Physics-informed neural networks(PINNs)have shown remarkable prospects in solving the forward and inverse problems involving partial differential equations(PDEs).The method embeds PDEs into the neural network by calcu...Physics-informed neural networks(PINNs)have shown remarkable prospects in solving the forward and inverse problems involving partial differential equations(PDEs).The method embeds PDEs into the neural network by calculating the PDE loss at a set of collocation points,providing advantages such as meshfree and more convenient adaptive sampling.However,when solving PDEs using nonuniform collocation points,PINNs still face challenge regarding inefficient convergence of PDE residuals or even failure.In this work,we first analyze the ill-conditioning of the PDE loss in PINNs under nonuniform collocation points.To address the issue,we define volume weighting residual and propose volume weighting physics-informed neural networks(VW-PINNs).Through weighting the PDE residuals by the volume that the collocation points occupy within the computational domain,we embed explicitly the distribution characteristics of collocation points in the loss evaluation.The fast and sufficient convergence of the PDE residuals for the problems involving nonuniform collocation points is guaranteed.Considering the meshfree characteristics of VW-PINNs,we also develop a volume approximation algorithm based on kernel density estimation to calculate the volume of the collocation points.We validate the universality of VW-PINNs by solving the forward problems involving flow over a circular cylinder and flow over the NACA0012 airfoil under different inflow conditions,where conventional PINNs fail.By solving the Burgers’equation,we verify that VW-PINNs can enhance the efficiency of existing the adaptive sampling method in solving the forward problem by three times,and can reduce the relative L 2 error of conventional PINNs in solving the inverse problem by more than one order of magnitude.展开更多
Physics-informed neural networks(PINNs)are promising to replace conventional mesh-based partial tial differen-equation(PDE)solvers by offering more accurate and flexible PDE solutions.However,PINNs are hampered by the...Physics-informed neural networks(PINNs)are promising to replace conventional mesh-based partial tial differen-equation(PDE)solvers by offering more accurate and flexible PDE solutions.However,PINNs are hampered by the relatively slow convergence and the need to perform additional,potentially expensive training for new PDE parameters.To solve this limitation,we introduce LatentPINN,a framework that utilizes latent representations of the PDE parameters as additional(to the coordinates)inputs into PINNs and allows for training over the distribution of these parameters.Motivated by the recent progress on generative models,we promote using latent diffusion models to learn compressed latent representations of the distribution of PDE parameters as they act as input parameters for NN functional solutions.We use a two-stage training scheme in which,in the first stage,we learn the latent representations for the distribution of PDE parameters.In the second stage,we train a physics-informed neural network over inputs given by randomly drawn samples from the coordinate space within the solution domain and samples from the learned latent representation of the PDE parameters.Considering their importance in capturing evolving interfaces and fronts in various fields,we test the approach on a class of level set equations given,for example,by the nonlinear Eikonal equation.We share results corresponding to three Eikonal parameters(velocity models)sets.The proposed method performs well on new phase velocity models without the need for any additional training.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
For the diagnostics and health management of lithium-ion batteries,numerous models have been developed to understand their degradation characteristics.These models typically fall into two categories:data-driven models...For the diagnostics and health management of lithium-ion batteries,numerous models have been developed to understand their degradation characteristics.These models typically fall into two categories:data-driven models and physical models,each offering unique advantages but also facing limitations.Physics-informed neural networks(PINNs)provide a robust framework to integrate data-driven models with physical principles,ensuring consistency with underlying physics while enabling generalization across diverse operational conditions.This study introduces a PINN-based approach to reconstruct open circuit voltage(OCV)curves and estimate key ageing parameters at both the cell and electrode levels.These parameters include available capacity,electrode capacities,and lithium inventory capacity.The proposed method integrates OCV reconstruction models as functional components into convolutional neural networks(CNNs)and is validated using a public dataset.The results reveal that the estimated ageing parameters closely align with those obtained through offline OCV tests,with errors in reconstructed OCV curves remaining within 15 mV.This demonstrates the ability of the method to deliver fast and accurate degradation diagnostics at the electrode level,advancing the potential for precise and efficient battery health management.展开更多
This research introduces a spectrum-based physics-informed neural network(SP-PINN)model to significantly improve the accuracy of calculation of two-phase flow parameters,surpassing existing methods that have limitatio...This research introduces a spectrum-based physics-informed neural network(SP-PINN)model to significantly improve the accuracy of calculation of two-phase flow parameters,surpassing existing methods that have limitations in global and continuous data sampling.SP-PINNs address the challenges of traditional methods in terms of continuous sampling by integrating the spectral analysis and pressure correction into the Navier-Stokes(N-S)equations,enhancing the predictive accuracy especially in critical regions like gas-phase boundaries and velocity peaks.The novel introduction of a pressure-correction module within SP-PINNs mitigates prediction errors,achieving a substantial reduction to 1‰compared with the conventional physics-informed neural network(PINN)approaches.Experimental applications validate the model’s ability to accurately and rapidly predict flow parameters with different sampling time intervals,with the computation time of predicting unsampled data less than 0.01 s.Such advancements signify a 100-fold improvement over traditional DNS calculations,underscoring the model’s potential in the real-time calculation and analysis of multiphase flow dynamics.展开更多
