In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence...In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence,asymptotic behavior and blow-up of solutions with initial energy J(u_(0))≤d.Moreover,we estimate the upper bound of the blow-up time for J(u_(0))≤0.展开更多
This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic diff...This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.展开更多
In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ...In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.展开更多
The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and e...The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and existence of uniform attractor under some suitable assumptions on the nonlinear term g(u),the nonlinear damping f(u_(t))and the external force h(x,t).Specifically,the asymptotic compactness of the semigroup is verified by the energy reconstruction method.展开更多
A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue prob...A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).展开更多
In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is de...In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is developed using the trigonometric scheme,which is based on zero,first,and second moments,and the direct discontinuous Galerkin(DDG)flux is used to discretize the diffusion term.Moreover,the DDG method directly applies the weak form of the parabolic equation to each computational cell,which can better capture the characteristics of the solution,especially the discontinuous solution.Meanwhile,the third-order TVD-Runge-Kutta method is applied for temporal discretization.Finally,the effectiveness and stability of the method constructed in this paper are evaluated through numerical tests.展开更多
The neutron diffusion equation plays a pivotal role in nuclear reactor analysis.Nevertheless,employing the physics-informed neural network(PINN)method for its solution entails certain limitations.Conventional PINN app...The neutron diffusion equation plays a pivotal role in nuclear reactor analysis.Nevertheless,employing the physics-informed neural network(PINN)method for its solution entails certain limitations.Conventional PINN approaches generally utilize a fully connected network(FCN)architecture that is susceptible to overfitting,training instability,and gradient vanishing as the network depth increases.These challenges result in accuracy bottlenecks in the solution.In response to these issues,the residual-based resample physics-informed neural network(R2-PINN)is proposed.It is an improved PINN architecture that replaces the FCN with a convolutional neural network with a shortcut(S-CNN).It incorporates skip connections to facilitate gradient propagation between network layers.Additionally,the incorporation of the residual adaptive resampling(RAR)mechanism dynamically increases the number of sampling points.This,in turn,enhances the spatial representation capabilities and overall predictive accuracy of the model.The experimental results illustrate that our approach significantly improves the convergence capability of the model and achieves high-precision predictions of the physical fields.Compared with conventional FCN-based PINN methods,R 2-PINN effectively overcomes the limitations inherent in current methods.Thus,it provides more accurate and robust solutions for neutron diffusion equations.展开更多
AIM:To build a functional generalized estimating equation(GEE)model to detect glaucomatous visual field progression and compare the performance of the proposed method with that of commonly employed algorithms.METHODS:...AIM:To build a functional generalized estimating equation(GEE)model to detect glaucomatous visual field progression and compare the performance of the proposed method with that of commonly employed algorithms.METHODS:Totally 716 eyes of 716 patients with primary open angle glaucoma(POAG)with at least 5 reliable 24-2 test results and 2y of follow-up were selected.The functional GEE model was used to detect perimetric progression in the training dataset(501 eyes).In the testing dataset(215 eyes),progression was evaluated the functional GEE model,mean deviation(MD)and visual field index(VFI)rates of change,Advanced Glaucoma Intervention Study(AGIS)and Collaborative Initial Glaucoma Treatment Study(CIGTS)scores,and pointwise linear regression(PLR).RESULTS:The proposed method showed the highest proportion of eyes detected as progression(54.4%),followed by the VFI rate(34.4%),PLR(23.3%),and MD rate(21.4%).The CIGTS and AGIS scores had a lower proportion of eyes detected as progression(7.9%and 5.1%,respectively).The time to detection of progression was significantly shorter for the proposed method than that of other algorithms(adjusted P≤0.019).The VFI rate displayed moderate pairwise agreement with the proposed method(k=0.47).CONCLUSION:The functional GEE model shows the highest proportion of eyes detected as perimetric progression and the shortest time to detect perimetric progression in patients with POAG.展开更多
