We propose a novel type of nonlinear solver acceleration for systems of nonlinear partial differential equations(PDEs)that is based on online/adaptive learning.It is applied in the context of multiphase flow in porous...We propose a novel type of nonlinear solver acceleration for systems of nonlinear partial differential equations(PDEs)that is based on online/adaptive learning.It is applied in the context of multiphase flow in porous media.The proposed method rely on four pillars:(i)dimensionless numbers as input parameters for the machine learning model,(ii)simplified numerical model(two-dimensional)for the offline training,(iii)dynamic control of a nonlinear solver tuning parameter(numerical relaxation),(iv)and online learning for time real-improvement of the machine learning model.This strategy decreases the number of nonlinear iterations by dynamically modifying a single global parameter,the relaxation factor,and by adaptively learning the attributes of each numerical model on-the-run.Furthermore,this work performs a sensitivity study in the dimensionless parameters(machine learning features),assess the efficacy of various machine learning models,demonstrate a decrease in nonlinear iterations using our method in more intricate,realistic three-dimensional models,and fully couple a machine learning model into an open-source multiphase flow simulator achieving up to 85%reduction in computational time.展开更多
In this paper we study the computational performance of variants of an algebraic additive Schwarz preconditioner for the Schur complement for the solution of large sparse linear systems.In earlier works,the local Schu...In this paper we study the computational performance of variants of an algebraic additive Schwarz preconditioner for the Schur complement for the solution of large sparse linear systems.In earlier works,the local Schur complements were computed exactly using a sparse direct solver.The robustness of the preconditioner comes at the price of this memory and time intensive computation that is the main bottleneck of the approach for tackling huge problems.In this work we investigate the use of sparse approximation of the dense local Schur complements.These approximations are computed using a partial incomplete LU factorization.Such a numerical calculation is the core of the multi-level incomplete factorization such as the one implemented in pARMS. The numerical and computing performance of the new numerical scheme is illustrated on a set of large 3D convection-diffusion problems;preliminary experiments on linear systems arising from structural mechanics are also reported.展开更多
In this paper, a S-CR method with inexact solvers on the subdomains is presented, and then its convergence property is proved under very general conditions. This result is important because it guarantees the effective...In this paper, a S-CR method with inexact solvers on the subdomains is presented, and then its convergence property is proved under very general conditions. This result is important because it guarantees the effectiveness of the Schwarz alternating method when executed on message-passing distributed memory multiprocessor system.展开更多
Solving for detailed chemical kinetics remains one of the major bottlenecks for computational fluid dynamics simulations of reacting flows using a finite-rate-chemistry approach.This has motivated the use of neural ne...Solving for detailed chemical kinetics remains one of the major bottlenecks for computational fluid dynamics simulations of reacting flows using a finite-rate-chemistry approach.This has motivated the use of neural networks to predict stiff chemical source terms as functions of the thermochemical state of the combustion system.However,due to the nonlinearities and multi-scale nature of combustion,the predicted solution often diverges from the true solution when these machine learning models are coupled with a computational fluid dynamics solver.This is because these approaches minimize the error during training without guaranteeing successful integration with ordinary differential equation solvers.In the present work,a novel neural ordinary differential equations approach to modeling chemical kinetics,termed as ChemNODE,is developed.In this machine learning framework,the chemical source terms predicted by the neural networks are integrated during training,and by computing the required derivatives,the neural network weights are adjusted accordingly to minimize the difference between the predicted and ground-truth solution.A proof-of-concept study is performed with ChemNODE for homogeneous autoignition of hydrogen-air mixture over a range of composition and thermodynamic conditions.It is shown that ChemNODE accurately captures the chemical kinetic behavior and reproduces the results obtained using the detailed kinetic mechanism at a fraction of the computational cost.展开更多
