近几年来,深度学习无所不在,赋能于各个领域.尤其是人工智能与传统科学的结合(AI for science,AI4Science)引发广泛关注.在AI4Science领域,利用人工智能算法求解PDEs(AI4PDEs)已成为计算力学研究的焦点.AI4PDEs的核心是将数据与方程相融...近几年来,深度学习无所不在,赋能于各个领域.尤其是人工智能与传统科学的结合(AI for science,AI4Science)引发广泛关注.在AI4Science领域,利用人工智能算法求解PDEs(AI4PDEs)已成为计算力学研究的焦点.AI4PDEs的核心是将数据与方程相融合,并且几乎可以求解任何偏微分方程问题,由于其融合数据的优势,相较于传统算法,其计算效率通常提升数万倍.因此,本文全面综述了AI4PDEs的研究,总结了现有AI4PDEs算法、理论,并讨论了其在固体力学中的应用,包括正问题和反问题,展望了未来研究方向,尤其是必然会出现的计算力学大模型.现有AI4PDEs算法包括基于物理信息神经网络(physicsinformed neural network,PINNs)、深度能量法(deep energy methods,DEM)、算子学习(operator learning),以及基于物理神经网络算子(physics-informed neural operator,PINO).AI4PDEs在科学计算中有许多应用,本文聚焦于固体力学,正问题包括线弹性、弹塑性,超弹性、以及断裂力学;反问题包括材料参数,本构,缺陷的识别,以及拓朴优化.AI4PDEs代表了一种全新的科学模拟方法,通过利用大量数据在特定问题上提供近似解,然后根据具体的物理方程进行微调,避免了像传统算法那样从头开始计算,因此AI4PDEs是未来计算力学大模型的雏形,能够大大加速传统数值算法.我们相信,利用人工智能助力科学计算不仅仅是计算领域的未来重要方向,同时也是计算力学的未来,即是智能计算力学。展开更多
In this work, an efficient spectral method is proposed to solve the fourth-order eigenvalue problem in cylinder domain. Firstly, the key point of this method is to decompose the original model into a kind of decoupled...In this work, an efficient spectral method is proposed to solve the fourth-order eigenvalue problem in cylinder domain. Firstly, the key point of this method is to decompose the original model into a kind of decoupled two-dimensional eigenvalue problem by cylindrical coordinate transformation and Fourier series expansion, and deduce the crucial essential pole conditions. Secondly, we define a kind of weighted Sobolev spaces, and establish a suitable variational formula and its discrete form for each two-dimensional eigenvalue problem. Furthermore, we derive the equivalent operator formulas and obtain some prior error estimates of spectral theory of compact operators. More importantly, we further obtained error estimates for approximating eigenvalues and eigenfunctions by using two newly constructed projection operators. Finally,some numerical experiments are performed to validate our theoretical results and algorithm.展开更多
Failure analyses of piezoelectric structures and devices are of engineering and scientific significance.In this paper,a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilt...Failure analyses of piezoelectric structures and devices are of engineering and scientific significance.In this paper,a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilton principle.Three typical electric boundary conditions are involved in the present model to characterize the fracture behaviors in various physical situations.A staggered algorithm is used to simulate the crack propagation.The polynomial splines over hierarchical T-meshes(PHT-splines)are adopted as the basis function,which owns the C1continuity.Systematic numerical simulations are performed to study the influence of the electric boundary conditions and the applied electric field on the fracture behaviors of piezoelectric materials.The electric boundary conditions may influence crack paths and fracture loads significantly.The present research may be helpful for the reliability evaluation of the piezoelectric structure in the future applications.展开更多
The deferred correction(DeC)is an iterative procedure,characterized by increasing the accuracy at each iteration,which can be used to design numerical methods for systems of ODEs.The main advantage of such framework i...The deferred correction(DeC)is an iterative procedure,characterized by increasing the accuracy at each iteration,which can be used to design numerical methods for systems of ODEs.The main advantage of such framework is the automatic way of getting arbitrarily high order methods,which can be put in the Runge-Kutta(RK)form.The drawback is the larger computational cost with respect to the most used RK methods.To reduce such cost,in an explicit setting,we propose an efcient modifcation:we introduce interpolation processes between the DeC iterations,decreasing the computational cost associated to the low order ones.We provide the Butcher tableaux of the new modifed methods and we study their stability,showing that in some cases the computational advantage does not afect the stability.The fexibility of the novel modifcation allows nontrivial applications to PDEs and construction of adaptive methods.The good performances of the introduced methods are broadly tested on several benchmarks both in ODE and PDE contexts.展开更多