Physics-informed neural networks(PINNs)are vital for machine learning and exhibit significant advantages when handling complex physical problems.The PINN method can rapidly predict ^(220)Rn progeny concentration and i...Physics-informed neural networks(PINNs)are vital for machine learning and exhibit significant advantages when handling complex physical problems.The PINN method can rapidly predict ^(220)Rn progeny concentration and is very important for regulating and measuring this property.To construct a PINN model,training data are typically preprocessed;however,this approach changes the physical characteristics of the data,with the preprocessed data potentially no longer directly conforming to the original physical equations.As a result,the original physical equations cannot be directly employed in the PINN.Consequently,an effective method for transforming physical equations is crucial for accurately constraining PINNs to model the ^(220)Rn progeny concentration prediction.This study presents an equation adaptation approach for neural networks,which is designed to improve prediction of ^(220)Rn progeny concentration.Five neural network models based on three architectures are established:a classical network,a physics-informed network without equation adaptation,and a physics-informed network with equation adaptation.The transport equation of the ^(220)Rn progeny concentration is transformed via equation adaption and integrated with the PINN model.The compatibility and robustness of the model with equation adaption is then analyzed.The results show that PINNs with equation adaption converge consistently with classical neural networks in terms of the training and validation loss and achieve the same level of prediction accuracy.This outcome indicates that the proposed method can be integrated into the neural network architecture.Moreover,the prediction performance of classical neural networks declines significantly when interference data are encountered,whereas the PINNs with equation adaption exhibit stable prediction accuracy.This performance demonstrates that the proposed method successfully harnesses the constraining power of physical equations,significantly enhancing the robustness of the resultant PINN models.Thus,the use of a physics-informed network with equation adaption can guarantee accurate prediction of ^(220)Rn progeny concentration.展开更多
Physics-informed neural networks(PINNs),as a novel artificial intelligence method for solving partial differential equations,are applicable to solve both forward and inverse problems.This study evaluates the performan...Physics-informed neural networks(PINNs),as a novel artificial intelligence method for solving partial differential equations,are applicable to solve both forward and inverse problems.This study evaluates the performance of PINNs in solving the temperature diffusion equation of the seawater across six scenarios,including forward and inverse problems under three different boundary conditions.Results demonstrate that PINNs achieved consistently higher accuracy with the Dirichlet and Neumann boundary conditions compared to the Robin boundary condition for both forward and inverse problems.Inaccurate weighting of terms in the loss function can reduce model accuracy.Additionally,the sensitivity of model performance to the positioning of sampling points varied between different boundary conditions.In particular,the model under the Dirichlet boundary condition exhibited superior robustness to variations in point positions during the solutions of inverse problems.In contrast,for the Neumann and Robin boundary conditions,accuracy declines when points were sampled from identical positions or at the same time.Subsequently,the Argo observations were used to reconstruct the vertical diffusion of seawater temperature in the north-central Pacific for the applicability of PINNs in the real ocean.The PINNs successfully captured the vertical diffusion characteristics of seawater temperature,reflected the seasonal changes of vertical temperature under different topographic conditions,and revealed the influence of topography on the temperature diffusion coefficient.The PINNs were proved effective in solving the temperature diffusion equation of seawater with limited data,providing a promising technique for simulating or predicting ocean phenomena using sparse observations.展开更多
The strong convergence of an explicit full-discrete scheme is investigated for the stochastic Burgers-Huxley equation driven by additive space-time white noise,which possesses both Burgers-type and cubic nonlinearitie...The strong convergence of an explicit full-discrete scheme is investigated for the stochastic Burgers-Huxley equation driven by additive space-time white noise,which possesses both Burgers-type and cubic nonlinearities.To discretize the continuous problem in space,we utilize a spectral Galerkin method.Subsequently,we introduce a nonlinear-tamed exponential integrator scheme,resulting in a fully discrete scheme.Within the framework of semigroup theory,this study provides precise estimations of the Sobolev regularity,L^(∞) regularity in space,and Hölder continuity in time for the mild solution,as well as for its semi-discrete and full-discrete approximations.Building upon these results,we establish moment boundedness for the numerical solution and obtain strong convergence rates in both spatial and temporal dimensions.A numerical example is presented to validate the theoretical findings.展开更多