The Internet of Things(IoT)ecosystem faces growing security challenges because it is projected to have 76.88 billion devices by 2025 and $1.4 trillion market value by 2027,operating in distributed networks with resour...The Internet of Things(IoT)ecosystem faces growing security challenges because it is projected to have 76.88 billion devices by 2025 and $1.4 trillion market value by 2027,operating in distributed networks with resource limitations and diverse system architectures.The current conventional intrusion detection systems(IDS)face scalability problems and trust-related issues,but blockchain-based solutions face limitations because of their low transaction throughput(Bitcoin:7 TPS(Transactions Per Second),Ethereum:15-30 TPS)and high latency.The research introduces MBID(Multi-Tier Blockchain Intrusion Detection)as a groundbreaking Multi-Tier Blockchain Intrusion Detection System with AI-Enhanced Detection,which solves the problems in huge IoT networks.The MBID system uses a four-tier architecture that includes device,edge,fog,and cloud layers with blockchain implementations and Physics-Informed Neural Networks(PINNs)for edge-based anomaly detection and a dual consensus mechanism that uses Honesty-based Distributed Proof-of-Authority(HDPoA)and Delegated Proof of Stake(DPoS).The system achieves scalability and efficiency through the combination of dynamic sharding and Interplanetary File System(IPFS)integration.Experimental evaluations demonstrate exceptional performance,achieving a detection accuracy of 99.84%,an ultra-low false positive rate of 0.01% with a False Negative Rate of 0.15%,and a near-instantaneous edge detection latency of 0.40 ms.The system demonstrated an aggregate throughput of 214.57 TPS in a 3-shard configuration,providing a clear,evidence-based path for horizontally scaling to support overmillions of devices with exceeding throughput.The proposed architecture represents a significant advancement in blockchain-based security for IoT networks,effectively balancing the trade-offs between scalability,security,and decentralization.展开更多
In the electroslag remelting(ESR)process,it mainly relies on thermal experiments or analysis via mechanistic models to realize the physical fields simulation of the electromagnetic field and temperature field coupled ...In the electroslag remelting(ESR)process,it mainly relies on thermal experiments or analysis via mechanistic models to realize the physical fields simulation of the electromagnetic field and temperature field coupled transfer,which has the limitations of high cost,a large amount of calculating data and high computing power requirements.A novel network based on physics-informed neural network(PINN)was designed to realize the fast and high-fidelity prediction of the distribution of electromagnetic field and temperature field in ESR process.The physical laws were combined with the deep learning network through PINN,and physical constraints were embedded to achieve effective solution of partial differential equations(PDEs).PINN was used to minimize the loss function consisting of data error,physical information error and boundary condition error.The physical laws and boundary condition constraints in the ESR process were considered to maintain high PDE solution accuracy under different spatial and temporal resolutions.Automatic differentiation(Autodiff)technique and gradient descent algorithm were used to optimize the network parameters.The experimental results show that compared with the mechanistic models,PINN can effectively replace thermal experiments to realize the physical field simulation of ESR process with only a few experimental data,which can avoid the disadvantages of pure data-driven network simulation that requires a large amount of training data.Moreover,the solution of PINN has good physical interpretability and reliability of simulation results.For simulating electromagnetic field and temperature field distribution,the training time of the network is only 140 and 203 s,and the regression indicators of root mean square error can reach 12.65 and 13.76,respectively.展开更多
Numerical simulation plays an important role in the dynamic analysis of multibody system.With the rapid development of computer science,the numerical solution technology has been further developed.Recently,data-driven...Numerical simulation plays an important role in the dynamic analysis of multibody system.With the rapid development of computer science,the numerical solution technology has been further developed.Recently,data-driven method has become a very popular computing method.However,due to lack of necessary mechanism information of the traditional pure data-driven methods based on neural network,its numerical accuracy cannot be guaranteed for strong nonlinear system.Therefore,this work proposes a mechanism-data hybrid-driven strategy for solving nonlinear multibody system based on physics-informed neural network to overcome the limitation of traditional data-driven methods.The strategy proposed in this paper introduces scaling coefficients to introduce the dynamic model of multibody system into neural network,ensuring that the training results of neural network conform to the mechanics principle of the system,thereby ensuring the good reliability of the data-driven method.Finally,the stability,generalization ability and numerical accuracy of the proposed method are discussed and analyzed using three typical multibody systems,and the constrained default situations can be controlled within the range of 10^(-2)-10^(-4).展开更多
Accurately estimating the battery state of health(SOH)is essential for ensuring the safe and reliable operation of battery systems of electric vehicles.However,due to the complex and variable operating conditions enco...Accurately estimating the battery state of health(SOH)is essential for ensuring the safe and reliable operation of battery systems of electric vehicles.However,due to the complex and variable operating conditions encountered in practical applications,achieving precise and physics-informed SOH estimation remains challenging.To address these problems,this paper develops a lightweight two-stage physicsinformed neural network(TSPINN)method for SOH estimation of lithium-ion batteries with different chemistries.Specifically,this paper utilizes firstly relaxation voltage data obtained after a full charge to determine the aging-related parameters of physical equivalent circuit model(ECM).Additionally,incremental capacity(IC)feature is extracted by analyzing peak values of the IC curve during the charging phase,which thereby constitutes the first stage of the proposed TSPINN,termed as physics-informed data augmentation for SOH estimation.Additionally,the physical information can be further embedded by incorporating feature knowledge related to mechanisms into the loss function,and ultimately,the second stage of the proposed TSPINN is developed,which is named the physics-informed loss function.The effectiveness of the TSPINN method was confirmed through the experimental data for LiNi_(0.86)Co_(0.11)Al_(0.03)O_(2)(NCA)and LiNi_(0.83)Co_(0.11)Mn_(0.07)O_(2)(NCM)battery materials under different temperature conditions.The final experimental results indicate that the TSPINN method achieved SOH estimation with a mean absolute error(MAE)of 0.675%,showing improvements of approximately 29.3%,60.3%,and 8.1% compared to methods using only ECM,IC,and integrated features,respectively.The results validate the effectiveness and adaptability of TSPINN,establishing it as a reliable solution for advanced battery management systems.展开更多
