the waveform inversion and the multi-grid method can overcome the inverse problems local minima defect and accelerate convergence. The local inhomogeneous three-hole model simulated results and the Marmousi model certify the algorithm effectiveness.展开更多
We investigate the dynamics of pedestrian counter flow by using a multi-grid topological pedestrian counter flow model. In the model, each pedestrian occupies multi- rather than only one grid, and interacts with other...We investigate the dynamics of pedestrian counter flow by using a multi-grid topological pedestrian counter flow model. In the model, each pedestrian occupies multi- rather than only one grid, and interacts with others in the form of topological interaction, which means that a moving pedestrian interacts with a fixed number of those nearest neighbours coming from the opposite direction to determine his/her own moving direction. Thus the discretization of space and time are much finer, the decision making process of the pedestrian is more reliable, which all together makes the moving behaviour and boundary conditions much more realistic. When compared with field observations, it can be found that the modified model is able to reproduce well fitted pedestrian collective behaviour such as dynamical variation of lane formation, clustering of pedestrians in the same direction, etc. The fundamental diagram produced by the model fits also well with field data in thc frce flow region. Further analyses indicate that with the increase of the size of pedestrian counter flow system, it becomes harder for the system to transit into a jamming state, while the increase of interaction range does not change the transition point from free flow to jamming flow in the multi-grid topological counter flow model. It is also found that the asymmetry of the injection rate of pedestrians on the boundaries has direct influence on the process of transition from free flow to jamming flow, i.e., a symmetric injection makes it easier for the system to transit into jamming flow.展开更多
In order to enhance the authenticity and accuracy of passenger evacuation simulation in ships, a new multi-grid model was proposed on the basis of a traditional cellular automata model. In the new model finer lattices...In order to enhance the authenticity and accuracy of passenger evacuation simulation in ships, a new multi-grid model was proposed on the basis of a traditional cellular automata model. In the new model finer lattices were used, interaction of force among pedestrians or between pedestrians and constructions was considered, and static floor fields in a multi-level exit environment were simplified into cabin and exit static floor fields. Compared with the traditional cellular automata model, the multi-grid model enhanced the continuity of the passengers'track and the precision of the boundary qualifications. The functions of the dislocation distribution of passengers as well as partial overlap of tracks due to congestion were realized. Furthermore, taking the typical cabin environment as an example, the two models were used to analyze passenger evacuation under the same conditions. It was found that the laws of passenger evacuation simulated by the two models are similar, while the simulation's authenticity and accuracy are enhanced by the multi-grid model.展开更多
In this paper we describe a multi-grid algorithm for mixed problems with penalty by the linear finite element approximation. It is proved that the convergence rate of the algorithm is bound ed away from 1 independentl...In this paper we describe a multi-grid algorithm for mixed problems with penalty by the linear finite element approximation. It is proved that the convergence rate of the algorithm is bound ed away from 1 independently of the meshsize. For convenience, we only discuss Jacobi relaxation as smoothing operator in detail.展开更多
In this paper the algebraic multi-grid principle is applied to the multilevel moment method, which makes the new multilevel method easier to implement and more adaptive to structure. Moreover, the error spectrum is an...In this paper the algebraic multi-grid principle is applied to the multilevel moment method, which makes the new multilevel method easier to implement and more adaptive to structure. Moreover, the error spectrum is analyzed, and the reason why conjugate gradient iteration is not a good relaxation scheme for multi-grid algorithm is explored. The numerical results show that our algebraic block Gauss Seidel multi-grid algorithm is very effective.展开更多
In order to improve the interference rejection performance in the measurement of average ion velocity by multi-grid probe, an integral expression is proposed. The integral expression, differing from other expressions ...In order to improve the interference rejection performance in the measurement of average ion velocity by multi-grid probe, an integral expression is proposed. The integral expression, differing from other expressions for probe measurement, avoids the differential operation on the I-V characteristics of multi-grid probe measurement; and by this method, the ion average velocity can be figured out directly by the I-V characteristics of multi-grid probe measurement.展开更多