Owing to intensified globalization and informatization,the structures of the urban scale hierarchy and urban networks between cities have become increasingly intertwined,resulting in different spatial effects.Therefor...Owing to intensified globalization and informatization,the structures of the urban scale hierarchy and urban networks between cities have become increasingly intertwined,resulting in different spatial effects.Therefore,this paper analyzes the spatial interaction between urban scale hierarchy and urban networks in China from 2019 to 2023,drawing on Baidu migration data and employing a spatial simultaneous equation model.The results reveal a significant positive spatial correlation between cities with higher hierarchy and those with greater network centrality.Within a static framework,we identify a positive interaction between urban scale hierarchy and urban network centrality,while their spatial cross-effects manifest as negative neighborhood interactions based on geographical distance and positive cross-scale interactions shaped by network connections.Within a dynamic framework,changes in urban scale hierarchy and urban networks are mutually reinforcing,thereby widening disparities within the urban hierarchy.Furthermore,an increase in a city’s network centrality had a dampening effect on the population growth of neighboring cities and network-connected cities.This study enhances understanding of the spatial organisation of urban systems and offers insights for coordinated regional development.展开更多
In this paper,we propose and analyze two second-order accurate finite difference schemes for the one-dimensional heat equation with concentrated capacity on a computa-tional domain=[a,b].We first transform the target ...In this paper,we propose and analyze two second-order accurate finite difference schemes for the one-dimensional heat equation with concentrated capacity on a computa-tional domain=[a,b].We first transform the target equation into the standard heat equation on the domain excluding the singular point equipped with an inner interface matching(IIM)condition on the singular point x=ξ∈(a,b),then adopt Taylor’s ex-pansion to approximate the IIM condition at the singular point and apply second-order finite difference method to approximate the standard heat equation at the nonsingular points.This discrete procedure allows us to choose different grid sizes to partition the two sub-domains[a,ξ]and[ξ,b],which ensures that x=ξ is a grid point,and hence the pro-posed schemes can be generalized to the heat equation with more than one concentrated capacities.We prove that the two proposed schemes are uniquely solvable.And through in-depth analysis of the local truncation errors,we rigorously prove that the two schemes are second-order accurate both in temporal and spatial directions in the maximum norm without any constraint on the grid ratio.Numerical experiments are carried out to verify our theoretical conclusions.展开更多
This paper deals with the numerical solutions of two-dimensional(2D)semi-linear reaction-diffusion equations(SLRDEs)with piecewise continuous argument(PCA)in reaction term.A high-order compact difference method called...This paper deals with the numerical solutions of two-dimensional(2D)semi-linear reaction-diffusion equations(SLRDEs)with piecewise continuous argument(PCA)in reaction term.A high-order compact difference method called Ⅰ-type basic scheme is developed for solving the equations and it is proved under the suitable conditions that this method has the computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4)),where τ,h_(x )and h_(y) are the calculation stepsizes of the method in t-,x-and y-direction,respectively.With the above method and Newton linearized technique,a Ⅱ-type basic scheme is also suggested.Based on the both basic schemes,the corresponding Ⅰ-and Ⅱ-type alternating direction implicit(ADI)schemes are derived.Finally,with a series of numerical experiments,the computational accuracy and efficiency of the four numerical schemes are further illustrated.展开更多
Addressing the limitations of inadequate stochastic disturbance characterization during wind turbine degradation processes that result in constrained modeling accuracy,replacement-based maintenance practices that devi...Addressing the limitations of inadequate stochastic disturbance characterization during wind turbine degradation processes that result in constrained modeling accuracy,replacement-based maintenance practices that deviate from actual operational conditions,and static maintenance strategies that fail to adapt to accelerated deterioration trends leading to suboptimal remaining useful life utilization,this study proposes a Time-Based Incomplete Maintenance(TBIM)strategy incorporating reliability constraints through stochastic differential equations(SDE).By quantifying stochastic interference via Brownian motion terms and characterizing nonlinear degradation features through state influence rate functions,a high-precision SDE degradation model is constructed,achieving 16%residual reduction compared to conventional ordinary differential equation(ODE)methods.The introduction of age reduction factors and failure rate growth factors establishes an incomplete maintenance mechanism that transcends traditional“as-good-as-new”assumptions,with the TBIM model demonstrating an additional 8.5%residual reduction relative to baseline SDE approaches.A dynamic maintenance interval optimization model driven by dual parameters—preventive maintenance threshold R_(p) and replacement threshold R_(r)—is designed to achieve synergistic optimization of equipment reliability and maintenance economics.Experimental validation demonstrates that the optimized TBIM extends equipment lifespan by 4.4%and reducesmaintenance costs by 4.16%at R_(p)=0.80,while achieving 17.2%lifespan enhancement and 14.6%cost reduction at R_(p)=0.90.This methodology provides a solution for wind turbine preventive maintenance that integrates condition sensitivity with strategic foresight.展开更多