This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations(FODEs)which have been widely used in modeling various phenomena in engineering a...This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations(FODEs)which have been widely used in modeling various phenomena in engineering and science.An approximate solution of the system is sought in the formof the finite series over the Müntz polynomials.By using the collocation procedure in the time interval,one gets the linear algebraic system for the coefficient of the expansion which can be easily solved numerically by a standard procedure.This technique also serves as the basis for solving the time-fractional partial differential equations(PDEs).The modified radial basis functions are used for spatial approximation of the solution.The collocation in the solution domain transforms the equation into a system of fractional ordinary differential equations similar to the one mentioned above.Several examples have verified the performance of the proposed novel technique with high accuracy and efficiency.展开更多
GPU computing is expected to play an integral part in all modern Exascale supercomputers.It is also expected that higher order Godunov schemes will make up about a significant fraction of the application mix on such s...GPU computing is expected to play an integral part in all modern Exascale supercomputers.It is also expected that higher order Godunov schemes will make up about a significant fraction of the application mix on such supercomputers.It is,therefore,very important to prepare the community of users of higher order schemes for hyperbolic PDEs for this emerging opportunity.Not every algorithm that is used in the space-time update of the solution of hyperbolic PDEs will take well to GPUs.However,we identify a small core of algorithms that take exceptionally well to GPU computing.Based on an analysis of available options,we have been able to identify weighted essentially non-oscillatory(WENO)algorithms for spatial reconstruction along with arbitrary derivative(ADER)algorithms for time extension followed by a corrector step as the winning three-part algorithmic combination.Even when a winning subset of algorithms has been identified,it is not clear that they will port seamlessly to GPUs.The low data throughput between CPU and GPU,as well as the very small cache sizes on modern GPUs,implies that we have to think through all aspects of the task of porting an application to GPUs.For that reason,this paper identifies the techniques and tricks needed for making a successful port of this very useful class of higher order algorithms to GPUs.Application codes face a further challenge—the GPU results need to be practically indistinguishable from the CPU results—in order for the legacy knowledge bases embedded in these applications codes to be preserved during the port of GPUs.This requirement often makes a complete code rewrite impossible.For that reason,it is safest to use an approach based on OpenACC directives,so that most of the code remains intact(as long as it was originally well-written).This paper is intended to be a one-stop shop for anyone seeking to make an OpenACC-based port of a higher order Godunov scheme to GPUs.We focus on three broad and high-impact areas where higher order Godunov schemes are used.The first area is computational fluid dynamics(CFD).The second is computational magnetohydrodynamics(MHD)which has an involution constraint that has to be mimetically preserved.The third is computational electrodynamics(CED)which has involution constraints and also extremely stiff source terms.Together,these three diverse uses of higher order Godunov methodology,cover many of the most important applications areas.In all three cases,we show that the optimal use of algorithms,techniques,and tricks,along with the use of OpenACC,yields superlative speedups on GPUs.As a bonus,we find a most remarkable and desirable result:some higher order schemes,with their larger operations count per zone,show better speedup than lower order schemes on GPUs.In other words,the GPU is an optimal stratagem for overcoming the higher computational complexities of higher order schemes.Several avenues for future improvement have also been identified.A scalability study is presented for a real-world application using GPUs and comparable numbers of high-end multicore CPUs.It is found that GPUs offer a substantial performance benefit over comparable number of CPUs,especially when all the methods designed in this paper are used.展开更多
This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones a...This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.展开更多
Idiopathic pulmonary fibrosis(IPF)is a progressive lung disease and its incidence rate is rapidly rising.However,effective therapies for the treatment of IPF are still lacking.Phosphodiesterase 4(PDE4)inhibitors were ...Idiopathic pulmonary fibrosis(IPF)is a progressive lung disease and its incidence rate is rapidly rising.However,effective therapies for the treatment of IPF are still lacking.Phosphodiesterase 4(PDE4)inhibitors were reported to be potential anti-fibrotic agents.Herein,structure-based hit-to-lead optimization of natural isoaurostatin(8.98μmol/L)resulted in several potent inhibitors of PDE4 with half maximal inhibitory concentration(IC_(50))values ranging from 35 nmol/L to 126 nmol/L.Co-crystal structures revealed that isoaurostatin compounds exhibited different binding patterns from the classic PDE4 inhibitor rolipram and the analogues would favor to be Z configurations other than the corresponding E isomers.Finally,lead 2–9 showed remarkable in vitro/in vivo anti-fibrotic effects indicating its potential as a novel anti-IPF agent.展开更多