Accurately forecasting peak particle velocity(PPV)during blasting operations plays a crucial role in mitigating vibration-related hazards and preventing economic losses.This research introduces an approach to PPV pred...Accurately forecasting peak particle velocity(PPV)during blasting operations plays a crucial role in mitigating vibration-related hazards and preventing economic losses.This research introduces an approach to PPV prediction by combining conventional empirical equations with physics-informed neural networks(PINN)and optimizing the model parameters via the Particle Swarm Optimization(PSO)algorithm.The proposed PSO-PINN framework was rigorously benchmarked against seven established machine learning approaches:Multilayer Perceptron(MLP),Extreme Gradient Boosting(XGBoost),Random Forest(RF),Support Vector Regression(SVR),Gradient Boosting Decision Tree(GBDT),Adaptive Boosting(Adaboost),and Gene Expression Programming(GEP).Comparative analysis showed that PSO-PINN outperformed these models,achieving RMSE reductions of 17.82-37.63%,MSE reductions of 32.47-61.10%,AR improvements of 2.97-21.19%,and R^(2)enhancements of 7.43-29.21%,demonstrating superior accuracy and generalization.Furthermore,the study determines the impact of incorporating empirical formulas as physical constraints in neural networks and examines the effects of different empirical equations,particle swarm size,iteration count in PSO,regularization coefficient,and learning rate in PINN on model performance.Lastly,a predictive system for blast vibration PPV is designed and implemented.The research outcomes offer theoretical references and practical recommendations for blast vibration forecasting in similar engineering applications.展开更多
Dynamic wake field information is vital for the optimized design and control of wind farms.Combined with sparse measurement data from light detection and ranging(LiDAR),the physics-informed neural network(PINN)framewo...Dynamic wake field information is vital for the optimized design and control of wind farms.Combined with sparse measurement data from light detection and ranging(LiDAR),the physics-informed neural network(PINN)frameworks have recently been employed for forecasting freestream wind and wake fields.However,these PINN frameworks face challenges of low prediction accuracy and long training times.Therefore,this paper constructed a PINN framework for dynamic wake field prediction by integrating two accuracy improvement strategies and a step-by-step training time saving strategy.The results showed that the different performance improvement routes significantly improved the overall performance of the PINN.The accuracy and efficiency of the PINN with spatiotemporal improvement strategies were validated via LiDAR-measured data from a wind farm in Shandong province,China.This paper sheds light on load reduction,efficiency improvement,intelligent operation and maintenance of wind farms.展开更多
Enforcing initial and boundary conditions(I/BCs)poses challenges in physics-informed neural networks(PINNs).Several PINN studies have gained significant achievements in developing techniques for imposing BCs in static...Enforcing initial and boundary conditions(I/BCs)poses challenges in physics-informed neural networks(PINNs).Several PINN studies have gained significant achievements in developing techniques for imposing BCs in static problems;however,the simultaneous enforcement of I/BCs in dynamic problems remains challenging.To overcome this limitation,a novel approach called decoupled physics-informed neural network(d PINN)is proposed in this work.The d PINN operates based on the core idea of converting a partial differential equation(PDE)to a system of ordinary differential equations(ODEs)via the space-time decoupled formulation.To this end,the latent solution is expressed in the form of a linear combination of approximation functions and coefficients,where approximation functions are admissible and coefficients are unknowns of time that must be solved.Subsequently,the system of ODEs is obtained by implementing the weighted-residual form of the original PDE over the spatial domain.A multi-network structure is used to parameterize the set of coefficient functions,and the loss function of d PINN is established based on minimizing the residuals of the gained ODEs.In this scheme,the decoupled formulation leads to the independent handling of I/BCs.Accordingly,the BCs are automatically satisfied based on suitable selections of admissible functions.Meanwhile,the original ICs are replaced by the Galerkin form of the ICs concerning unknown coefficients,and the neural network(NN)outputs are modified to satisfy the gained ICs.Several benchmark problems involving different types of PDEs and I/BCs are used to demonstrate the superior performance of d PINN compared with regular PINN in terms of solution accuracy and computational cost.展开更多
In this paper,we propose a symmetric difference data enhancement physics-informed neural network(SDE-PINN)to study soliton solutions for discrete nonlinear lattice equations(NLEs).By considering known and unknown symm...In this paper,we propose a symmetric difference data enhancement physics-informed neural network(SDE-PINN)to study soliton solutions for discrete nonlinear lattice equations(NLEs).By considering known and unknown symmetric points,numerical simulations are conducted to one-soliton and two-soliton solutions of a discrete KdV equation,as well as a one-soliton solution of a discrete Toda lattice equation.Compared with the existing discrete deep learning approach,the numerical results reveal that within the specified spatiotemporal domain,the prediction accuracy by SDE-PINN is excellent regardless of the interior or extrapolation prediction,with a significant reduction in training time.The proposed data enhancement technique and symmetric structure development provides a new perspective for the deep learning approach to solve discrete NLEs.The newly proposed SDE-PINN can also be applied to solve continuous nonlinear equations and other discrete NLEs numerically.展开更多
Physics-informed neural networks(PINNs)have become an attractive machine learning framework for obtaining solutions to partial differential equations(PDEs).PINNs embed initial,boundary,and PDE constraints into the los...Physics-informed neural networks(PINNs)have become an attractive machine learning framework for obtaining solutions to partial differential equations(PDEs).PINNs embed initial,boundary,and PDE constraints into the loss function.The performance of PINNs is generally affected by both training and sampling.Specifically,training methods focus on how to overcome the training difficulties caused by the special PDE residual loss of PINNs,and sampling methods are concerned with the location and distribution of the sampling points upon which evaluations of PDE residual loss are accomplished.However,a common problem among these original PINNs is that they omit special temporal information utilization during the training or sampling stages when dealing with an important PDE category,namely,time-dependent PDEs,where temporal information plays a key role in the algorithms used.There is one method,called Causal PINN,that considers temporal causality at the training level but not special temporal utilization at the sampling level.Incorporating temporal knowledge into sampling remains to be studied.To fill this gap,we propose a novel temporal causality-based adaptive sampling method that dynamically determines the sampling ratio according to both PDE residual and temporal causality.By designing a sampling ratio determined by both residual loss and temporal causality to control the number and location of sampled points in each temporal sub-domain,we provide a practical solution by incorporating temporal information into sampling.Numerical experiments of several nonlinear time-dependent PDEs,including the Cahn–Hilliard,Korteweg–de Vries,Allen–Cahn and wave equations,show that our proposed sampling method can improve the performance.We demonstrate that using such a relatively simple sampling method can improve prediction performance by up to two orders of magnitude compared with the results from other methods,especially when points are limited.展开更多
