In the generation and propagation of nonlinear Rossby solitary waves within the atmosphere and ocean,topography occupies a pivotal role.This paper focuses on elucidating the impact of topography on such Rossby solitar...In the generation and propagation of nonlinear Rossby solitary waves within the atmosphere and ocean,topography occupies a pivotal role.This paper focuses on elucidating the impact of topography on such Rossby solitary waves.Utilizing the perturbation expansion method and spatialtemporal transformations,we derive the Korteweg–de Vries and modified Korteweg–de Vries equation(Gardner equation)governing the amplitude of nonlinear Rossby waves.A fundamental issue addressed herein is a Sturm–Liouville-type ordinary differential equation characterized by variable coefficients and fixed boundary conditions.To numerically solve the derived Korteweg–de Vries and modified Korteweg–de Vries equations,we employ a physical-informed neural network.Both qualitative and quantitative analyses are conducted to discuss the influences of topography andβeffects,respectively.展开更多
The Stokes production coefficient(E_(6))constitutes a critical parameter within the Mellor-Yamada type(MY-type)Langmuir turbulence(LT)parameterization schemes,significantly affecting the simulation of turbulent kineti...The Stokes production coefficient(E_(6))constitutes a critical parameter within the Mellor-Yamada type(MY-type)Langmuir turbulence(LT)parameterization schemes,significantly affecting the simulation of turbulent kinetic energy,turbulent length scale,and vertical diffusivity coefficient for turbulent kinetic energy in the upper ocean.However,the accurate determination of its value remains a pressing scientific challenge.This study adopted an innovative approach by leveraging deep learning technology to address this challenge of inferring the E_(6).Through the integration of the information of the turbulent length scale equation into a physical-informed neural network(PINN),we achieved an accurate and physically meaningful inference of E_(6).Multiple cases were examined to assess the feasibility of PINN in this task,revealing that under optimal settings,the average mean squared error of the E_(6) inference was only 0.01,attesting to the effectiveness of PINN.The optimal hyperparameter combination was identified using the Tanh activation function,along with a spatiotemporal sampling interval of 1 s and 0.1 m.This resulted in a substantial reduction in the average bias of the E_(6) inference,ranging from O(10^(1))to O(10^(2))times compared with other combinations.This study underscores the potential application of PINN in intricate marine environments,offering a novel and efficient method for optimizing MY-type LT parameterization schemes.展开更多
Kirchhoff integral migration imaging is widely used in industrial production due to its advantages of not being limited by observation systems,good target imaging effects,and high computational efficiency.Vertical tra...Kirchhoff integral migration imaging is widely used in industrial production due to its advantages of not being limited by observation systems,good target imaging effects,and high computational efficiency.Vertical transversely isotropic(VTI)media,as a typical anisotropic media,has always been a primary focus of anisotropic migration imaging research.We focus on the problems of low accuracy and efficiency in travel-time calculations associated with conventional Kirchhoff integral migration for VTI media.A travel-time calculation method based on physical-informed neural network(PINN)for VTI media is introduced into the process of Kirchhoff integral migration imaging.Model experiments and field data processing have shown that the travel-time calculation based on PINN can significantly improve both the accuracy and efficiency when compared to traditional finite difference algorithms,there-by enabling high-precision Kirchhoff integral migration imaging for VTI media.展开更多
With the rapid development of deep learning neural networks,new solutions have emerged for addressing fluid flow problems in porous media.Combining data-driven approaches with physical constraints has become a hot res...With the rapid development of deep learning neural networks,new solutions have emerged for addressing fluid flow problems in porous media.Combining data-driven approaches with physical constraints has become a hot research direction,with physics-informed neural networks(PINNs) being the most popular hybrid model.PINNs have gained widespread attention in subsurface fluid flow simulations due to their low computational resource requirements,fast training speeds,strong generalization capabilities,and broad applicability.Despite success in homogeneous settings,standard PINNs face challenges in accurately calculating flux between irregular Eulerian cells with disparate properties and capturing global field influences on local cells.This limits their suitability for heterogeneous reservoirs and the irregular Eulerian grids frequently used in reservoir.To address these challenges,this study proposes a physics-informed graph neural network(PIGNN) model.The PIGNN model treats the entire field as a whole,integrating information from neighboring grids and physical laws into the solution for the target grid,thereby improving the accuracy of solving partial differential equations in heterogeneous and Eulerian irregular grids.The optimized model was applied to pressure field prediction in a spatially heterogeneous reservoir,achieving an average L_(2) error and R_(2) score of 6.710×10^(-4)and 0.998,respectively,which confirms the effectiveness of model.Compared to the conventional PINN model,the average L_(2) error was reduced by 76.93%,the average R_(2) score increased by 3.56%.Moreover,evaluating robustness,training the PIGNN model using only 54% and 76% of the original data yielded average relative L_(2) error reductions of 58.63% and 56.22%,respectively,compared to the PINN model.These results confirm the superior performance of this approach compared to PINN.展开更多