New direct spectral solvers for the 3D Helmholtz equation in a finite cylindrical region are presented.A purely variational(no collocation)formulation of the problem is adopted,based on Fourier series expansion of the...New direct spectral solvers for the 3D Helmholtz equation in a finite cylindrical region are presented.A purely variational(no collocation)formulation of the problem is adopted,based on Fourier series expansion of the angular dependence and Legendre polynomials for the axial dependence.A new Jacobi basis is proposed for the radial direction overcoming the main disadvantages of previously developed bases for the Dirichlet problem.Nonhomogeneous Dirichlet boundary conditions are enforced by a discrete lifting and the vector problem is solved by means of a classical uncoupling technique.In the considered formulation,boundary conditions on the axis of the cylindrical domain are never mentioned,by construction.The solution algorithms for the scalar equations are based on double diagonalization along the radial and axial directions.The spectral accuracy of the proposed algorithms is verified by numerical tests.展开更多
Physics-informed neural networks(PINNs)are promising to replace conventional mesh-based partial tial differen-equation(PDE)solvers by offering more accurate and flexible PDE solutions.However,PINNs are hampered by the...Physics-informed neural networks(PINNs)are promising to replace conventional mesh-based partial tial differen-equation(PDE)solvers by offering more accurate and flexible PDE solutions.However,PINNs are hampered by the relatively slow convergence and the need to perform additional,potentially expensive training for new PDE parameters.To solve this limitation,we introduce LatentPINN,a framework that utilizes latent representations of the PDE parameters as additional(to the coordinates)inputs into PINNs and allows for training over the distribution of these parameters.Motivated by the recent progress on generative models,we promote using latent diffusion models to learn compressed latent representations of the distribution of PDE parameters as they act as input parameters for NN functional solutions.We use a two-stage training scheme in which,in the first stage,we learn the latent representations for the distribution of PDE parameters.In the second stage,we train a physics-informed neural network over inputs given by randomly drawn samples from the coordinate space within the solution domain and samples from the learned latent representation of the PDE parameters.Considering their importance in capturing evolving interfaces and fronts in various fields,we test the approach on a class of level set equations given,for example,by the nonlinear Eikonal equation.We share results corresponding to three Eikonal parameters(velocity models)sets.The proposed method performs well on new phase velocity models without the need for any additional training.展开更多
We are intrigued by the issues of shock instability,with a particular emphasis on numerical schemes that address the carbuncle phenomenon by reducing dissipation rather than increasing it.For a specific class of plana...We are intrigued by the issues of shock instability,with a particular emphasis on numerical schemes that address the carbuncle phenomenon by reducing dissipation rather than increasing it.For a specific class of planar flow fields where the transverse direction exhibits vanishing but non-zero velocity components,such as a disturbed onedimensional(1D)steady shock wave,we conduct a formal asymptotic analysis for the Euler system and associated numerical methods.This analysis aims to illustrate the discrepancies among various low-dissipative numerical algorithms.Furthermore,a numerical stability analysis of steady shock is undertaken to identify the key factors underlying shock-stable algorithms.To verify the stability mechanism,a consistent,low-dissipation,and shock-stable HLLC-type Riemann solver is presented.展开更多
To explore the relationship between dynamic characteristics and wake patterns,numerical simulations were conducted on three equal-diameter cylinders arranged in an equilateral triangle.The simulations varied reduced v...To explore the relationship between dynamic characteristics and wake patterns,numerical simulations were conducted on three equal-diameter cylinders arranged in an equilateral triangle.The simulations varied reduced velocities and gap spacing to observe flow-induced vibrations(FIVs).The immersed boundary–lattice Boltzmann flux solver(IB–LBFS)was applied as a numerical solution method,allowing for straightforward application on a simple Cartesian mesh.The accuracy and rationality of this method have been verified through comparisons with previous numerical results,including studies on flow past three stationary circular cylinders arranged in a similar pattern and vortex-induced vibrations of a single cylinder across different reduced velocities.When examining the FIVs of three cylinders,numerical simulations were carried out across a range of reduced velocities(3.0≤Ur≤13.0)and gap spacing(L=3D,4D,and 5D).The observed vibration response included several regimes:the desynchronization regime,the initial branch,and the lower branch.Notably,the transverse amplitude peaked,and a double vortex street formed in the wake when the reduced velocity reached the lower branch.This arrangement of three cylinders proved advantageous for energy capture as the upstream cylinder’s vibration response mirrored that of an isolated cylinder,while the response of each downstream cylinder was significantly enhanced.Compared to a single cylinder,the vibration and flow characteristics of this system are markedly more complex.The maximum transverse amplitudes of the downstream cylinders are nearly identical and exceed those observed in a single-cylinder set-up.Depending on the gap spacing,the flow pattern varied:it was in-phase for L=3D,antiphase for L=4D,and exhibited vortex shedding for L=5D.The wake configuration mainly featured double vortex streets for L=3D and evolved into two pairs of double vortex streets for L=5D.Consequently,it well illustrates the coupling mechanism that dynamics characteristics and wake vortex change with gap spacing and reduced velocities.展开更多