In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondl...In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondly,the existence and uniqueness of local solutions are proved by the Sobolev embedding theorem and the comparison principle.Finally,according to the relevant research data and contents of red fire ants,the diffusion area and nest number of red fire ants were simulated without external disturbance.This paper mainly simulates the early diffusion process of red fire ants.In the early diffusion stage,red fire ants grow slowly and then spread over a large area after reaching a certain number.展开更多
Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay di...Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay differential equations(DDEs)and delay integrodifferential equations(DIDEs)with constant delays,primarily due to their low regularity at delayinduced breaking points.In this paper,a DNN method that combines multi-task learning(MTL)which is proposed to solve both the forward and inverse problems of DIDEs.The core idea of this approach is to divide the original equation into multiple tasks based on the delay,using auxiliary outputs to represent the integral terms,followed by the use of MTL to seamlessly incorporate the properties at the breaking points into the loss function.Furthermore,given the increased training dificulty associated with multiple tasks and outputs,we employ a sequential training scheme to reduce training complexity and provide reference solutions for subsequent tasks.This approach significantly enhances the approximation accuracy of solving DIDEs with DNNs,as demonstrated by comparisons with traditional DNN methods.We validate the effectiveness of this method through several numerical experiments,test various parameter sharing structures in MTL and compare the testing results of these structures.Finally,this method is implemented to solve the inverse problem of nonlinear DIDE and the results show that the unknown parameters of DIDE can be discovered with sparse or noisy data.展开更多
In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error...In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.展开更多
An equation of state(EOS)was obtained that accurately describes the thermodynamics of the system H_(2)O–CO_(2) at temperatures of 50–350°C and pressures of 0.2–3.5 kbar.The equation is based on experimental da...An equation of state(EOS)was obtained that accurately describes the thermodynamics of the system H_(2)O–CO_(2) at temperatures of 50–350°C and pressures of 0.2–3.5 kbar.The equation is based on experimental data on the compositions of the coexisting liquid and gas phases and the Van Laar model,within which the values of the Van Laar parameters A12 and A21 were found for each experimental P-T point.For the resulting sets A12(P,T),A21(P,T),approximation formulas describing the dependences of these quantities on temperature and pressure were found and the parameters contained in the formulas were fitted.This two-stage approach made it possible to obtain an adequate thermodynamic description of the system,which allows,in addition to determining the phase state of the system(homogeneous or heterogeneous),to calculate the excess free energy of mixing of H_(2)O and CO_(2),the activities of H_(2)O and CO_(2),and other thermodynamic characteristics of the system.The possibility of such calculations creates the basis for using the obtained EOS in thermodynamic models of more complicated fluid systems in P-T conditions of the middle and upper crust.These fluids play an important role in many geological processes including the transport of ore matter and forming hydrothermal ore deposits,in particular,the most of the world’s gold deposits.The knowledge of thermodynamics of these fluids is important in the technology of drilling oil and gas wells.In particular,this concerns the prevention of precipitation of solid salts in the well.展开更多
This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ...This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ^(N)with N≥1.展开更多
基金Supported by NSFC(No.12101482)the Natural Science Foundation of Shaanxi Province,China(No.2018JQ1052)。
文摘In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence,asymptotic behavior and blow-up of solutions with initial energy J(u_(0))≤d.Moreover,we estimate the upper bound of the blow-up time for J(u_(0))≤0.
基金Supported by the National Natural Science Foundation of China(12001074)the Research Innovation Program of Graduate Students in Hunan Province(CX20220258)+1 种基金the Research Innovation Program of Graduate Students of Central South University(1053320214147)the Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110025)。
文摘This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.
基金Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government's Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
文摘In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11961059,1210502)the University Innovation Project of Gansu Province(Grant No.2023B-062)the Gansu Province Basic Research Innovation Group Project(Grant No.23JRRA684).