The multi-grid method has been known as an efficient iterative method for the linear systems and nonlinear systems that arise from finite difference approximations for partial differential equations. In this paper, th...The multi-grid method has been known as an efficient iterative method for the linear systems and nonlinear systems that arise from finite difference approximations for partial differential equations. In this paper, the multigrid method is extended to the application of solving integral equations which appear in electromagnetic scattering problems. The diakoptic theory is used for this purpose. Compared with other methods, the numerical results show that the multigrid method is powerful to solve electromagnetic scattering problems and can be used to compute electromagnetic scattering problems with electrically large bodies and complex structures.展开更多
The aim of the paper is to solve the problem of over-segmentation problem generated by Watershed segmentation algorithm or unstable clarity judgment by small areas in image fusion. A multi-focus image fusion algorithm...The aim of the paper is to solve the problem of over-segmentation problem generated by Watershed segmentation algorithm or unstable clarity judgment by small areas in image fusion. A multi-focus image fusion algorithm is proposed based on CNN segmentation and algebraic multi-grid method (CNN-AMG). Firstly, the CNN segmentation result was utilized to instruct the merging process of the regions generated by the Watershed segmentation method. Then the clear regions were selected into the temporary fusion image and the final fusion process was performed according to the clarity evaluation index, which was computed with the algebraic multi-grid method (AMG). The experimental results show that the fused image quality obtained by the CNNAMG algorithm outperforms the traditional fusion methods such as DSIFT fusion method, CNN fusion method, ASR fusion method, GFF fusion method and so on with some evaluation indexes.展开更多
In this paper, an optimum tactic of multi-grid parallel algorithmwith virtual boundary forecast method is disscussed, and a two-stage implementationis presented. The numerical results of solving a non-linear heat tran...In this paper, an optimum tactic of multi-grid parallel algorithmwith virtual boundary forecast method is disscussed, and a two-stage implementationis presented. The numerical results of solving a non-linear heat transfer equationshow that the optimum implementation is much better than the non-optimum one.展开更多
基金supported by the Hong Kong Research Grants under Competitive Earmarked Research Grant No.16206320.
文摘Recent progress in topology optimization(TO)has seen a growing integration of machine learning to accelerate computation.Among these,online learning stands out as a promising strategy for large-scale TO tasks,as it eliminates the need for pre-collected training datasets by updating surrogate models dynamically using intermediate optimization data.Stress-constrained lightweight design is an important class of problem with broad engineering relevance.Most existing frameworks use pixel or voxel-based representations and employ the finite element method(FEM)for analysis.The limited continuity across finite elements often compromises the accuracy of stress evaluation.To overcome this limitation,isogeometric analysis is employed as it enables smooth representation of structures and thus more accurate stress computation.However,the complexity of the stress-constrained design problem together with the isogeometric representation results in a large computational cost.This work proposes a multi-grid,single-mesh online learning framework for isogeometric topology optimization(ITO),leveraging the Fourier Neural Operator(FNO)as a surrogate model.Operating entirely within the isogeometric analysis setting,the framework provides smooth geometry representation and precise stress computation,without requiring traditional mesh generation.A localized training approach is employed to enhance scalability,while a multi-grid decomposition scheme incorporates global structural context into local predictions to boost FNO accuracy.By learning the mapping from spatial features to sensitivity fields,the framework enables efficient single-resolution optimization,avoiding the computational burden of two-resolution simulations.The proposed method is validated through 2D stress-constrained design examples,and the effect of key parameters is studied.
基金supported by the China State Key Science and Technology Project on Marine Carbonate Reservoir Characterization (No. 2011ZX05004-003)the Basic Research Programs of CNPC during the 12th Five-Year Plan Period (NO.2011A-3603)+1 种基金the Natural Science Foundation of China (No.41104066)the RIPED Young Professional Innovation Fund (NO.2010-13-16-02, 2010-A-26-02)
文摘Although full waveform inversion in the frequency domain can overcome the local minima problem in the time direction, such problem still exists in the space direction because of the media subsurface complexity. Based on the optimal steep descent methods, we present an algorithm which combines the preconditioned bi-conjugated gradient stable method and the multi-grid method to compute the wave propagation and the gradient space. The multiple scale prosperity of the waveform inversion and the multi-grid method can overcome the inverse problems local minima defect and accelerate convergence. The local inhomogeneous three-hole model simulated results and the Marmousi model certify the algorithm effectiveness.