To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical c...To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical computation of such models.This efficient solver employs algorithms based on discrete cosine transformations(DCT)or discrete sine transformations(DST)and is not restricted by any spatio-temporal schemes.Our proposed methodology is appropriate for a variety of phase-field models and is especially efficient when combined with flow field systems.Meanwhile,this study has conducted an extensive numerical comparison and found that employing DCT and DST techniques not only yields results comparable to those obtained via the Multigrid(MG)method,a conventional approach used in the resolution of the Poisson equations,but also enhances computational efficiency by over 90%.展开更多
An efficient neural mode-solving operator is proposed for evaluating the propagation properties of optical fibers.By incorporating the governing Helmholtz equation into training,the working mechanism of the proposed o...An efficient neural mode-solving operator is proposed for evaluating the propagation properties of optical fibers.By incorporating the governing Helmholtz equation into training,the working mechanism of the proposed operator adheres to the physics essence of fiber analysis.The training of the mode-solving operator adopts a hybrid physics-informed and data-driven approach,providing the advantages of strong physical consistency,enhanced prediction accuracy,and reduced data dependency in comparison with purely datadriven methods.Benefiting from the improvements in network input-output mapping formulation,the proposed operator offers broader applicability to different fiber types and greater flexibility for property optimization.Combined with the particle swarm optimization and refractive index optimization,the operator demonstrates its capacity for the inverse design of multi-step-index fibers(MSIFs)and graded-index fibers(GRIFs).For MSIFs,to ensure a low mode crosstalk for short-distance transmission systems,optimized refractive index profiles(RIPs)of both three-ring and four-ring structures are obtained from large structure parameter search spaces.For GRIFs,to ensure a low receiving complexity for long-haul transmission systems,optimized RIP with low root mean square mode group delay is obtained through point-wise fine-tuning.Moreover,the operator is capable of analyzing the effect of dopant diffusion in manufacturing.展开更多
Due to the high-order B-spline basis functions utilized in isogeometric analysis(IGA)and the repeatedly updating global stiffness matrix of topology optimization,Isogeometric topology optimization(ITO)intrinsically su...Due to the high-order B-spline basis functions utilized in isogeometric analysis(IGA)and the repeatedly updating global stiffness matrix of topology optimization,Isogeometric topology optimization(ITO)intrinsically suffers from the computationally demanding process.In this work,we address the efficiency problem existing in the assembling stiffness matrix and sensitivity analysis using B˙ezier element stiffness mapping.The Element-wise and Interaction-wise parallel computing frameworks for updating the global stiffness matrix are proposed for ITO with B˙ezier element stiffness mapping,which differs from these ones with the traditional Gaussian integrals utilized.Since the explicit stiffness computation formula derived from B˙ezier element stiffness mapping possesses a typical parallel structure,the presented GPU-enabled ITO method can greatly accelerate the computation speed while maintaining its high memory efficiency unaltered.Numerical examples demonstrate threefold speedup:1)the assembling stiffness matrix is accelerated by 10×maximumly with the proposed GPU strategy;2)the solution efficiency of a sparse linear system is enhanced by up to 30×with Eigen replaced by AMGCL;3)the efficiency of sensitivity analysis is promoted by 100×with GPU applied.Therefore,the proposed method is a promising way to enhance the numerical efficiency of ITO for both single-patch and multiple-patch design problems.展开更多
Ising problems are critical for a wide range of applications.Solving these problems on a photonic platform takes advantage of the unique properties of photons,such as high speed,low power consumption,and large bandwid...Ising problems are critical for a wide range of applications.Solving these problems on a photonic platform takes advantage of the unique properties of photons,such as high speed,low power consumption,and large bandwidth.Recently,there has been growing interest in using photonic platforms to accelerate the optimization of Ising models,paving the way for the development of ultrafast hardware in machine learning.However,these proposed systems face challenges in simultaneously achieving high spin scalability,encoding flexibility,and low system complexity.We propose a wavelength-domain optical Ising machine that utilizes optical signals at different wavelengths to represent distinct Ising spins for Ising simulation.We design and experimentally validate a chip-scale Ising machine capable of solving classical non-deterministic polynomial-time problems.The proposed Ising machine supports 32 spins and features 2 distinct coupling encoding schemes.Furthermore,we demonstrate the feasibility of scaling the system to 256 spins.This approach verifies the viability of performing Ising simulations in the wavelength dimension,offering substantial advantages in scalability.These advancements lay the groundwork for future large-scale expansion and practical applications in cloud computing.展开更多