文摘The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and existence of uniform attractor under some suitable assumptions on the nonlinear term g(u),the nonlinear damping f(u_(t))and the external force h(x,t).Specifically,the asymptotic compactness of the semigroup is verified by the energy reconstruction method.
基金supported by the National Natural Science Foundation of China(12401482)the second author was supported by the National Natural Science Foundation of China(12371371,12261160361,11971366)supported by the Open Research Fund of Hubei Key Laboratory of Computational Science,Wuhan University.
文摘A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).
基金The Natural Science Foundation of Xinjiang Uygur Autonomous Region of China“RBF-Hermite difference scheme for the time-fractional kdv-Burgers equation”(2024D01C43)。
文摘In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is developed using the trigonometric scheme,which is based on zero,first,and second moments,and the direct discontinuous Galerkin(DDG)flux is used to discretize the diffusion term.Moreover,the DDG method directly applies the weak form of the parabolic equation to each computational cell,which can better capture the characteristics of the solution,especially the discontinuous solution.Meanwhile,the third-order TVD-Runge-Kutta method is applied for temporal discretization.Finally,the effectiveness and stability of the method constructed in this paper are evaluated through numerical tests.
基金supported by the Science and Technology on Reactor System Design Technology Laboratory(No.LRSDT12023108)supported in part by the Chongqing Postdoctoral Science Foundation(No.cstc2021jcyj-bsh0252)+2 种基金the National Natural Science Foundation of China(No.12005030)Sichuan Province to unveil the list of marshal industry common technology research projects(No.23jBGOV0001)Special Program for Stabilizing Support to Basic Research of National Basic Research Institutes(No.WDZC-2023-05-03-05).
文摘The neutron diffusion equation plays a pivotal role in nuclear reactor analysis.Nevertheless,employing the physics-informed neural network(PINN)method for its solution entails certain limitations.Conventional PINN approaches generally utilize a fully connected network(FCN)architecture that is susceptible to overfitting,training instability,and gradient vanishing as the network depth increases.These challenges result in accuracy bottlenecks in the solution.In response to these issues,the residual-based resample physics-informed neural network(R2-PINN)is proposed.It is an improved PINN architecture that replaces the FCN with a convolutional neural network with a shortcut(S-CNN).It incorporates skip connections to facilitate gradient propagation between network layers.Additionally,the incorporation of the residual adaptive resampling(RAR)mechanism dynamically increases the number of sampling points.This,in turn,enhances the spatial representation capabilities and overall predictive accuracy of the model.The experimental results illustrate that our approach significantly improves the convergence capability of the model and achieves high-precision predictions of the physical fields.Compared with conventional FCN-based PINN methods,R 2-PINN effectively overcomes the limitations inherent in current methods.Thus,it provides more accurate and robust solutions for neutron diffusion equations.
基金Supported by the Korea Health Technology R&D Project through the Korea Health Industry Development Institute(KHIDI),funded by the Ministry of Health&Welfare,Republic of Korea(No.HR20C0026)the National Research Foundation of Korea(NRF)(No.RS-2023-00247504)the Patient-Centered Clinical Research Coordinating Center,funded by the Ministry of Health&Welfare,Republic of Korea(No.HC19C0276).
文摘AIM:To build a functional generalized estimating equation(GEE)model to detect glaucomatous visual field progression and compare the performance of the proposed method with that of commonly employed algorithms.METHODS:Totally 716 eyes of 716 patients with primary open angle glaucoma(POAG)with at least 5 reliable 24-2 test results and 2y of follow-up were selected.The functional GEE model was used to detect perimetric progression in the training dataset(501 eyes).In the testing dataset(215 eyes),progression was evaluated the functional GEE model,mean deviation(MD)and visual field index(VFI)rates of change,Advanced Glaucoma Intervention Study(AGIS)and Collaborative Initial Glaucoma Treatment Study(CIGTS)scores,and pointwise linear regression(PLR).RESULTS:The proposed method showed the highest proportion of eyes detected as progression(54.4%),followed by the VFI rate(34.4%),PLR(23.3%),and MD rate(21.4%).The CIGTS and AGIS scores had a lower proportion of eyes detected as progression(7.9%and 5.1%,respectively).The time to detection of progression was significantly shorter for the proposed method than that of other algorithms(adjusted P≤0.019).The VFI rate displayed moderate pairwise agreement with the proposed method(k=0.47).CONCLUSION:The functional GEE model shows the highest proportion of eyes detected as perimetric progression and the shortest time to detect perimetric progression in patients with POAG.