Multi-scale system remains a classical scientific problem in fluid dynamics,biology,etc.In the present study,a scheme of multi-scale Physics-informed neural networks is proposed to solve the boundary layer flow at hig...Multi-scale system remains a classical scientific problem in fluid dynamics,biology,etc.In the present study,a scheme of multi-scale Physics-informed neural networks is proposed to solve the boundary layer flow at high Reynolds numbers without any data.The flow is divided into several regions with different scales based on Prandtl's boundary theory.Different regions are solved with governing equations in different scales.The method of matched asymptotic expansions is used to make the flow field continuously.A flow on a semi infinite flat plate at a high Reynolds number is considered a multi-scale problem because the boundary layer scale is much smaller than the outer flow scale.The results are compared with the reference numerical solutions,which show that the msPINNs can solve the multi-scale problem of the boundary layer in high Reynolds number flows.This scheme can be developed for more multi-scale problems in the future.展开更多
We consider solving the forward and inverse partial differential equations(PDEs)which have sharp solutions with physics-informed neural networks(PINNs)in this work.In particular,to better capture the sharpness of the ...We consider solving the forward and inverse partial differential equations(PDEs)which have sharp solutions with physics-informed neural networks(PINNs)in this work.In particular,to better capture the sharpness of the solution,we propose the adaptive sampling methods(ASMs)based on the residual and the gradient of the solution.We first present a residual only-based ASM denoted by ASMⅠ.In this approach,we first train the neural network using a small number of residual points and divide the computational domain into a certain number of sub-domains,then we add new residual points in the sub-domain which has the largest mean absolute value of the residual,and those points which have the largest absolute values of the residual in this sub-domain as new residual points.We further develop a second type of ASM(denoted by ASMⅡ)based on both the residual and the gradient of the solution due to the fact that only the residual may not be able to efficiently capture the sharpness of the solution.The procedure of ASMⅡis almost the same as that of ASMⅠ,and we add new residual points which have not only large residuals but also large gradients.To demonstrate the effectiveness of the present methods,we use both ASMⅠand ASMⅡto solve a number of PDEs,including the Burger equation,the compressible Euler equation,the Poisson equation over an Lshape domain as well as the high-dimensional Poisson equation.It has been shown from the numerical results that the sharp solutions can be well approximated by using either ASMⅠor ASMⅡ,and both methods deliver much more accurate solutions than the original PINNs with the same number of residual points.Moreover,the ASMⅡalgorithm has better performance in terms of accuracy,efficiency,and stability compared with the ASMⅠalgorithm.This means that the gradient of the solution improves the stability and efficiency of the adaptive sampling procedure as well as the accuracy of the solution.Furthermore,we also employ the similar adaptive sampling technique for the data points of boundary conditions(BCs)if the sharpness of the solution is near the boundary.The result of the L-shape Poisson problem indicates that the present method can significantly improve the efficiency,stability,and accuracy.展开更多
Accurate insight into the heat generation rate(HGR) of lithium-ion batteries(LIBs) is one of key issues for battery management systems to formulate thermal safety warning strategies in advance.For this reason,this pap...Accurate insight into the heat generation rate(HGR) of lithium-ion batteries(LIBs) is one of key issues for battery management systems to formulate thermal safety warning strategies in advance.For this reason,this paper proposes a novel physics-informed neural network(PINN) approach for HGR estimation of LIBs under various driving conditions.Specifically,a single particle model with thermodynamics(SPMT) is first constructed for extracting the critical physical knowledge related with battery HGR.Subsequently,the surface concentrations of positive and negative electrodes in battery SPMT model are integrated into the bidirectional long short-term memory(BiLSTM) networks as physical information.And combined with other feature variables,a novel PINN approach to achieve HGR estimation of LIBs with higher accuracy is constituted.Additionally,some critical hyperparameters of BiLSTM used in PINN approach are determined through Bayesian optimization algorithm(BOA) and the results of BOA-based BiLSTM are compared with other traditional BiLSTM/LSTM networks.Eventually,combined with the HGR data generated from the validated virtual battery,it is proved that the proposed approach can well predict the battery HGR under the dynamic stress test(DST) and worldwide light vehicles test procedure(WLTP),the mean absolute error under DST is 0.542 kW/m^(3),and the root mean square error under WLTP is1.428 kW/m^(3)at 25℃.Lastly,the investigation results of this paper also show a new perspective in the application of the PINN approach in battery HGR estimation.展开更多
With the explosive growth of computational resources and data generation,deep machine learning has been successfully employed in various applications.One important and emerging scientific application of deep learning ...With the explosive growth of computational resources and data generation,deep machine learning has been successfully employed in various applications.One important and emerging scientific application of deep learning involves solving differential equations.Here,physics-informed neural networks(PINNs)are developed to solve the differential equations associated with a specific scientific problem.As such,algorithms for solving the differential equations by embedding their initial and boundary conditions in the cost function of the artificial neural networks using algorithmic differentiation must also be developed.In this study,various PINNs are adopted to estimate the stresses in the tablets and the interphase of a single lap joint.The proposed model is represented by two fourth-order non-homogeneous coupled partial differential equations,with the axial stresses in the upper and lower tablets adopted as the dependent variables.The axial stresses are a function of the tablet length,which presents the independent variable.Therefore,the axial stresses in the tablets are estimated by solving the coupled partial differential equations when subjected to the boundary conditions,whereas the remaining stress components are expressed in terms of axial stresses.The results obtained using the developed methodology are validated using the results obtained via MAPLE software.展开更多
Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions.However,material identification is a challenging task,especially when the ch...Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions.However,material identification is a challenging task,especially when the characteristic of the material is highly nonlinear in nature,as is common in biological tissue.In this work,we identify unknown material properties in continuum solid mechanics via physics-informed neural networks(PINNs).To improve the accuracy and efficiency of PINNs,we develop efficient strategies to nonuniformly sample observational data.We also investigate different approaches to enforce Dirichlet-type boundary conditions(BCs)as soft or hard constraints.Finally,we apply the proposed methods to a diverse set of time-dependent and time-independent solid mechanic examples that span linear elastic and hyperelastic material space.The estimated material parameters achieve relative errors of less than 1%.As such,this work is relevant to diverse applications,including optimizing structural integrity and developing novel materials.展开更多
This paper proposes a physics-informed neural network(PINN)framework to analyze the nonlinear buckling behavior of a three-dimensional(3D)FG porous,slender beam resting on a Winkler-Pasternak foundation.PINNs need muc...This paper proposes a physics-informed neural network(PINN)framework to analyze the nonlinear buckling behavior of a three-dimensional(3D)FG porous,slender beam resting on a Winkler-Pasternak foundation.PINNs need much less training data to obtain high accuracy using a straightforward network.The powerful tool used in this work can handle any class of PDEs.We use the deep learning platform TensorFlow and DeepXDE library to design our network.In this study,the PINNs framework takes information from the governing differential equations of the beam system and the data from boundary conditions and outputs the critical nonlinear buckling load.The mathematical model is developed using Hamilton’s principle,considering geometry’s nonlinearity.The accuracy of the modeling framework is carefully examined by applying it to various boundary condition cases as well as the physical parameters such as 3D FG indexes on the nonlinear mechanical behaviors.Finally,the PINNs results are validated with those extracted from the generalized differential quadrature method(GDQM).It is found that the proposed PINN framework can characterize the nonlinear buckling behavior of 3D FG porous,slender beams with satisfactory accuracy.Furthermore,PINN is presented to accurately predict the nonlinear buckling behavior of the beam up to 71 times faster than the numerical method.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.92152301)the National Key Research and Development Program of China(Grant No.2022YFB4300200)the Shaanxi Provincial Key Research and Development Program(Grant No.2023-ZDLGY-27).
文摘Physics-informed neural networks(PINNs)have shown remarkable prospects in solving the forward and inverse problems involving partial differential equations(PDEs).The method embeds PDEs into the neural network by calculating the PDE loss at a set of collocation points,providing advantages such as meshfree and more convenient adaptive sampling.However,when solving PDEs using nonuniform collocation points,PINNs still face challenge regarding inefficient convergence of PDE residuals or even failure.In this work,we first analyze the ill-conditioning of the PDE loss in PINNs under nonuniform collocation points.To address the issue,we define volume weighting residual and propose volume weighting physics-informed neural networks(VW-PINNs).Through weighting the PDE residuals by the volume that the collocation points occupy within the computational domain,we embed explicitly the distribution characteristics of collocation points in the loss evaluation.The fast and sufficient convergence of the PDE residuals for the problems involving nonuniform collocation points is guaranteed.Considering the meshfree characteristics of VW-PINNs,we also develop a volume approximation algorithm based on kernel density estimation to calculate the volume of the collocation points.We validate the universality of VW-PINNs by solving the forward problems involving flow over a circular cylinder and flow over the NACA0012 airfoil under different inflow conditions,where conventional PINNs fail.By solving the Burgers’equation,we verify that VW-PINNs can enhance the efficiency of existing the adaptive sampling method in solving the forward problem by three times,and can reduce the relative L 2 error of conventional PINNs in solving the inverse problem by more than one order of magnitude.
基金King Abdullah University of Science and Technol-ogy(KAUST)for supporting this research and the Seismic Wave Anal-ysis group for the supportive and encouraging environment.
文摘Physics-informed neural networks(PINNs)are promising to replace conventional mesh-based partial tial differen-equation(PDE)solvers by offering more accurate and flexible PDE solutions.However,PINNs are hampered by the relatively slow convergence and the need to perform additional,potentially expensive training for new PDE parameters.To solve this limitation,we introduce LatentPINN,a framework that utilizes latent representations of the PDE parameters as additional(to the coordinates)inputs into PINNs and allows for training over the distribution of these parameters.Motivated by the recent progress on generative models,we promote using latent diffusion models to learn compressed latent representations of the distribution of PDE parameters as they act as input parameters for NN functional solutions.We use a two-stage training scheme in which,in the first stage,we learn the latent representations for the distribution of PDE parameters.In the second stage,we train a physics-informed neural network over inputs given by randomly drawn samples from the coordinate space within the solution domain and samples from the learned latent representation of the PDE parameters.Considering their importance in capturing evolving interfaces and fronts in various fields,we test the approach on a class of level set equations given,for example,by the nonlinear Eikonal equation.We share results corresponding to three Eikonal parameters(velocity models)sets.The proposed method performs well on new phase velocity models without the need for any additional training.
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.
基金supported by the Beijing Natural Science Foundation(Grant No.L223013)。
文摘For the diagnostics and health management of lithium-ion batteries,numerous models have been developed to understand their degradation characteristics.These models typically fall into two categories:data-driven models and physical models,each offering unique advantages but also facing limitations.Physics-informed neural networks(PINNs)provide a robust framework to integrate data-driven models with physical principles,ensuring consistency with underlying physics while enabling generalization across diverse operational conditions.This study introduces a PINN-based approach to reconstruct open circuit voltage(OCV)curves and estimate key ageing parameters at both the cell and electrode levels.These parameters include available capacity,electrode capacities,and lithium inventory capacity.The proposed method integrates OCV reconstruction models as functional components into convolutional neural networks(CNNs)and is validated using a public dataset.The results reveal that the estimated ageing parameters closely align with those obtained through offline OCV tests,with errors in reconstructed OCV curves remaining within 15 mV.This demonstrates the ability of the method to deliver fast and accurate degradation diagnostics at the electrode level,advancing the potential for precise and efficient battery health management.