In this paper,a number of ordinary differential equation(ODE)conversion techniques for trans- formation of nonstandard ODE boundary value problems into standard forms are summarised,together with their applications to...In this paper,a number of ordinary differential equation(ODE)conversion techniques for trans- formation of nonstandard ODE boundary value problems into standard forms are summarised,together with their applications to a variety of boundary value problems in computational solid mechanics,such as eigenvalue problem,geometrical and material nonlinear problem,elastic contact problem and optimal design problems through some simple and representative examples,The advantage of such approach is that various ODE bounda- ry value problems in computational mechanics can be solved effectively in a unified manner by invoking a stand- ard ODE solver.展开更多
A lattice Boltzmann flux solver(LBFS)is presented for simulation of fluid flows.Like the conventional computational fluid dynamics(CFD)solvers,the new solver also applies the finite volume method to discretize the gov...A lattice Boltzmann flux solver(LBFS)is presented for simulation of fluid flows.Like the conventional computational fluid dynamics(CFD)solvers,the new solver also applies the finite volume method to discretize the governing differential equations,but the numerical flux at the cell interface is not evaluated by the smooth function approximation or Riemann solvers.Instead,it is evaluated from local solution of lattice Boltzmann equation(LBE)at cell interface.Two versions of LBFS are presented in this paper.One is to locally apply one-dimensional compressible lattice Boltzmann(LB)model along the normal direction to the cell interface for simulation of compressible inviscid flows with shock waves.The other is to locally apply multi-dimensional LB model at cell interface for simulation of incompressible viscous and inviscid flows.The present solver removes the drawbacks of conventional lattice Boltzmann method(LBM)such as limitation to uniform mesh,tie-up of mesh spacing and time interval,limitation to viscous flows.Numerical examples show that the present solver can be well applied to simulate fluid flows with non-uniform mesh and curved boundary.展开更多
基金MUFFINS,MUltiphase Flow-induced Fluid-flexible structure InteractioN in Subsea applications(EP/P033180/1)the PREMIERE programme grant(EP/T000414/1)SMARTRES,Smart assessment,management and optimization of urban geothermal resources(NE/X005607/1).
文摘We propose a novel type of nonlinear solver acceleration for systems of nonlinear partial differential equations(PDEs)that is based on online/adaptive learning.It is applied in the context of multiphase flow in porous media.The proposed method rely on four pillars:(i)dimensionless numbers as input parameters for the machine learning model,(ii)simplified numerical model(two-dimensional)for the offline training,(iii)dynamic control of a nonlinear solver tuning parameter(numerical relaxation),(iv)and online learning for time real-improvement of the machine learning model.This strategy decreases the number of nonlinear iterations by dynamically modifying a single global parameter,the relaxation factor,and by adaptively learning the attributes of each numerical model on-the-run.Furthermore,this work performs a sensitivity study in the dimensionless parameters(machine learning features),assess the efficacy of various machine learning models,demonstrate a decrease in nonlinear iterations using our method in more intricate,realistic three-dimensional models,and fully couple a machine learning model into an open-source multiphase flow simulator achieving up to 85%reduction in computational time.
基金developed in the framework of the associated team PhyLeas(Study of parallel hybrid sparse linear solvers) funded by INRIA where the partners are INRIA,T.U.Brunswick and University of Minnesotasupported by the US Department of Energy under grant DE-FG-08ER25841 and by the Minnesota Supercomputer Institute.
文摘In this paper we study the computational performance of variants of an algebraic additive Schwarz preconditioner for the Schur complement for the solution of large sparse linear systems.In earlier works,the local Schur complements were computed exactly using a sparse direct solver.The robustness of the preconditioner comes at the price of this memory and time intensive computation that is the main bottleneck of the approach for tackling huge problems.In this work we investigate the use of sparse approximation of the dense local Schur complements.These approximations are computed using a partial incomplete LU factorization.Such a numerical calculation is the core of the multi-level incomplete factorization such as the one implemented in pARMS. The numerical and computing performance of the new numerical scheme is illustrated on a set of large 3D convection-diffusion problems;preliminary experiments on linear systems arising from structural mechanics are also reported.