基金supported by the National Natural Science Foundation of China(Nos.12375310,118750356,and 62006110)Graduate Research and Innovation Projects of Hunan Province(CX20230964).
文摘Physics-informed neural networks(PINNs)are vital for machine learning and exhibit significant advantages when handling complex physical problems.The PINN method can rapidly predict ^(220)Rn progeny concentration and is very important for regulating and measuring this property.To construct a PINN model,training data are typically preprocessed;however,this approach changes the physical characteristics of the data,with the preprocessed data potentially no longer directly conforming to the original physical equations.As a result,the original physical equations cannot be directly employed in the PINN.Consequently,an effective method for transforming physical equations is crucial for accurately constraining PINNs to model the ^(220)Rn progeny concentration prediction.This study presents an equation adaptation approach for neural networks,which is designed to improve prediction of ^(220)Rn progeny concentration.Five neural network models based on three architectures are established:a classical network,a physics-informed network without equation adaptation,and a physics-informed network with equation adaptation.The transport equation of the ^(220)Rn progeny concentration is transformed via equation adaption and integrated with the PINN model.The compatibility and robustness of the model with equation adaption is then analyzed.The results show that PINNs with equation adaption converge consistently with classical neural networks in terms of the training and validation loss and achieve the same level of prediction accuracy.This outcome indicates that the proposed method can be integrated into the neural network architecture.Moreover,the prediction performance of classical neural networks declines significantly when interference data are encountered,whereas the PINNs with equation adaption exhibit stable prediction accuracy.This performance demonstrates that the proposed method successfully harnesses the constraining power of physical equations,significantly enhancing the robustness of the resultant PINN models.Thus,the use of a physics-informed network with equation adaption can guarantee accurate prediction of ^(220)Rn progeny concentration.
基金Supported by the National Key Research and Development Program of China(No.2023YFC3008200)the Independent Research Project of Southern Marine Science and Engineering Guangdong Laboratory(Zhuhai)(No.SML2022SP505)。
文摘Physics-informed neural networks(PINNs),as a novel artificial intelligence method for solving partial differential equations,are applicable to solve both forward and inverse problems.This study evaluates the performance of PINNs in solving the temperature diffusion equation of the seawater across six scenarios,including forward and inverse problems under three different boundary conditions.Results demonstrate that PINNs achieved consistently higher accuracy with the Dirichlet and Neumann boundary conditions compared to the Robin boundary condition for both forward and inverse problems.Inaccurate weighting of terms in the loss function can reduce model accuracy.Additionally,the sensitivity of model performance to the positioning of sampling points varied between different boundary conditions.In particular,the model under the Dirichlet boundary condition exhibited superior robustness to variations in point positions during the solutions of inverse problems.In contrast,for the Neumann and Robin boundary conditions,accuracy declines when points were sampled from identical positions or at the same time.Subsequently,the Argo observations were used to reconstruct the vertical diffusion of seawater temperature in the north-central Pacific for the applicability of PINNs in the real ocean.The PINNs successfully captured the vertical diffusion characteristics of seawater temperature,reflected the seasonal changes of vertical temperature under different topographic conditions,and revealed the influence of topography on the temperature diffusion coefficient.The PINNs were proved effective in solving the temperature diffusion equation of seawater with limited data,providing a promising technique for simulating or predicting ocean phenomena using sparse observations.
基金partially supported by the National Natural Science Foundation of China(Grant No.12071073)financial support by the Jiangsu Provincial Scientific Research Center of Applied Mathematics(Grant No.BK20233002).