This paper investigates the issue of fault-tolerant control for swarm systems subject to switched graphs,actuator faults and obstacles.A geometric-based partial differential equation(PDE)framework is proposed to unify...This paper investigates the issue of fault-tolerant control for swarm systems subject to switched graphs,actuator faults and obstacles.A geometric-based partial differential equation(PDE)framework is proposed to unify collision-free trajectory generation and fault-tolerant control.To deal with the fault-induced force imbalances,the Riemannian metric is proposed to coordinate nominal controllers and the global one.Then,Riemannianbased trajectory length optimization is solved by gradient's dynamic model-heat flow PDE,under which a feasible trajectory satisfying motion constraints is achieved to guide the faulty system.Such virtual control force emerges autonomously through this metric adjustments.Further,the tracking error is rigorously proven to be exponential boundedness.Simulation results confirm the validity of these theoretical findings.展开更多
Icariin is a pure compound derived from Epimedium brevicornu Maxim,and it helps the regulation of male reproduction.Nevertheless,the role and underlying mechanisms of Icariin in mediating male germ cell development re...Icariin is a pure compound derived from Epimedium brevicornu Maxim,and it helps the regulation of male reproduction.Nevertheless,the role and underlying mechanisms of Icariin in mediating male germ cell development remain to be clarified.Here,we have demonstrated that Icariin promoted proliferation and DNA synthesis of mouse spermatogonial stem cells(SSCs).Furthermore,surface plasmon resonance iron(SPRi)and molecular docking(MOE)assays revealed that phosphodiesterase 5A(PDE5A)was an important target of Icariin in mouse SSCs.Mechanically,Icariin decreased the expression level of PDE5A.Interestingly,hydrogen peroxides(H2O2)enhanced the expression level of phosphorylation H2A.X(p-H2A.X),whereas Icariin diminished the expression level of p-H2A.X and DNA damage caused by H2O2 in mouse SSCs.Finally,our in vivo animal study indicated that Icariin protected male reproduction.Collectively,these results implicate that Icariin targets PDE5A to regulate mouse SSC viability and DNA damage and improves male reproductive capacity.This study thus sheds new insights into molecular mechanisms underlying the fate decisions of mammalian SSCs and offers a scientific basis for the clinical application of Icariin in male reproduction.展开更多
文摘近几年来,深度学习无所不在,赋能于各个领域.尤其是人工智能与传统科学的结合(AI for science,AI4Science)引发广泛关注.在AI4Science领域,利用人工智能算法求解PDEs(AI4PDEs)已成为计算力学研究的焦点.AI4PDEs的核心是将数据与方程相融合,并且几乎可以求解任何偏微分方程问题,由于其融合数据的优势,相较于传统算法,其计算效率通常提升数万倍.因此,本文全面综述了AI4PDEs的研究,总结了现有AI4PDEs算法、理论,并讨论了其在固体力学中的应用,包括正问题和反问题,展望了未来研究方向,尤其是必然会出现的计算力学大模型.现有AI4PDEs算法包括基于物理信息神经网络(physicsinformed neural network,PINNs)、深度能量法(deep energy methods,DEM)、算子学习(operator learning),以及基于物理神经网络算子(physics-informed neural operator,PINO).AI4PDEs在科学计算中有许多应用,本文聚焦于固体力学,正问题包括线弹性、弹塑性,超弹性、以及断裂力学;反问题包括材料参数,本构,缺陷的识别,以及拓朴优化.AI4PDEs代表了一种全新的科学模拟方法,通过利用大量数据在特定问题上提供近似解,然后根据具体的物理方程进行微调,避免了像传统算法那样从头开始计算,因此AI4PDEs是未来计算力学大模型的雏形,能够大大加速传统数值算法.我们相信,利用人工智能助力科学计算不仅仅是计算领域的未来重要方向,同时也是计算力学的未来,即是智能计算力学。
基金Supported by the National Natural Science Foundation of China(Grant No.12261017)the Scientific Research Foundation of Guizhou University of Finance and Economics(Grant No.2022ZCZX077)。
文摘In this work, an efficient spectral method is proposed to solve the fourth-order eigenvalue problem in cylinder domain. Firstly, the key point of this method is to decompose the original model into a kind of decoupled two-dimensional eigenvalue problem by cylindrical coordinate transformation and Fourier series expansion, and deduce the crucial essential pole conditions. Secondly, we define a kind of weighted Sobolev spaces, and establish a suitable variational formula and its discrete form for each two-dimensional eigenvalue problem. Furthermore, we derive the equivalent operator formulas and obtain some prior error estimates of spectral theory of compact operators. More importantly, we further obtained error estimates for approximating eigenvalues and eigenfunctions by using two newly constructed projection operators. Finally,some numerical experiments are performed to validate our theoretical results and algorithm.