文摘In this paper, a S-CR method with inexact solvers on the subdomains is presented, and then its convergence property is proved under very general conditions. This result is important because it guarantees the effectiveness of the Schwarz alternating method when executed on message-passing distributed memory multiprocessor system.
基金This work was supported by the U.S.Department of Energy,Office of Science under contract DE-AC02-06CH11357The research work was funded by Argonne’s Laboratory Directed Research and Development(LDRD)Innovate project#2020-0203.The authors acknowledge the computing resources available via Bebop,a high-performance computing cluster operated by the Laboratory Computing Resource Center(LCRC)at Argonne National Laboratory.
文摘Solving for detailed chemical kinetics remains one of the major bottlenecks for computational fluid dynamics simulations of reacting flows using a finite-rate-chemistry approach.This has motivated the use of neural networks to predict stiff chemical source terms as functions of the thermochemical state of the combustion system.However,due to the nonlinearities and multi-scale nature of combustion,the predicted solution often diverges from the true solution when these machine learning models are coupled with a computational fluid dynamics solver.This is because these approaches minimize the error during training without guaranteeing successful integration with ordinary differential equation solvers.In the present work,a novel neural ordinary differential equations approach to modeling chemical kinetics,termed as ChemNODE,is developed.In this machine learning framework,the chemical source terms predicted by the neural networks are integrated during training,and by computing the required derivatives,the neural network weights are adjusted accordingly to minimize the difference between the predicted and ground-truth solution.A proof-of-concept study is performed with ChemNODE for homogeneous autoignition of hydrogen-air mixture over a range of composition and thermodynamic conditions.It is shown that ChemNODE accurately captures the chemical kinetic behavior and reproduces the results obtained using the detailed kinetic mechanism at a fraction of the computational cost.
文摘New direct spectral solvers for the 3D Helmholtz equation in a finite cylindrical region are presented.A purely variational(no collocation)formulation of the problem is adopted,based on Fourier series expansion of the angular dependence and Legendre polynomials for the axial dependence.A new Jacobi basis is proposed for the radial direction overcoming the main disadvantages of previously developed bases for the Dirichlet problem.Nonhomogeneous Dirichlet boundary conditions are enforced by a discrete lifting and the vector problem is solved by means of a classical uncoupling technique.In the considered formulation,boundary conditions on the axis of the cylindrical domain are never mentioned,by construction.The solution algorithms for the scalar equations are based on double diagonalization along the radial and axial directions.The spectral accuracy of the proposed algorithms is verified by numerical tests.
基金King Abdullah University of Science and Technol-ogy(KAUST)for supporting this research and the Seismic Wave Anal-ysis group for the supportive and encouraging environment.
文摘Physics-informed neural networks(PINNs)are promising to replace conventional mesh-based partial tial differen-equation(PDE)solvers by offering more accurate and flexible PDE solutions.However,PINNs are hampered by the relatively slow convergence and the need to perform additional,potentially expensive training for new PDE parameters.To solve this limitation,we introduce LatentPINN,a framework that utilizes latent representations of the PDE parameters as additional(to the coordinates)inputs into PINNs and allows for training over the distribution of these parameters.Motivated by the recent progress on generative models,we promote using latent diffusion models to learn compressed latent representations of the distribution of PDE parameters as they act as input parameters for NN functional solutions.We use a two-stage training scheme in which,in the first stage,we learn the latent representations for the distribution of PDE parameters.In the second stage,we train a physics-informed neural network over inputs given by randomly drawn samples from the coordinate space within the solution domain and samples from the learned latent representation of the PDE parameters.Considering their importance in capturing evolving interfaces and fronts in various fields,we test the approach on a class of level set equations given,for example,by the nonlinear Eikonal equation.We share results corresponding to three Eikonal parameters(velocity models)sets.The proposed method performs well on new phase velocity models without the need for any additional training.
