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Physics-constrained graph neural networks for solving adjoint equations 认领 引用
1
作者 Jinpeng Xiang Shufang Song +2 位作者 Wenbo Cao Kuijun Zuo Weiwei Zhang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2026年第1期178-191,共14页
The adjoint method is widely used in gradient-based optimization with high-dimensional design variables.However,the cost of solving the adjoint equations in each iteration is comparable to that of solving the flow fie... The adjoint method is widely used in gradient-based optimization with high-dimensional design variables.However,the cost of solving the adjoint equations in each iteration is comparable to that of solving the flow field,resulting in expensive computational costs.To improve the efficiency of solving adjoint equations,we propose a physics-constrained graph neural networks for solving adjoint equations,named ADJ-PCGN.ADJ-PCGN establishes a mapping relationship between flow characteristics and adjoint vector based on data,serving as a replacement for the computationally expensive numerical solution of adjoint equations.A physics-based graph structure and message-passing mechanism are designed to endow its strong fitting and generalization capabilities.Taking transonic drag reduction and maximum lift-drag ratio of the airfoil as examples,results indicate that ADJ-PCGN attains a similar optimal shape as the classical direct adjoint loop method.In addition,ADJ-PCGN demonstrates strong generalization capabilities across different mesh topologies,mesh densities,and out-of-distribution conditions.It holds the potential to become a universal model for aerodynamic shape optimization involving states,geometries,and meshes. 展开更多
关键词 Adjoint method Deep learning Graph neural network Physics-constrained Fast aerodynamic analysis
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A physics-constrained neural network for predicting excavationinduced ground surface settlement in clay 认领 引用 被引量：2
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作者 Yifeng Yang Shaoming Liao +3 位作者 Bak Koon Teoh Zewen Li Mengbo Liu Lisheng Chen 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2025年第5期2665-2681,共17页
Accurate prediction of ground surface settlement(GSS)adjacent to an excavation is important to prevent potential damage to the surrounding environment.Previous studies have extensively delved into this topic but all u... Accurate prediction of ground surface settlement(GSS)adjacent to an excavation is important to prevent potential damage to the surrounding environment.Previous studies have extensively delved into this topic but all under the limitations of either imprecise theories or insufficient data.In the present study,we proposed a physics-constrained neural network(PhyNN)for predicting excavation-induced GSS to fully integrate the theory of elasticity with observations and make full use of the strong fitting ability of neural networks(NNs).This model incorporates an analytical solution as an additional regularization term in the loss function to guide the training of NN.Moreover,we introduced three trainable parameters into the analytical solution so that it can be adaptively modified during the training process.The performance of the proposed PhyNN model is verified using data from a case study project.Results show that our PhyNN model achieves higher prediction accuracy,better generalization ability,and robustness than the purely data-driven NN model when confronted with data containing noise and outliers.Remarkably,by incorporating physical constraints,the admissible solution space of PhyNN is significantly narrowed,leading to a substantial reduction in the need for the amount of training data.The proposed PhyNN can be utilized as a general framework for integrating physical constraints into data-driven machine-learning models. 展开更多
关键词 Data-physics collaboratively driven Excavation Ground surface settlement(GSS) Physics-constrained loss function Robustness Generalization ability
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Physics-constrained deep learning for data assimilation of subsurface transport 认领 引用 被引量：8
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作者 Haiyi Wu Rui Qiao 《Energy and AI》 EI 2021年第1期104-114,共11页