Recent advances in deep learning have expanded new possibilities for fluid flow simulation in petroleum reservoirs.However,the predominant approach in existing research is to train neural networks using high-fidelity ...Recent advances in deep learning have expanded new possibilities for fluid flow simulation in petroleum reservoirs.However,the predominant approach in existing research is to train neural networks using high-fidelity numerical simulation data.This presents a significant challenge because the sole source of authentic wellbore production data for training is sparse.In response to this challenge,this work introduces a novel architecture called physics-informed neural network based on domain decomposition(PINN-DD),aiming to effectively utilize the sparse production data of wells for reservoir simulation with large-scale systems.To harness the capabilities of physics-informed neural networks(PINNs)in handling small-scale spatial-temporal domain while addressing the challenges of large-scale systems with sparse labeled data,the computational domain is divided into two distinct sub-domains:the well-containing and the well-free sub-domain.Moreover,the two sub-domains and the interface are rigorously constrained by the governing equations,data matching,and boundary conditions.The accuracy of the proposed method is evaluated on two problems,and its performance is compared against state-of-the-art PINNs through numerical analysis as a benchmark.The results demonstrate the superiority of PINN-DD in handling large-scale reservoir simulation with limited data and show its potential to outperform conventional PINNs in such scenarios.展开更多
Recent advances in deep neural networks have shed new light on physics,engineering,and scientific computing.Reconciling the data-centered viewpoint with physical simulation is one of the research hotspots.The physicsi...Recent advances in deep neural networks have shed new light on physics,engineering,and scientific computing.Reconciling the data-centered viewpoint with physical simulation is one of the research hotspots.The physicsinformedneural network(PINN)is currently the most general framework,which is more popular due to theconvenience of constructing NNs and excellent generalization ability.The automatic differentiation(AD)-basedPINN model is suitable for the homogeneous scientific problem;however,it is unclear how AD can enforce fluxcontinuity across boundaries between cells of different properties where spatial heterogeneity is represented bygrid cells with different physical properties.In this work,we propose a criss-cross physics-informed convolutionalneural network(CC-PINN)learning architecture,aiming to learn the solution of parametric PDEs with spatialheterogeneity of physical properties.To achieve the seamless enforcement of flux continuity and integration ofphysicalmeaning into CNN,a predefined 2D convolutional layer is proposed to accurately express transmissibilitybetween adjacent cells.The efficacy of the proposedmethodwas evaluated through predictions of several petroleumreservoir problems with spatial heterogeneity and compared against state-of-the-art(PINN)through numericalanalysis as a benchmark,which demonstrated the superiority of the proposed method over the PINN.展开更多
Physics-informed neural networks(PINNs)have shown considerable promise for performing numerical simulations in fluid mechanics.They provide mesh-free,end-to-end approaches by embedding physical laws into their loss fu...Physics-informed neural networks(PINNs)have shown considerable promise for performing numerical simulations in fluid mechanics.They provide mesh-free,end-to-end approaches by embedding physical laws into their loss functions.However,when addressing complex flow problems,PINNs still face some challenges such as activation saturation and vanishing gradients in deep network training,leading to slow convergence and insufficient prediction accuracy.We present physics-informed neural networks incorporating lattice Boltzmann method optimized by tanh robust weight initialization(T-PINN-LBM)to address these challenges.This approach fuses the mesoscopic lattice Boltzmann model with the automatic differentiation framework of PINNs.It also implements a tanh robust weight initialization method derived from fixed point analysis.This model effectively mitigates activation and gradient decay in deep networks,improving convergence speed and data efficiency in multiscale flow simulations.We validate the effectiveness of the model on the classical arithmetic example of lid-driven cavity flow.Compared to the traditional Xavier initialized PINN and PINN-LBM,T-PINNLBM reduces the mean absolute error(MAE)by one order of magnitude at the same network depth and maintains stable convergence in deeper networks.The results demonstrate that this model can accurately capture complex flow structures without prior data,providing a new feasible pathway for data-free driven fluid simulation.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12462021,12102205,12262025)the Central Guidance for Local Scientific and Technological Development Funding Projects(Grant No.2024ZY0117)+2 种基金the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(Grant No.NJYT23098)the Scientific Starting and the Innovative Research Team in the Universities of Inner Mongolia Autonomous Region of China(Grant No.NMGIRT2208)the National College Students Innovation and Entrepreneurship Training Program(Grant No.202410126024)。
文摘In the generation and propagation of nonlinear Rossby solitary waves within the atmosphere and ocean,topography occupies a pivotal role.This paper focuses on elucidating the impact of topography on such Rossby solitary waves.Utilizing the perturbation expansion method and spatialtemporal transformations,we derive the Korteweg–de Vries and modified Korteweg–de Vries equation(Gardner equation)governing the amplitude of nonlinear Rossby waves.A fundamental issue addressed herein is a Sturm–Liouville-type ordinary differential equation characterized by variable coefficients and fixed boundary conditions.To numerically solve the derived Korteweg–de Vries and modified Korteweg–de Vries equations,we employ a physical-informed neural network.Both qualitative and quantitative analyses are conducted to discuss the influences of topography andβeffects,respectively.