基金Project supported by the National Natural Science Foundation of China(Nos.12471367 and12361076)the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region(Nos.NJZY19186,NJZY22036,and NJZY23003)。
文摘We are intrigued by the issues of shock instability,with a particular emphasis on numerical schemes that address the carbuncle phenomenon by reducing dissipation rather than increasing it.For a specific class of planar flow fields where the transverse direction exhibits vanishing but non-zero velocity components,such as a disturbed onedimensional(1D)steady shock wave,we conduct a formal asymptotic analysis for the Euler system and associated numerical methods.This analysis aims to illustrate the discrepancies among various low-dissipative numerical algorithms.Furthermore,a numerical stability analysis of steady shock is undertaken to identify the key factors underlying shock-stable algorithms.To verify the stability mechanism,a consistent,low-dissipation,and shock-stable HLLC-type Riemann solver is presented.
基金Supported by the National Natural Science Foundation of China(52201350,52201394,and 52271301)the Innovation Group Project of Southern Marine Science and Engineering Guangdong Laboratory(Zhuhai)(Grant No.SML2022008).
文摘To explore the relationship between dynamic characteristics and wake patterns,numerical simulations were conducted on three equal-diameter cylinders arranged in an equilateral triangle.The simulations varied reduced velocities and gap spacing to observe flow-induced vibrations(FIVs).The immersed boundary–lattice Boltzmann flux solver(IB–LBFS)was applied as a numerical solution method,allowing for straightforward application on a simple Cartesian mesh.The accuracy and rationality of this method have been verified through comparisons with previous numerical results,including studies on flow past three stationary circular cylinders arranged in a similar pattern and vortex-induced vibrations of a single cylinder across different reduced velocities.When examining the FIVs of three cylinders,numerical simulations were carried out across a range of reduced velocities(3.0≤Ur≤13.0)and gap spacing(L=3D,4D,and 5D).The observed vibration response included several regimes:the desynchronization regime,the initial branch,and the lower branch.Notably,the transverse amplitude peaked,and a double vortex street formed in the wake when the reduced velocity reached the lower branch.This arrangement of three cylinders proved advantageous for energy capture as the upstream cylinder’s vibration response mirrored that of an isolated cylinder,while the response of each downstream cylinder was significantly enhanced.Compared to a single cylinder,the vibration and flow characteristics of this system are markedly more complex.The maximum transverse amplitudes of the downstream cylinders are nearly identical and exceed those observed in a single-cylinder set-up.Depending on the gap spacing,the flow pattern varied:it was in-phase for L=3D,antiphase for L=4D,and exhibited vortex shedding for L=5D.The wake configuration mainly featured double vortex streets for L=3D and evolved into two pairs of double vortex streets for L=5D.Consequently,it well illustrates the coupling mechanism that dynamics characteristics and wake vortex change with gap spacing and reduced velocities.
基金Supported by Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)+3 种基金National Natural Science Foundation of China(12301556)Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)Basic Research Plan of Shanxi Province(202203021211129)。
文摘To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical computation of such models.This efficient solver employs algorithms based on discrete cosine transformations(DCT)or discrete sine transformations(DST)and is not restricted by any spatio-temporal schemes.Our proposed methodology is appropriate for a variety of phase-field models and is especially efficient when combined with flow field systems.Meanwhile,this study has conducted an extensive numerical comparison and found that employing DCT and DST techniques not only yields results comparable to those obtained via the Multigrid(MG)method,a conventional approach used in the resolution of the Poisson equations,but also enhances computational efficiency by over 90%.
基金supported by the National Natural Science Foundation of China(Grant Nos.U24B20133 and 62522104)the Beijing Nova Program(Grant No.20230484331).
文摘An efficient neural mode-solving operator is proposed for evaluating the propagation properties of optical fibers.By incorporating the governing Helmholtz equation into training,the working mechanism of the proposed operator adheres to the physics essence of fiber analysis.The training of the mode-solving operator adopts a hybrid physics-informed and data-driven approach,providing the advantages of strong physical consistency,enhanced prediction accuracy,and reduced data dependency in comparison with purely datadriven methods.Benefiting from the improvements in network input-output mapping formulation,the proposed operator offers broader applicability to different fiber types and greater flexibility for property optimization.Combined with the particle swarm optimization and refractive index optimization,the operator demonstrates its capacity for the inverse design of multi-step-index fibers(MSIFs)and graded-index fibers(GRIFs).For MSIFs,to ensure a low mode crosstalk for short-distance transmission systems,optimized refractive index profiles(RIPs)of both three-ring and four-ring structures are obtained from large structure parameter search spaces.For GRIFs,to ensure a low receiving complexity for long-haul transmission systems,optimized RIP with low root mean square mode group delay is obtained through point-wise fine-tuning.Moreover,the operator is capable of analyzing the effect of dopant diffusion in manufacturing.