Data assimilation of subsurface transport is important in many energy and environmental applications,but its solution is typically challenging.In this work,we build physics-constrained deep learning models to predict ... Data assimilation of subsurface transport is important in many energy and environmental applications,but its solution is typically challenging.In this work,we build physics-constrained deep learning models to predict the full-scale hydraulic conductivity,hydraulic head,and concentration fields in porous media from sparse measure-ment of these observables.The model is developed based on convolutional neural networks with the encoding-decoding process.The model is trained by minimizing a loss function that incorporates residuals of governing equations of subsurface transport instead of using labeled data.Once trained,the model predicts the unknown conductivity,hydraulic head,and concentration fields with an average relative error<10%when the data of these observables is available at 12.2%of the grid points in the porous media.The model has a robust predictive performance for porous media with different conductivities and transport under different Péclet number(0.5<Pe<500).We also quantify the predictive uncertainty of the model and evaluate the reliability of its prediction by incorporating a variational parameter into the model. 展开更多
关键词 Physics-constrained deep learning Data assimilation Subsurface transport Convolutional encoder-decoder
Physics-constrained graph modeling for building thermal dynamics 认领 引用 被引量：2
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作者 Ziyao Yang Amol D.Gaidhane +4 位作者 Ján Drgoňa Vikas Chandan Mahantesh M.Halappanavar Frank Liu Yu Cao 《Energy and AI》 EI 2024年第2期150-157,共8页
In this paper,we propose a graph model embedded with compact physical equations for modeling the thermal dynamics of buildings.The principles of heat flow across various components in the building,such as walls and do... In this paper,we propose a graph model embedded with compact physical equations for modeling the thermal dynamics of buildings.The principles of heat flow across various components in the building,such as walls and doors,fit the message-passing strategy used by Graph Neural networks(GNNs).The proposed method is to represent the multi-zone building as a graph,in which only zones are considered as nodes,and any heat flow between zones is modeled as an edge based on prior knowledge of the building structure.Furthermore,the thermal dynamics of these components are described by compact models in the graph.GNNs are further employed to train model parameters from collected data.During model training,our proposed method enforces physical constraints(e.g.,zone sizes and connections)on model parameters and propagates the penalty in the loss function of GNN.Such constraints are essential to ensure model robustness and interpretability.We evaluate the effectiveness of the proposed modeling approach on a realistic dataset with multiple zones.The results demonstrate a satisfactory accuracy in the prediction of multi-zone temperature.Moreover,we illustrate that the new model can reliably learn hidden physical parameters with incomplete data. 展开更多
关键词 Physics-constrained learning Graph Neural Networks Compact model Building thermal dynamics
An intelligent injection-production model based on graph connection element driven by data and physics 认领 引用
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作者 ZHAO Hui XU Yunfeng +3 位作者 JIA Deli RAO Xiang ZHOU Yuhui MENG Fankun 《Petroleum Exploration and Development》 SCIE 2026年第3期832-843,共12页
To address the challenges of connectivity characterization,dynamic prediction efficiency,and real-time optimization in complex reservoir injection-production systems,this study proposes a physics-and deep learning-int... To address the challenges of connectivity characterization,dynamic prediction efficiency,and real-time optimization in complex reservoir injection-production systems,this study proposes a physics-and deep learning-integrated intelligent injection-production modeling framework based on the graph connection element method.The method adopts the connection element method as the physical foundation and constructs a non-Euclidean graph representation to describe interwell connectivity,enabling characterization of the physical topology and dynamic interactions within the well pattern system.By incorporating an adaptive attention mechanism into a graph convolutional network and embedding time-dependent node attributes,a physics-consistent reservoir performance prediction model is developed.Furthermore,a hybrid optimization strategy integrating differential evolution and particle swarm optimization is employed to establish an intelligent optimization framework taking the economic net present value as the objective.Based on rapid prediction of injection and production behaviors,the proposed approach enables optimization of injection-production parameters and improvement of reservoir development economics.Field applications demonstrate that the proposed intelligent injection-production model based on graph connection element accurately reproduces water-cut behavior of producers and provides quantitative uncertainty estimation.It achieves rapid history matching and dynamic response forecasting for complex injection-production systems,exhibiting high accuracy and stability.It enables optimization of production strategies with NPV as the objective,demonstrating strong engineering applicability and scalability. 展开更多