基金Supported by the National Natural Science Foundation of China(No.62304022)。
文摘This research introduces a spectrum-based physics-informed neural network(SP-PINN)model to significantly improve the accuracy of calculation of two-phase flow parameters,surpassing existing methods that have limitations in global and continuous data sampling.SP-PINNs address the challenges of traditional methods in terms of continuous sampling by integrating the spectral analysis and pressure correction into the Navier-Stokes(N-S)equations,enhancing the predictive accuracy especially in critical regions like gas-phase boundaries and velocity peaks.The novel introduction of a pressure-correction module within SP-PINNs mitigates prediction errors,achieving a substantial reduction to 1‰compared with the conventional physics-informed neural network(PINN)approaches.Experimental applications validate the model’s ability to accurately and rapidly predict flow parameters with different sampling time intervals,with the computation time of predicting unsampled data less than 0.01 s.Such advancements signify a 100-fold improvement over traditional DNS calculations,underscoring the model’s potential in the real-time calculation and analysis of multiphase flow dynamics.
基金supported in part by Multimedia University under the Research Fellow Grant MMUI/250008in part by Telekom Research&Development Sdn Bhd underGrantRDTC/241149Princess Nourah bint Abdulrahman University Researchers Supporting Project number(PNURSP2025R140),Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabia.
文摘The Internet of Things(IoT)ecosystem faces growing security challenges because it is projected to have 76.88 billion devices by 2025 and $1.4 trillion market value by 2027,operating in distributed networks with resource limitations and diverse system architectures.The current conventional intrusion detection systems(IDS)face scalability problems and trust-related issues,but blockchain-based solutions face limitations because of their low transaction throughput(Bitcoin:7 TPS(Transactions Per Second),Ethereum:15-30 TPS)and high latency.The research introduces MBID(Multi-Tier Blockchain Intrusion Detection)as a groundbreaking Multi-Tier Blockchain Intrusion Detection System with AI-Enhanced Detection,which solves the problems in huge IoT networks.The MBID system uses a four-tier architecture that includes device,edge,fog,and cloud layers with blockchain implementations and Physics-Informed Neural Networks(PINNs)for edge-based anomaly detection and a dual consensus mechanism that uses Honesty-based Distributed Proof-of-Authority(HDPoA)and Delegated Proof of Stake(DPoS).The system achieves scalability and efficiency through the combination of dynamic sharding and Interplanetary File System(IPFS)integration.Experimental evaluations demonstrate exceptional performance,achieving a detection accuracy of 99.84%,an ultra-low false positive rate of 0.01% with a False Negative Rate of 0.15%,and a near-instantaneous edge detection latency of 0.40 ms.The system demonstrated an aggregate throughput of 214.57 TPS in a 3-shard configuration,providing a clear,evidence-based path for horizontally scaling to support overmillions of devices with exceeding throughput.The proposed architecture represents a significant advancement in blockchain-based security for IoT networks,effectively balancing the trade-offs between scalability,security,and decentralization.
基金supported by National Natural Science Foundation of China(52274323 and 524743495)the Postdoctoral Fellowship Program of CPSF under Grant Number GZC20240231.
文摘In the electroslag remelting(ESR)process,it mainly relies on thermal experiments or analysis via mechanistic models to realize the physical fields simulation of the electromagnetic field and temperature field coupled transfer,which has the limitations of high cost,a large amount of calculating data and high computing power requirements.A novel network based on physics-informed neural network(PINN)was designed to realize the fast and high-fidelity prediction of the distribution of electromagnetic field and temperature field in ESR process.The physical laws were combined with the deep learning network through PINN,and physical constraints were embedded to achieve effective solution of partial differential equations(PDEs).PINN was used to minimize the loss function consisting of data error,physical information error and boundary condition error.The physical laws and boundary condition constraints in the ESR process were considered to maintain high PDE solution accuracy under different spatial and temporal resolutions.Automatic differentiation(Autodiff)technique and gradient descent algorithm were used to optimize the network parameters.The experimental results show that compared with the mechanistic models,PINN can effectively replace thermal experiments to realize the physical field simulation of ESR process with only a few experimental data,which can avoid the disadvantages of pure data-driven network simulation that requires a large amount of training data.Moreover,the solution of PINN has good physical interpretability and reliability of simulation results.For simulating electromagnetic field and temperature field distribution,the training time of the network is only 140 and 203 s,and the regression indicators of root mean square error can reach 12.65 and 13.76,respectively.
基金supported by the National Natural Science Foundation of China(Grant No.U2241263)the fellowship of China Postdoctoral Science Foundation(Grant No.2024M750310).
文摘Numerical simulation plays an important role in the dynamic analysis of multibody system.With the rapid development of computer science,the numerical solution technology has been further developed.Recently,data-driven method has become a very popular computing method.However,due to lack of necessary mechanism information of the traditional pure data-driven methods based on neural network,its numerical accuracy cannot be guaranteed for strong nonlinear system.Therefore,this work proposes a mechanism-data hybrid-driven strategy for solving nonlinear multibody system based on physics-informed neural network to overcome the limitation of traditional data-driven methods.The strategy proposed in this paper introduces scaling coefficients to introduce the dynamic model of multibody system into neural network,ensuring that the training results of neural network conform to the mechanics principle of the system,thereby ensuring the good reliability of the data-driven method.Finally,the stability,generalization ability and numerical accuracy of the proposed method are discussed and analyzed using three typical multibody systems,and the constrained default situations can be controlled within the range of 10^(-2)-10^(-4).
