This study introduces a novel mathematical model that combines the finite integral transform(FIT)and gradientenhanced physics-informed neural network(g-PINN)to address thermomechanical problems in functionally graded ...This study introduces a novel mathematical model that combines the finite integral transform(FIT)and gradientenhanced physics-informed neural network(g-PINN)to address thermomechanical problems in functionally graded materials with varying properties.The model employs a multilayer heterostructure homogeneous approach within the FIT to linearize and approximate various parameters,such as the thermal conductivity,specific heat,density,stiffness,thermal expansion coefficient,and Poisson’s ratio.The provided FIT and g-PINN techniques are highly proficient in solving the PDEs of energy equations and equations of motion in a spherical domain,particularly when dealing with space-time dependent boundary conditions.The FIT method simplifies the governing partial differential equations into ordinary differential equations for efficient solutions,whereas the g-PINN bypasses linearization,achieving high accuracy with fewer training data(error<3.8%).The approach is applied to a spherical pressure vessel,solving energy and motion equations under complex boundary conditions.Furthermore,extensive parametric studies are conducted herein to demonstrate the impact of different property profiles and radial locations on the transient evolution and dynamic propagation of thermomechanical stresses.However,the accuracy of the presented approach is evaluated by comparing the g-PINN results,which have an error of less than 3.8%.Moreover,this model offers significant potential for optimizing materials in hightemperature reactors and chemical plants,improving safety,extending lifespan,and reducing thermal fatigue under extreme processing conditions.展开更多
In this paper,we discuss a gradient-enhancedℓ_(1)approach for the recovery of sparse Fourier expansions.By gradient-enhanced approaches we mean that the directional derivatives along given vectors are utilized to impr...In this paper,we discuss a gradient-enhancedℓ_(1)approach for the recovery of sparse Fourier expansions.By gradient-enhanced approaches we mean that the directional derivatives along given vectors are utilized to improve the sparse approximations.We first consider the case where both the function values and the directional derivatives at sampling points are known.We show that,under some mild conditions,the inclusion of the derivatives information can indeed decrease the coherence of measurementmatrix,and thus leads to the improved the sparse recovery conditions of theℓ_(1)minimization.We also consider the case where either the function values or the directional derivatives are known at the sampling points,in which we present a sufficient condition under which the measurement matrix satisfies RIP,provided that the samples are distributed according to the uniform measure.This result shows that the derivatives information plays a similar role as that of the function values.Several numerical examples are presented to support the theoretical statements.Potential applications to function(Hermite-type)interpolations and uncertainty quantification are also discussed.展开更多
Efficiently solving partial differential equations(PDEs)is a long-standing challenge in mathematics and physics research.In recent years,the rapid development of artificial intelligence technology has brought deep lea...Efficiently solving partial differential equations(PDEs)is a long-standing challenge in mathematics and physics research.In recent years,the rapid development of artificial intelligence technology has brought deep learning-based methods to the forefront of research on numerical methods for partial differential equations.Among them,physics-informed neural networks(PINNs)are a new class of deep learning methods that show great potential in solving PDEs and predicting complex physical phenomena.In the field of nonlinear science,solitary waves and rogue waves have been important research topics.In this paper,we propose an improved PINN that enhances the physical constraints of the neural network model by adding gradient information constraints.In addition,we employ meta-learning optimization to speed up the training process.We apply the improved PINNs to the numerical simulation and prediction of solitary and rogue waves.We evaluate the accuracy of the prediction results by error analysis.The experimental results show that the improved PINNs can make more accurate predictions in less time than that of the original PINNs.展开更多
Histogram of collinear gradient-enhanced coding （HCGEC）, a robust key point descriptor for multi-spectral image matching, is proposed. The HCGEC mainly encodes rough structures within an image and suppresses detaile...Histogram of collinear gradient-enhanced coding （HCGEC）, a robust key point descriptor for multi-spectral image matching, is proposed. The HCGEC mainly encodes rough structures within an image and suppresses detailed textural information, which is desirable in multi-spectral image matching. Experiments on two multi-spectral data sets demonstrate that the proposed descriptor can yield significantly better results than some state-of- the-art descriptors.展开更多