关键词 non-Euclidean space graph neural networks graph connection element physics-constrained learning surrogate model differential evolution-particle swarm optimization production optimization
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Physics-informed machine learning for enhanced prediction of condensation heat transfer 认领 引用 被引量：3
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作者 Haeun Lee Cheonkyu Lee Hyoungsoon Lee 《Energy and AI》 EI CSCD 2025年第2期112-124,共13页
Developing a universal model for predicting condensation heat transfer coefficients remains challenging,particularly for steam–non-condensable gas mixtures,owing to the intricate nonlinear interactions between multip... Developing a universal model for predicting condensation heat transfer coefficients remains challenging,particularly for steam–non-condensable gas mixtures,owing to the intricate nonlinear interactions between multiphase flow,heat,and mass transfer phenomena.Data-driven machine learning(ML)shows promise in efficiently and accurately predicting condensation heat transfer coefficients.Research has employed various ML methods—multilayer perceptron neural networks,convolutional-neural-network–based DenseNet,backpropagation neural networks,etc.—to investigate steam condensation with non-condensable gases.However,these exhibit limited extrapolation ability and heavily rely on data quantity owing to their black-box nature.This study proposes a physics-informed ML model that combines physical constraints derived from the modified Nusselt model with conventional data-driven ML techniques.The model's predictive performance is evaluated using a comprehensive database(879 datapoints from 13 studies).A physics-constrained and eight data-driven ML methods are assessed.The results reveal that the physics-constrained approach combined with XGBoost significantly outperforms conventional ML methods on extrapolation datasets(199 datapoints from 3 studies),achieving a mean absolute percentage error of 11.22%,which is approximately half that of the best-performing fully data-driven model at 21.63%.The model demonstrates consistent and reliable performance across diverse datasets,making it an effective tool for predicting heat transfer coefficients in steam–non-condensable gas mixtures.By deepening the understanding of the underlying physical processes,the proposed model supports the development of precise and efficient engineering solutions for condensation heat transfer. 展开更多
关键词 Physics-constrained Deep learning Heat transfer Condensation Nusselt model XGBoost
Learning Invariant Representation of Multiscale Hyperelastic Constitutive Law from Sparse Experimental Data 认领 引用 被引量：1
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作者 Rui He Junzhi Cui +2 位作者 Zihao Yang Jieqiong Zhang Xiaofei Guan 《Communications in Computational Physics》 SCIE 2023年第7期392-417,共26页
Constitutive modeling of heterogeneous hyperelastic materials is still a challenge due to their complex and variable microstructures.We propose a multiscale datadriven approach with a hierarchical learning strategy fo... Constitutive modeling of heterogeneous hyperelastic materials is still a challenge due to their complex and variable microstructures.We propose a multiscale datadriven approach with a hierarchical learning strategy for the discovery of a generic physics-constrained anisotropic constitutive model for the heterogeneous hyperelastic materials.Based on the sparse multiscale experimental data,the constitutive artificial neural networks for hyperelastic component phases containing composite interfaces are established by the particle swarm optimization algorithm.A microscopic finite element coupled constitutive artificial neural networks solver is introduced to obtain the homogenized stress-stretch relation of heterogeneous materials with different microstructures.And a dense stress-stretch relation dataset is generated by training a neural network through the FE results.Further,a generic invariant representation of strain energy function(SEF)is proposed with a parameter set being implicitly expressed by artificial neural networks(SANN),which describes the hyperelastic properties of heterogeneous materials with different microstructures.A convexity constraint is imposed on the SEF to ensure that the multiscale constitutive model is physically relevant,and the ℓ1 regularization combined with thresholding is introduced to the loss function of SANN to improve the interpretability of this model.Finally,the multiscale model is hierarchically trained,cross-validated and tested using the experimental data of cord-rubber composite materials with different microstructures.The proposed multiscale model provides a convenient and general methodology for constitutive modeling of heterogeneous hyperelastic materials. 展开更多
关键词 Heterogeneous hyperelastic materials data-driven approach multiscale generic constitutive model physics-constrained
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