基金supported by the Scientific Research and Innovation Team Program of Sichuan University of Science and Engineering(No.SUSE652B005)Anhui Province Applied Peak Discipline Mechanical Engineering(No.XK-XJGF004)。
文摘Accurately estimating the battery state of health(SOH)is essential for ensuring the safe and reliable operation of battery systems of electric vehicles.However,due to the complex and variable operating conditions encountered in practical applications,achieving precise and physics-informed SOH estimation remains challenging.To address these problems,this paper develops a lightweight two-stage physicsinformed neural network(TSPINN)method for SOH estimation of lithium-ion batteries with different chemistries.Specifically,this paper utilizes firstly relaxation voltage data obtained after a full charge to determine the aging-related parameters of physical equivalent circuit model(ECM).Additionally,incremental capacity(IC)feature is extracted by analyzing peak values of the IC curve during the charging phase,which thereby constitutes the first stage of the proposed TSPINN,termed as physics-informed data augmentation for SOH estimation.Additionally,the physical information can be further embedded by incorporating feature knowledge related to mechanisms into the loss function,and ultimately,the second stage of the proposed TSPINN is developed,which is named the physics-informed loss function.The effectiveness of the TSPINN method was confirmed through the experimental data for LiNi_(0.86)Co_(0.11)Al_(0.03)O_(2)(NCA)and LiNi_(0.83)Co_(0.11)Mn_(0.07)O_(2)(NCM)battery materials under different temperature conditions.The final experimental results indicate that the TSPINN method achieved SOH estimation with a mean absolute error(MAE)of 0.675%,showing improvements of approximately 29.3%,60.3%,and 8.1% compared to methods using only ECM,IC,and integrated features,respectively.The results validate the effectiveness and adaptability of TSPINN,establishing it as a reliable solution for advanced battery management systems.
基金supported by the National Natural Science Foundation of China(Grant No.52409143)the Basic Scientific Research Fund of Changjiang River Scientific Research Institute for Central-level Public Welfare Research Institutes(Grant No.CKSF2025184/YT)the Hubei Provincial Natural Science Foundation of China(Grant No.2022CFB673).
文摘Accurately forecasting peak particle velocity(PPV)during blasting operations plays a crucial role in mitigating vibration-related hazards and preventing economic losses.This research introduces an approach to PPV prediction by combining conventional empirical equations with physics-informed neural networks(PINN)and optimizing the model parameters via the Particle Swarm Optimization(PSO)algorithm.The proposed PSO-PINN framework was rigorously benchmarked against seven established machine learning approaches:Multilayer Perceptron(MLP),Extreme Gradient Boosting(XGBoost),Random Forest(RF),Support Vector Regression(SVR),Gradient Boosting Decision Tree(GBDT),Adaptive Boosting(Adaboost),and Gene Expression Programming(GEP).Comparative analysis showed that PSO-PINN outperformed these models,achieving RMSE reductions of 17.82-37.63%,MSE reductions of 32.47-61.10%,AR improvements of 2.97-21.19%,and R^(2)enhancements of 7.43-29.21%,demonstrating superior accuracy and generalization.Furthermore,the study determines the impact of incorporating empirical formulas as physical constraints in neural networks and examines the effects of different empirical equations,particle swarm size,iteration count in PSO,regularization coefficient,and learning rate in PINN on model performance.Lastly,a predictive system for blast vibration PPV is designed and implemented.The research outcomes offer theoretical references and practical recommendations for blast vibration forecasting in similar engineering applications.
基金supported by the National Natural Science Foundation of China(Grant Nos.12072105,11932006,and 52308498)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20220976).
文摘Dynamic wake field information is vital for the optimized design and control of wind farms.Combined with sparse measurement data from light detection and ranging(LiDAR),the physics-informed neural network(PINN)frameworks have recently been employed for forecasting freestream wind and wake fields.However,these PINN frameworks face challenges of low prediction accuracy and long training times.Therefore,this paper constructed a PINN framework for dynamic wake field prediction by integrating two accuracy improvement strategies and a step-by-step training time saving strategy.The results showed that the different performance improvement routes significantly improved the overall performance of the PINN.The accuracy and efficiency of the PINN with spatiotemporal improvement strategies were validated via LiDAR-measured data from a wind farm in Shandong province,China.This paper sheds light on load reduction,efficiency improvement,intelligent operation and maintenance of wind farms.
基金Project supported by the Basic Science Research Program through the National Research Foundation(NRF)of Korea funded by the Ministry of Science and ICT(No.RS-2024-00337001)。
文摘Enforcing initial and boundary conditions(I/BCs)poses challenges in physics-informed neural networks(PINNs).Several PINN studies have gained significant achievements in developing techniques for imposing BCs in static problems;however,the simultaneous enforcement of I/BCs in dynamic problems remains challenging.To overcome this limitation,a novel approach called decoupled physics-informed neural network(d PINN)is proposed in this work.The d PINN operates based on the core idea of converting a partial differential equation(PDE)to a system of ordinary differential equations(ODEs)via the space-time decoupled formulation.To this end,the latent solution is expressed in the form of a linear combination of approximation functions and coefficients,where approximation functions are admissible and coefficients are unknowns of time that must be solved.Subsequently,the system of ODEs is obtained by implementing the weighted-residual form of the original PDE over the spatial domain.A multi-network structure is used to parameterize the set of coefficient functions,and the loss function of d PINN is established based on minimizing the residuals of the gained ODEs.In this scheme,the decoupled formulation leads to the independent handling of I/BCs.Accordingly,the BCs are automatically satisfied based on suitable selections of admissible functions.Meanwhile,the original ICs are replaced by the Galerkin form of the ICs concerning unknown coefficients,and the neural network(NN)outputs are modified to satisfy the gained ICs.Several benchmark problems involving different types of PDEs and I/BCs are used to demonstrate the superior performance of d PINN compared with regular PINN in terms of solution accuracy and computational cost.
基金supported by the National Natural Science Foundation of China(Grant No.12071042)the Beijing Natural Science Foundation(Grant No.1202004)Promoting the Development of University Classification-Student Innovation and Entrepreneurship Training Programme(Grant No.5112410857)。
文摘In this paper,we propose a symmetric difference data enhancement physics-informed neural network(SDE-PINN)to study soliton solutions for discrete nonlinear lattice equations(NLEs).By considering known and unknown symmetric points,numerical simulations are conducted to one-soliton and two-soliton solutions of a discrete KdV equation,as well as a one-soliton solution of a discrete Toda lattice equation.Compared with the existing discrete deep learning approach,the numerical results reveal that within the specified spatiotemporal domain,the prediction accuracy by SDE-PINN is excellent regardless of the interior or extrapolation prediction,with a significant reduction in training time.The proposed data enhancement technique and symmetric structure development provides a new perspective for the deep learning approach to solve discrete NLEs.The newly proposed SDE-PINN can also be applied to solve continuous nonlinear equations and other discrete NLEs numerically.