文摘The strong convergence of an explicit full-discrete scheme is investigated for the stochastic Burgers-Huxley equation driven by additive space-time white noise,which possesses both Burgers-type and cubic nonlinearities.To discretize the continuous problem in space,we utilize a spectral Galerkin method.Subsequently,we introduce a nonlinear-tamed exponential integrator scheme,resulting in a fully discrete scheme.Within the framework of semigroup theory,this study provides precise estimations of the Sobolev regularity,L^(∞) regularity in space,and Hölder continuity in time for the mild solution,as well as for its semi-discrete and full-discrete approximations.Building upon these results,we establish moment boundedness for the numerical solution and obtain strong convergence rates in both spatial and temporal dimensions.A numerical example is presented to validate the theoretical findings.
基金Under the auspices of the National Natural Science Foundation of China(No.42371222,41971167)Fundamental Scientific Research Funds of Central China Normal University(No.CCNU24ZZ120)。
文摘Owing to intensified globalization and informatization,the structures of the urban scale hierarchy and urban networks between cities have become increasingly intertwined,resulting in different spatial effects.Therefore,this paper analyzes the spatial interaction between urban scale hierarchy and urban networks in China from 2019 to 2023,drawing on Baidu migration data and employing a spatial simultaneous equation model.The results reveal a significant positive spatial correlation between cities with higher hierarchy and those with greater network centrality.Within a static framework,we identify a positive interaction between urban scale hierarchy and urban network centrality,while their spatial cross-effects manifest as negative neighborhood interactions based on geographical distance and positive cross-scale interactions shaped by network connections.Within a dynamic framework,changes in urban scale hierarchy and urban networks are mutually reinforcing,thereby widening disparities within the urban hierarchy.Furthermore,an increase in a city’s network centrality had a dampening effect on the population growth of neighboring cities and network-connected cities.This study enhances understanding of the spatial organisation of urban systems and offers insights for coordinated regional development.
基金supported by the National Natural Science Foundation of China(Grant No.11571181)by the Natural Science Foundation of Jiangsu Province(Grant No.BK20171454).
文摘In this paper,we propose and analyze two second-order accurate finite difference schemes for the one-dimensional heat equation with concentrated capacity on a computa-tional domain=[a,b].We first transform the target equation into the standard heat equation on the domain excluding the singular point equipped with an inner interface matching(IIM)condition on the singular point x=ξ∈(a,b),then adopt Taylor’s ex-pansion to approximate the IIM condition at the singular point and apply second-order finite difference method to approximate the standard heat equation at the nonsingular points.This discrete procedure allows us to choose different grid sizes to partition the two sub-domains[a,ξ]and[ξ,b],which ensures that x=ξ is a grid point,and hence the pro-posed schemes can be generalized to the heat equation with more than one concentrated capacities.We prove that the two proposed schemes are uniquely solvable.And through in-depth analysis of the local truncation errors,we rigorously prove that the two schemes are second-order accurate both in temporal and spatial directions in the maximum norm without any constraint on the grid ratio.Numerical experiments are carried out to verify our theoretical conclusions.
文摘This paper deals with the numerical solutions of two-dimensional(2D)semi-linear reaction-diffusion equations(SLRDEs)with piecewise continuous argument(PCA)in reaction term.A high-order compact difference method called Ⅰ-type basic scheme is developed for solving the equations and it is proved under the suitable conditions that this method has the computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4)),where τ,h_(x )and h_(y) are the calculation stepsizes of the method in t-,x-and y-direction,respectively.With the above method and Newton linearized technique,a Ⅱ-type basic scheme is also suggested.Based on the both basic schemes,the corresponding Ⅰ-and Ⅱ-type alternating direction implicit(ADI)schemes are derived.Finally,with a series of numerical experiments,the computational accuracy and efficiency of the four numerical schemes are further illustrated.
基金supported in part by the National Natural Science Foundation of China(No.52467008)Gansu Provincial Depatment of Education Youth Doctoral Suppo Project(2024QB-051).