文摘This study introduces a novel mathematical model that combines the finite integral transform(FIT)and gradientenhanced physics-informed neural network(g-PINN)to address thermomechanical problems in functionally graded materials with varying properties.The model employs a multilayer heterostructure homogeneous approach within the FIT to linearize and approximate various parameters,such as the thermal conductivity,specific heat,density,stiffness,thermal expansion coefficient,and Poisson’s ratio.The provided FIT and g-PINN techniques are highly proficient in solving the PDEs of energy equations and equations of motion in a spherical domain,particularly when dealing with space-time dependent boundary conditions.The FIT method simplifies the governing partial differential equations into ordinary differential equations for efficient solutions,whereas the g-PINN bypasses linearization,achieving high accuracy with fewer training data(error<3.8%).The approach is applied to a spherical pressure vessel,solving energy and motion equations under complex boundary conditions.Furthermore,extensive parametric studies are conducted herein to demonstrate the impact of different property profiles and radial locations on the transient evolution and dynamic propagation of thermomechanical stresses.However,the accuracy of the presented approach is evaluated by comparing the g-PINN results,which have an error of less than 3.8%.Moreover,this model offers significant potential for optimizing materials in hightemperature reactors and chemical plants,improving safety,extending lifespan,and reducing thermal fatigue under extreme processing conditions.
基金Zhiqiang Xuwas supported by NSFC grant(91630203,11422113,11331012,11688101)by National Basic Research Program of China(973 Program 2015CB856000)+1 种基金Tao Zhou was supported by the NSF of China(under grant numbers 11688101,91630312,91630203,11571351,and 11731006)the science challenge project(No.TZ2018001),NCMIS,and the youth innovation promotion association(CAS).
文摘In this paper,we discuss a gradient-enhancedℓ_(1)approach for the recovery of sparse Fourier expansions.By gradient-enhanced approaches we mean that the directional derivatives along given vectors are utilized to improve the sparse approximations.We first consider the case where both the function values and the directional derivatives at sampling points are known.We show that,under some mild conditions,the inclusion of the derivatives information can indeed decrease the coherence of measurementmatrix,and thus leads to the improved the sparse recovery conditions of theℓ_(1)minimization.We also consider the case where either the function values or the directional derivatives are known at the sampling points,in which we present a sufficient condition under which the measurement matrix satisfies RIP,provided that the samples are distributed according to the uniform measure.This result shows that the derivatives information plays a similar role as that of the function values.Several numerical examples are presented to support the theoretical statements.Potential applications to function(Hermite-type)interpolations and uncertainty quantification are also discussed.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.42005003 and 41475094).
文摘Efficiently solving partial differential equations(PDEs)is a long-standing challenge in mathematics and physics research.In recent years,the rapid development of artificial intelligence technology has brought deep learning-based methods to the forefront of research on numerical methods for partial differential equations.Among them,physics-informed neural networks(PINNs)are a new class of deep learning methods that show great potential in solving PDEs and predicting complex physical phenomena.In the field of nonlinear science,solitary waves and rogue waves have been important research topics.In this paper,we propose an improved PINN that enhances the physical constraints of the neural network model by adding gradient information constraints.In addition,we employ meta-learning optimization to speed up the training process.We apply the improved PINNs to the numerical simulation and prediction of solitary and rogue waves.We evaluate the accuracy of the prediction results by error analysis.The experimental results show that the improved PINNs can make more accurate predictions in less time than that of the original PINNs.
文摘Histogram of collinear gradient-enhanced coding （HCGEC）, a robust key point descriptor for multi-spectral image matching, is proposed. The HCGEC mainly encodes rough structures within an image and suppresses detailed textural information, which is desirable in multi-spectral image matching. Experiments on two multi-spectral data sets demonstrate that the proposed descriptor can yield significantly better results than some state-of- the-art descriptors.