基金Project supported by the National Natural Science Foundation of China(Nos.12072297 and12202370)the Natural Science Foundation of Sichuan Province of China(No.24NSFSC4777)。
文摘Failure analyses of piezoelectric structures and devices are of engineering and scientific significance.In this paper,a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilton principle.Three typical electric boundary conditions are involved in the present model to characterize the fracture behaviors in various physical situations.A staggered algorithm is used to simulate the crack propagation.The polynomial splines over hierarchical T-meshes(PHT-splines)are adopted as the basis function,which owns the C1continuity.Systematic numerical simulations are performed to study the influence of the electric boundary conditions and the applied electric field on the fracture behaviors of piezoelectric materials.The electric boundary conditions may influence crack paths and fracture loads significantly.The present research may be helpful for the reliability evaluation of the piezoelectric structure in the future applications.
文摘The deferred correction(DeC)is an iterative procedure,characterized by increasing the accuracy at each iteration,which can be used to design numerical methods for systems of ODEs.The main advantage of such framework is the automatic way of getting arbitrarily high order methods,which can be put in the Runge-Kutta(RK)form.The drawback is the larger computational cost with respect to the most used RK methods.To reduce such cost,in an explicit setting,we propose an efcient modifcation:we introduce interpolation processes between the DeC iterations,decreasing the computational cost associated to the low order ones.We provide the Butcher tableaux of the new modifed methods and we study their stability,showing that in some cases the computational advantage does not afect the stability.The fexibility of the novel modifcation allows nontrivial applications to PDEs and construction of adaptive methods.The good performances of the introduced methods are broadly tested on several benchmarks both in ODE and PDE contexts.
基金funded by the National Key Research and Development Program of China(No.2021YFB2600704)the National Natural Science Foundation of China(No.52171272)the Significant Science and Technology Project of the Ministry of Water Resources of China(No.SKS-2022112).
文摘This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations(FODEs)which have been widely used in modeling various phenomena in engineering and science.An approximate solution of the system is sought in the formof the finite series over the Müntz polynomials.By using the collocation procedure in the time interval,one gets the linear algebraic system for the coefficient of the expansion which can be easily solved numerically by a standard procedure.This technique also serves as the basis for solving the time-fractional partial differential equations(PDEs).The modified radial basis functions are used for spatial approximation of the solution.The collocation in the solution domain transforms the equation into a system of fractional ordinary differential equations similar to the one mentioned above.Several examples have verified the performance of the proposed novel technique with high accuracy and efficiency.
基金support via the NSF grants NSF-19-04774,NSF-AST-2009776,NASA-2020-1241the NASA grant 80NSSC22K0628。
文摘GPU computing is expected to play an integral part in all modern Exascale supercomputers.It is also expected that higher order Godunov schemes will make up about a significant fraction of the application mix on such supercomputers.It is,therefore,very important to prepare the community of users of higher order schemes for hyperbolic PDEs for this emerging opportunity.Not every algorithm that is used in the space-time update of the solution of hyperbolic PDEs will take well to GPUs.However,we identify a small core of algorithms that take exceptionally well to GPU computing.Based on an analysis of available options,we have been able to identify weighted essentially non-oscillatory(WENO)algorithms for spatial reconstruction along with arbitrary derivative(ADER)algorithms for time extension followed by a corrector step as the winning three-part algorithmic combination.Even when a winning subset of algorithms has been identified,it is not clear that they will port seamlessly to GPUs.The low data throughput between CPU and GPU,as well as the very small cache sizes on modern GPUs,implies that we have to think through all aspects of the task of porting an application to GPUs.For that reason,this paper identifies the techniques and tricks needed for making a successful port of this very useful class of higher order algorithms to GPUs.Application codes face a further challenge—the GPU results need to be practically indistinguishable from the CPU results—in order for the legacy knowledge bases embedded in these applications codes to be preserved during the port of GPUs.This requirement often makes a complete code rewrite impossible.For that reason,it is safest to use an approach based on OpenACC directives,so that most of the code remains intact(as long as it was originally well-written).This paper is intended to be a one-stop shop for anyone seeking to make an OpenACC-based port of a higher order Godunov scheme to GPUs.We focus on three broad and high-impact areas where higher order Godunov schemes are used.The first area is computational fluid dynamics(CFD).The second is computational magnetohydrodynamics(MHD)which has an involution constraint that has to be mimetically preserved.The third is computational electrodynamics(CED)which has involution constraints and also extremely stiff source terms.Together,these three diverse uses of higher order Godunov methodology,cover many of the most important applications areas.In all three cases,we show that the optimal use of algorithms,techniques,and tricks,along with the use of OpenACC,yields superlative speedups on GPUs.As a bonus,we find a most remarkable and desirable result:some higher order schemes,with their larger operations count per zone,show better speedup than lower order schemes on GPUs.In other words,the GPU is an optimal stratagem for overcoming the higher computational complexities of higher order schemes.Several avenues for future improvement have also been identified.A scalability study is presented for a real-world application using GPUs and comparable numbers of high-end multicore CPUs.It is found that GPUs offer a substantial performance benefit over comparable number of CPUs,especially when all the methods designed in this paper are used.