文摘Addressing the limitations of inadequate stochastic disturbance characterization during wind turbine degradation processes that result in constrained modeling accuracy,replacement-based maintenance practices that deviate from actual operational conditions,and static maintenance strategies that fail to adapt to accelerated deterioration trends leading to suboptimal remaining useful life utilization,this study proposes a Time-Based Incomplete Maintenance(TBIM)strategy incorporating reliability constraints through stochastic differential equations(SDE).By quantifying stochastic interference via Brownian motion terms and characterizing nonlinear degradation features through state influence rate functions,a high-precision SDE degradation model is constructed,achieving 16%residual reduction compared to conventional ordinary differential equation(ODE)methods.The introduction of age reduction factors and failure rate growth factors establishes an incomplete maintenance mechanism that transcends traditional“as-good-as-new”assumptions,with the TBIM model demonstrating an additional 8.5%residual reduction relative to baseline SDE approaches.A dynamic maintenance interval optimization model driven by dual parameters—preventive maintenance threshold R_(p) and replacement threshold R_(r)—is designed to achieve synergistic optimization of equipment reliability and maintenance economics.Experimental validation demonstrates that the optimized TBIM extends equipment lifespan by 4.4%and reducesmaintenance costs by 4.16%at R_(p)=0.80,while achieving 17.2%lifespan enhancement and 14.6%cost reduction at R_(p)=0.90.This methodology provides a solution for wind turbine preventive maintenance that integrates condition sensitivity with strategic foresight.
基金Supported by National Natural Science Foundation of China(12101482)Postdoctoral Science Foundation of China(2022M722604)+2 种基金General Project of Science and Technology of Shaanxi Province(2023-YBSF-372)The Natural Science Foundation of Shaan Xi Province(2023-JCQN-0016)Shannxi Mathmatical Basic Science Research Project(23JSQ042)。
文摘In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondly,the existence and uniqueness of local solutions are proved by the Sobolev embedding theorem and the comparison principle.Finally,according to the relevant research data and contents of red fire ants,the diffusion area and nest number of red fire ants were simulated without external disturbance.This paper mainly simulates the early diffusion process of red fire ants.In the early diffusion stage,red fire ants grow slowly and then spread over a large area after reaching a certain number.
文摘Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay differential equations(DDEs)and delay integrodifferential equations(DIDEs)with constant delays,primarily due to their low regularity at delayinduced breaking points.In this paper,a DNN method that combines multi-task learning(MTL)which is proposed to solve both the forward and inverse problems of DIDEs.The core idea of this approach is to divide the original equation into multiple tasks based on the delay,using auxiliary outputs to represent the integral terms,followed by the use of MTL to seamlessly incorporate the properties at the breaking points into the loss function.Furthermore,given the increased training dificulty associated with multiple tasks and outputs,we employ a sequential training scheme to reduce training complexity and provide reference solutions for subsequent tasks.This approach significantly enhances the approximation accuracy of solving DIDEs with DNNs,as demonstrated by comparisons with traditional DNN methods.We validate the effectiveness of this method through several numerical experiments,test various parameter sharing structures in MTL and compare the testing results of these structures.Finally,this method is implemented to solve the inverse problem of nonlinear DIDE and the results show that the unknown parameters of DIDE can be discovered with sparse or noisy data.
文摘In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.
基金funded by the Research program FMUW-2021-0002 of the IPGG RAS.
文摘An equation of state(EOS)was obtained that accurately describes the thermodynamics of the system H_(2)O–CO_(2) at temperatures of 50–350°C and pressures of 0.2–3.5 kbar.The equation is based on experimental data on the compositions of the coexisting liquid and gas phases and the Van Laar model,within which the values of the Van Laar parameters A12 and A21 were found for each experimental P-T point.For the resulting sets A12(P,T),A21(P,T),approximation formulas describing the dependences of these quantities on temperature and pressure were found and the parameters contained in the formulas were fitted.This two-stage approach made it possible to obtain an adequate thermodynamic description of the system,which allows,in addition to determining the phase state of the system(homogeneous or heterogeneous),to calculate the excess free energy of mixing of H_(2)O and CO_(2),the activities of H_(2)O and CO_(2),and other thermodynamic characteristics of the system.The possibility of such calculations creates the basis for using the obtained EOS in thermodynamic models of more complicated fluid systems in P-T conditions of the middle and upper crust.These fluids play an important role in many geological processes including the transport of ore matter and forming hydrothermal ore deposits,in particular,the most of the world’s gold deposits.The knowledge of thermodynamics of these fluids is important in the technology of drilling oil and gas wells.In particular,this concerns the prevention of precipitation of solid salts in the well.
基金Supported by National Science Foundation of China(11971027,12171497)。
文摘This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ^(N)with N≥1.