基金supported by the National Key R&D Program of China(2023YFB2504601)National Natural Science Foundation of China(52205267).
文摘Due to the high-order B-spline basis functions utilized in isogeometric analysis(IGA)and the repeatedly updating global stiffness matrix of topology optimization,Isogeometric topology optimization(ITO)intrinsically suffers from the computationally demanding process.In this work,we address the efficiency problem existing in the assembling stiffness matrix and sensitivity analysis using B˙ezier element stiffness mapping.The Element-wise and Interaction-wise parallel computing frameworks for updating the global stiffness matrix are proposed for ITO with B˙ezier element stiffness mapping,which differs from these ones with the traditional Gaussian integrals utilized.Since the explicit stiffness computation formula derived from B˙ezier element stiffness mapping possesses a typical parallel structure,the presented GPU-enabled ITO method can greatly accelerate the computation speed while maintaining its high memory efficiency unaltered.Numerical examples demonstrate threefold speedup:1)the assembling stiffness matrix is accelerated by 10×maximumly with the proposed GPU strategy;2)the solution efficiency of a sparse linear system is enhanced by up to 30×with Eigen replaced by AMGCL;3)the efficiency of sensitivity analysis is promoted by 100×with GPU applied.Therefore,the proposed method is a promising way to enhance the numerical efficiency of ITO for both single-patch and multiple-patch design problems.
基金supported by the National Key Research and Development Program of China(Grant No.2022YFB2804203)the National Natural Science Foundation of China(Grant No.U21A20511)the Knowledge Innovation Program of Wuhan-Basic Research(Grant No.2023010201010049).
文摘Ising problems are critical for a wide range of applications.Solving these problems on a photonic platform takes advantage of the unique properties of photons,such as high speed,low power consumption,and large bandwidth.Recently,there has been growing interest in using photonic platforms to accelerate the optimization of Ising models,paving the way for the development of ultrafast hardware in machine learning.However,these proposed systems face challenges in simultaneously achieving high spin scalability,encoding flexibility,and low system complexity.We propose a wavelength-domain optical Ising machine that utilizes optical signals at different wavelengths to represent distinct Ising spins for Ising simulation.We design and experimentally validate a chip-scale Ising machine capable of solving classical non-deterministic polynomial-time problems.The proposed Ising machine supports 32 spins and features 2 distinct coupling encoding schemes.Furthermore,we demonstrate the feasibility of scaling the system to 256 spins.This approach verifies the viability of performing Ising simulations in the wavelength dimension,offering substantial advantages in scalability.These advancements lay the groundwork for future large-scale expansion and practical applications in cloud computing.
基金The project is supported by National Natural Science Foundation of China
文摘In this paper,a number of ordinary differential equation(ODE)conversion techniques for trans- formation of nonstandard ODE boundary value problems into standard forms are summarised,together with their applications to a variety of boundary value problems in computational solid mechanics,such as eigenvalue problem,geometrical and material nonlinear problem,elastic contact problem and optimal design problems through some simple and representative examples,The advantage of such approach is that various ODE bounda- ry value problems in computational mechanics can be solved effectively in a unified manner by invoking a stand- ard ODE solver.
基金Supported by the National Natural Science Foundation of China(11272153)
文摘A lattice Boltzmann flux solver(LBFS)is presented for simulation of fluid flows.Like the conventional computational fluid dynamics(CFD)solvers,the new solver also applies the finite volume method to discretize the governing differential equations,but the numerical flux at the cell interface is not evaluated by the smooth function approximation or Riemann solvers.Instead,it is evaluated from local solution of lattice Boltzmann equation(LBE)at cell interface.Two versions of LBFS are presented in this paper.One is to locally apply one-dimensional compressible lattice Boltzmann(LB)model along the normal direction to the cell interface for simulation of compressible inviscid flows with shock waves.The other is to locally apply multi-dimensional LB model at cell interface for simulation of incompressible viscous and inviscid flows.The present solver removes the drawbacks of conventional lattice Boltzmann method(LBM)such as limitation to uniform mesh,tie-up of mesh spacing and time interval,limitation to viscous flows.Numerical examples show that the present solver can be well applied to simulate fluid flows with non-uniform mesh and curved boundary.