基金Project supported by the National Natural Science Foundation of China (Grant No. 50678164)the Program for New Century Excellent Talents in University (Grant No. NCET-08-0518)the National Science and Technology Pillar Program,China(Grant No. 2006BAK06B00)
文摘We investigate the dynamics of pedestrian counter flow by using a multi-grid topological pedestrian counter flow model. In the model, each pedestrian occupies multi- rather than only one grid, and interacts with others in the form of topological interaction, which means that a moving pedestrian interacts with a fixed number of those nearest neighbours coming from the opposite direction to determine his/her own moving direction. Thus the discretization of space and time are much finer, the decision making process of the pedestrian is more reliable, which all together makes the moving behaviour and boundary conditions much more realistic. When compared with field observations, it can be found that the modified model is able to reproduce well fitted pedestrian collective behaviour such as dynamical variation of lane formation, clustering of pedestrians in the same direction, etc. The fundamental diagram produced by the model fits also well with field data in thc frce flow region. Further analyses indicate that with the increase of the size of pedestrian counter flow system, it becomes harder for the system to transit into a jamming state, while the increase of interaction range does not change the transition point from free flow to jamming flow in the multi-grid topological counter flow model. It is also found that the asymmetry of the injection rate of pedestrians on the boundaries has direct influence on the process of transition from free flow to jamming flow, i.e., a symmetric injection makes it easier for the system to transit into jamming flow.
基金Supported by the Ph.D Programs Foundation of Ministryof Education of China under Grant No.201023041108the Fundamental Research Funds for the Central Universities under Grant No.61004008
文摘In order to enhance the authenticity and accuracy of passenger evacuation simulation in ships, a new multi-grid model was proposed on the basis of a traditional cellular automata model. In the new model finer lattices were used, interaction of force among pedestrians or between pedestrians and constructions was considered, and static floor fields in a multi-level exit environment were simplified into cabin and exit static floor fields. Compared with the traditional cellular automata model, the multi-grid model enhanced the continuity of the passengers'track and the precision of the boundary qualifications. The functions of the dislocation distribution of passengers as well as partial overlap of tracks due to congestion were realized. Furthermore, taking the typical cabin environment as an example, the two models were used to analyze passenger evacuation under the same conditions. It was found that the laws of passenger evacuation simulated by the two models are similar, while the simulation's authenticity and accuracy are enhanced by the multi-grid model.
基金This work was supported by China State Major Key Project for Basic Researches
文摘In this paper we describe a multi-grid algorithm for mixed problems with penalty by the linear finite element approximation. It is proved that the convergence rate of the algorithm is bound ed away from 1 independently of the meshsize. For convenience, we only discuss Jacobi relaxation as smoothing operator in detail.
基金Supported by the Natlonal Natural Science Foundation of China
文摘In this paper the algebraic multi-grid principle is applied to the multilevel moment method, which makes the new multilevel method easier to implement and more adaptive to structure. Moreover, the error spectrum is analyzed, and the reason why conjugate gradient iteration is not a good relaxation scheme for multi-grid algorithm is explored. The numerical results show that our algebraic block Gauss Seidel multi-grid algorithm is very effective.
基金National Natural Science Foundation of China(No.50676026)
文摘In order to improve the interference rejection performance in the measurement of average ion velocity by multi-grid probe, an integral expression is proposed. The integral expression, differing from other expressions for probe measurement, avoids the differential operation on the I-V characteristics of multi-grid probe measurement; and by this method, the ion average velocity can be figured out directly by the I-V characteristics of multi-grid probe measurement.
文摘The multi-grid method has been known as an efficient iterative method for the linear systems and nonlinear systems that arise from finite difference approximations for partial differential equations. In this paper, the multigrid method is extended to the application of solving integral equations which appear in electromagnetic scattering problems. The diakoptic theory is used for this purpose. Compared with other methods, the numerical results show that the multigrid method is powerful to solve electromagnetic scattering problems and can be used to compute electromagnetic scattering problems with electrically large bodies and complex structures.
文摘The aim of the paper is to solve the problem of over-segmentation problem generated by Watershed segmentation algorithm or unstable clarity judgment by small areas in image fusion. A multi-focus image fusion algorithm is proposed based on CNN segmentation and algebraic multi-grid method (CNN-AMG). Firstly, the CNN segmentation result was utilized to instruct the merging process of the regions generated by the Watershed segmentation method. Then the clear regions were selected into the temporary fusion image and the final fusion process was performed according to the clarity evaluation index, which was computed with the algebraic multi-grid method (AMG). The experimental results show that the fused image quality obtained by the CNNAMG algorithm outperforms the traditional fusion methods such as DSIFT fusion method, CNN fusion method, ASR fusion method, GFF fusion method and so on with some evaluation indexes.
文摘In this paper, an optimum tactic of multi-grid parallel algorithmwith virtual boundary forecast method is disscussed, and a two-stage implementationis presented. The numerical results of solving a non-linear heat transfer equationshow that the optimum implementation is much better than the non-optimum one.