文摘This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.
基金supported by the Natural Science Foundation of China(Nos.22277019,82150204,22307031,22377023,22077143,and 82003594)Key Project of Guangdong Natural Science Foundation(No.2016A030311033)+2 种基金Fundamental Research Funds for Hainan University(Nos.KYQD(ZR)-21031,KYQD(ZR)-21108,KYQD(ZR)-23003,and XTCX2022JKA01)Guangdong Provincial Key Laboratory of Construction Foundation(No.2023B1212060022)Science Foundation of Hainan Province(Nos.KJRC2023B10,824YXQN420,and 324MS018)。
文摘Idiopathic pulmonary fibrosis(IPF)is a progressive lung disease and its incidence rate is rapidly rising.However,effective therapies for the treatment of IPF are still lacking.Phosphodiesterase 4(PDE4)inhibitors were reported to be potential anti-fibrotic agents.Herein,structure-based hit-to-lead optimization of natural isoaurostatin(8.98μmol/L)resulted in several potent inhibitors of PDE4 with half maximal inhibitory concentration(IC_(50))values ranging from 35 nmol/L to 126 nmol/L.Co-crystal structures revealed that isoaurostatin compounds exhibited different binding patterns from the classic PDE4 inhibitor rolipram and the analogues would favor to be Z configurations other than the corresponding E isomers.Finally,lead 2–9 showed remarkable in vitro/in vivo anti-fibrotic effects indicating its potential as a novel anti-IPF agent.
基金supported in part by the National Natural Science Foundation of China under Grant 62303144,62020106003,U22A2044in part by the Zhejiang Provincial Natural Science Foundation of China under Grant LQ23F030013.
文摘This paper investigates the issue of fault-tolerant control for swarm systems subject to switched graphs,actuator faults and obstacles.A geometric-based partial differential equation(PDE)framework is proposed to unify collision-free trajectory generation and fault-tolerant control.To deal with the fault-induced force imbalances,the Riemannian metric is proposed to coordinate nominal controllers and the global one.Then,Riemannianbased trajectory length optimization is solved by gradient's dynamic model-heat flow PDE,under which a feasible trajectory satisfying motion constraints is achieved to guide the faulty system.Such virtual control force emerges autonomously through this metric adjustments.Further,the tracking error is rigorously proven to be exponential boundedness.Simulation results confirm the validity of these theoretical findings.
基金supported by the grants from the National Nature Science Foundation of China(No.32170862)Developmental Biology and Breeding(No.2022XKQ0205)+2 种基金the Research Team for Reproduction Health and Translational Medicine of Hunan Normal University(No.2023JC101)Graduate Scientific Research Innovation Project of Hunan Province(No.CX2022520)Shanghai Key Laboratory of Reproductive Medicine(2022SKLRM01).
文摘Icariin is a pure compound derived from Epimedium brevicornu Maxim,and it helps the regulation of male reproduction.Nevertheless,the role and underlying mechanisms of Icariin in mediating male germ cell development remain to be clarified.Here,we have demonstrated that Icariin promoted proliferation and DNA synthesis of mouse spermatogonial stem cells(SSCs).Furthermore,surface plasmon resonance iron(SPRi)and molecular docking(MOE)assays revealed that phosphodiesterase 5A(PDE5A)was an important target of Icariin in mouse SSCs.Mechanically,Icariin decreased the expression level of PDE5A.Interestingly,hydrogen peroxides(H2O2)enhanced the expression level of phosphorylation H2A.X(p-H2A.X),whereas Icariin diminished the expression level of p-H2A.X and DNA damage caused by H2O2 in mouse SSCs.Finally,our in vivo animal study indicated that Icariin protected male reproduction.Collectively,these results implicate that Icariin targets PDE5A to regulate mouse SSC viability and DNA damage and improves male reproductive capacity.This study thus sheds new insights into molecular mechanisms underlying the fate decisions of mammalian SSCs and offers a scientific basis for the clinical application of Icariin in male reproduction.