基金The National Key Research and Development Program of China under contract No.2022YFC3105002the National Natural Science Foundation of China under contract No.42176020the project from the Key Laboratory of Marine Environmental Information Technology,Ministry of Natural Resources,under contract No.2023GFW-1047.
文摘The Stokes production coefficient(E_(6))constitutes a critical parameter within the Mellor-Yamada type(MY-type)Langmuir turbulence(LT)parameterization schemes,significantly affecting the simulation of turbulent kinetic energy,turbulent length scale,and vertical diffusivity coefficient for turbulent kinetic energy in the upper ocean.However,the accurate determination of its value remains a pressing scientific challenge.This study adopted an innovative approach by leveraging deep learning technology to address this challenge of inferring the E_(6).Through the integration of the information of the turbulent length scale equation into a physical-informed neural network(PINN),we achieved an accurate and physically meaningful inference of E_(6).Multiple cases were examined to assess the feasibility of PINN in this task,revealing that under optimal settings,the average mean squared error of the E_(6) inference was only 0.01,attesting to the effectiveness of PINN.The optimal hyperparameter combination was identified using the Tanh activation function,along with a spatiotemporal sampling interval of 1 s and 0.1 m.This resulted in a substantial reduction in the average bias of the E_(6) inference,ranging from O(10^(1))to O(10^(2))times compared with other combinations.This study underscores the potential application of PINN in intricate marine environments,offering a novel and efficient method for optimizing MY-type LT parameterization schemes.
基金funded by the Open Fund of No.1 Institute of Geology and Mineral Resources of Shan-dong Province(No.2022DY03)the National Natural Sci-ence Foundation of China(Nos.42074138 and 42206195)the Wenhai Program of the ST Fund of Laoshan Labo-ratory(No.LSKJ202204803).
文摘Kirchhoff integral migration imaging is widely used in industrial production due to its advantages of not being limited by observation systems,good target imaging effects,and high computational efficiency.Vertical transversely isotropic(VTI)media,as a typical anisotropic media,has always been a primary focus of anisotropic migration imaging research.We focus on the problems of low accuracy and efficiency in travel-time calculations associated with conventional Kirchhoff integral migration for VTI media.A travel-time calculation method based on physical-informed neural network(PINN)for VTI media is introduced into the process of Kirchhoff integral migration imaging.Model experiments and field data processing have shown that the travel-time calculation based on PINN can significantly improve both the accuracy and efficiency when compared to traditional finite difference algorithms,there-by enabling high-precision Kirchhoff integral migration imaging for VTI media.
基金supported by the National Natural Science Foundation of China (No. 52274048)Beijing Natural Science Foundation (No. 3222037)。
文摘With the rapid development of deep learning neural networks,new solutions have emerged for addressing fluid flow problems in porous media.Combining data-driven approaches with physical constraints has become a hot research direction,with physics-informed neural networks(PINNs) being the most popular hybrid model.PINNs have gained widespread attention in subsurface fluid flow simulations due to their low computational resource requirements,fast training speeds,strong generalization capabilities,and broad applicability.Despite success in homogeneous settings,standard PINNs face challenges in accurately calculating flux between irregular Eulerian cells with disparate properties and capturing global field influences on local cells.This limits their suitability for heterogeneous reservoirs and the irregular Eulerian grids frequently used in reservoir.To address these challenges,this study proposes a physics-informed graph neural network(PIGNN) model.The PIGNN model treats the entire field as a whole,integrating information from neighboring grids and physical laws into the solution for the target grid,thereby improving the accuracy of solving partial differential equations in heterogeneous and Eulerian irregular grids.The optimized model was applied to pressure field prediction in a spatially heterogeneous reservoir,achieving an average L_(2) error and R_(2) score of 6.710×10^(-4)and 0.998,respectively,which confirms the effectiveness of model.Compared to the conventional PINN model,the average L_(2) error was reduced by 76.93%,the average R_(2) score increased by 3.56%.Moreover,evaluating robustness,training the PIGNN model using only 54% and 76% of the original data yielded average relative L_(2) error reductions of 58.63% and 56.22%,respectively,compared to the PINN model.These results confirm the superior performance of this approach compared to PINN.
基金funded by the National Natural Science Foundation of China(Grant No.52274048)Beijing Natural Science Foundation(Grant No.3222037)+1 种基金the CNPC 14th Five-Year Perspective Fundamental Research Project(Grant No.2021DJ2104)the Science Foundation of China University of Petroleum-Beijing(No.2462021YXZZ010).
文摘Recent advances in deep learning have expanded new possibilities for fluid flow simulation in petroleum reservoirs.However,the predominant approach in existing research is to train neural networks using high-fidelity numerical simulation data.This presents a significant challenge because the sole source of authentic wellbore production data for training is sparse.In response to this challenge,this work introduces a novel architecture called physics-informed neural network based on domain decomposition(PINN-DD),aiming to effectively utilize the sparse production data of wells for reservoir simulation with large-scale systems.To harness the capabilities of physics-informed neural networks(PINNs)in handling small-scale spatial-temporal domain while addressing the challenges of large-scale systems with sparse labeled data,the computational domain is divided into two distinct sub-domains:the well-containing and the well-free sub-domain.Moreover,the two sub-domains and the interface are rigorously constrained by the governing equations,data matching,and boundary conditions.The accuracy of the proposed method is evaluated on two problems,and its performance is compared against state-of-the-art PINNs through numerical analysis as a benchmark.The results demonstrate the superiority of PINN-DD in handling large-scale reservoir simulation with limited data and show its potential to outperform conventional PINNs in such scenarios.
基金the National Natural Science Foundation of China(No.52274048)Beijing Natural Science Foundation(No.3222037)+1 种基金the CNPC 14th Five-Year Perspective Fundamental Research Project(No.2021DJ2104)the Science Foundation of China University of Petroleum,Beijing(No.2462021YXZZ010).
文摘Recent advances in deep neural networks have shed new light on physics,engineering,and scientific computing.Reconciling the data-centered viewpoint with physical simulation is one of the research hotspots.The physicsinformedneural network(PINN)is currently the most general framework,which is more popular due to theconvenience of constructing NNs and excellent generalization ability.The automatic differentiation(AD)-basedPINN model is suitable for the homogeneous scientific problem;however,it is unclear how AD can enforce fluxcontinuity across boundaries between cells of different properties where spatial heterogeneity is represented bygrid cells with different physical properties.In this work,we propose a criss-cross physics-informed convolutionalneural network(CC-PINN)learning architecture,aiming to learn the solution of parametric PDEs with spatialheterogeneity of physical properties.To achieve the seamless enforcement of flux continuity and integration ofphysicalmeaning into CNN,a predefined 2D convolutional layer is proposed to accurately express transmissibilitybetween adjacent cells.The efficacy of the proposedmethodwas evaluated through predictions of several petroleumreservoir problems with spatial heterogeneity and compared against state-of-the-art(PINN)through numericalanalysis as a benchmark,which demonstrated the superiority of the proposed method over the PINN.
基金supported by the National Natural Science Foundation of China(Grant Nos.12474453,12174085,and 12404530).
文摘Physics-informed neural networks(PINNs)have shown considerable promise for performing numerical simulations in fluid mechanics.They provide mesh-free,end-to-end approaches by embedding physical laws into their loss functions.However,when addressing complex flow problems,PINNs still face some challenges such as activation saturation and vanishing gradients in deep network training,leading to slow convergence and insufficient prediction accuracy.We present physics-informed neural networks incorporating lattice Boltzmann method optimized by tanh robust weight initialization(T-PINN-LBM)to address these challenges.This approach fuses the mesoscopic lattice Boltzmann model with the automatic differentiation framework of PINNs.It also implements a tanh robust weight initialization method derived from fixed point analysis.This model effectively mitigates activation and gradient decay in deep networks,improving convergence speed and data efficiency in multiscale flow simulations.We validate the effectiveness of the model on the classical arithmetic example of lid-driven cavity flow.Compared to the traditional Xavier initialized PINN and PINN-LBM,T-PINNLBM reduces the mean absolute error(MAE)by one order of magnitude at the same network depth and maintains stable convergence in deeper networks.The results demonstrate that this model can accurately capture complex flow structures without prior data,providing a new feasible pathway for data-free driven fluid simulation.