基金Project supported by the Key National Natural Science Foundation of China(Grant No.62136005)the National Natural Science Foundation of China(Grant Nos.61922087,61906201,and 62006238)。
文摘Physics-informed neural networks(PINNs)have become an attractive machine learning framework for obtaining solutions to partial differential equations(PDEs).PINNs embed initial,boundary,and PDE constraints into the loss function.The performance of PINNs is generally affected by both training and sampling.Specifically,training methods focus on how to overcome the training difficulties caused by the special PDE residual loss of PINNs,and sampling methods are concerned with the location and distribution of the sampling points upon which evaluations of PDE residual loss are accomplished.However,a common problem among these original PINNs is that they omit special temporal information utilization during the training or sampling stages when dealing with an important PDE category,namely,time-dependent PDEs,where temporal information plays a key role in the algorithms used.There is one method,called Causal PINN,that considers temporal causality at the training level but not special temporal utilization at the sampling level.Incorporating temporal knowledge into sampling remains to be studied.To fill this gap,we propose a novel temporal causality-based adaptive sampling method that dynamically determines the sampling ratio according to both PDE residual and temporal causality.By designing a sampling ratio determined by both residual loss and temporal causality to control the number and location of sampled points in each temporal sub-domain,we provide a practical solution by incorporating temporal information into sampling.Numerical experiments of several nonlinear time-dependent PDEs,including the Cahn–Hilliard,Korteweg–de Vries,Allen–Cahn and wave equations,show that our proposed sampling method can improve the performance.We demonstrate that using such a relatively simple sampling method can improve prediction performance by up to two orders of magnitude compared with the results from other methods,especially when points are limited.
文摘Multi-scale system remains a classical scientific problem in fluid dynamics,biology,etc.In the present study,a scheme of multi-scale Physics-informed neural networks is proposed to solve the boundary layer flow at high Reynolds numbers without any data.The flow is divided into several regions with different scales based on Prandtl's boundary theory.Different regions are solved with governing equations in different scales.The method of matched asymptotic expansions is used to make the flow field continuously.A flow on a semi infinite flat plate at a high Reynolds number is considered a multi-scale problem because the boundary layer scale is much smaller than the outer flow scale.The results are compared with the reference numerical solutions,which show that the msPINNs can solve the multi-scale problem of the boundary layer in high Reynolds number flows.This scheme can be developed for more multi-scale problems in the future.
基金Project supported by the National Key R&D Program of China(No.2022YFA1004504)the National Natural Science Foundation of China(Nos.12171404 and 12201229)the Fundamental Research Funds for Central Universities of China(No.20720210037)。
文摘We consider solving the forward and inverse partial differential equations(PDEs)which have sharp solutions with physics-informed neural networks(PINNs)in this work.In particular,to better capture the sharpness of the solution,we propose the adaptive sampling methods(ASMs)based on the residual and the gradient of the solution.We first present a residual only-based ASM denoted by ASMⅠ.In this approach,we first train the neural network using a small number of residual points and divide the computational domain into a certain number of sub-domains,then we add new residual points in the sub-domain which has the largest mean absolute value of the residual,and those points which have the largest absolute values of the residual in this sub-domain as new residual points.We further develop a second type of ASM(denoted by ASMⅡ)based on both the residual and the gradient of the solution due to the fact that only the residual may not be able to efficiently capture the sharpness of the solution.The procedure of ASMⅡis almost the same as that of ASMⅠ,and we add new residual points which have not only large residuals but also large gradients.To demonstrate the effectiveness of the present methods,we use both ASMⅠand ASMⅡto solve a number of PDEs,including the Burger equation,the compressible Euler equation,the Poisson equation over an Lshape domain as well as the high-dimensional Poisson equation.It has been shown from the numerical results that the sharp solutions can be well approximated by using either ASMⅠor ASMⅡ,and both methods deliver much more accurate solutions than the original PINNs with the same number of residual points.Moreover,the ASMⅡalgorithm has better performance in terms of accuracy,efficiency,and stability compared with the ASMⅠalgorithm.This means that the gradient of the solution improves the stability and efficiency of the adaptive sampling procedure as well as the accuracy of the solution.Furthermore,we also employ the similar adaptive sampling technique for the data points of boundary conditions(BCs)if the sharpness of the solution is near the boundary.The result of the L-shape Poisson problem indicates that the present method can significantly improve the efficiency,stability,and accuracy.
基金funded by the Artificial Intelligence Technology Project of Xi’an Science and Technology Bureau in China(No.21RGZN0014)。
文摘Accurate insight into the heat generation rate(HGR) of lithium-ion batteries(LIBs) is one of key issues for battery management systems to formulate thermal safety warning strategies in advance.For this reason,this paper proposes a novel physics-informed neural network(PINN) approach for HGR estimation of LIBs under various driving conditions.Specifically,a single particle model with thermodynamics(SPMT) is first constructed for extracting the critical physical knowledge related with battery HGR.Subsequently,the surface concentrations of positive and negative electrodes in battery SPMT model are integrated into the bidirectional long short-term memory(BiLSTM) networks as physical information.And combined with other feature variables,a novel PINN approach to achieve HGR estimation of LIBs with higher accuracy is constituted.Additionally,some critical hyperparameters of BiLSTM used in PINN approach are determined through Bayesian optimization algorithm(BOA) and the results of BOA-based BiLSTM are compared with other traditional BiLSTM/LSTM networks.Eventually,combined with the HGR data generated from the validated virtual battery,it is proved that the proposed approach can well predict the battery HGR under the dynamic stress test(DST) and worldwide light vehicles test procedure(WLTP),the mean absolute error under DST is 0.542 kW/m^(3),and the root mean square error under WLTP is1.428 kW/m^(3)at 25℃.Lastly,the investigation results of this paper also show a new perspective in the application of the PINN approach in battery HGR estimation.
基金Project supported by the Science and Engineering Research Board(SERB),Department of Science and Technology(DST),India(No.SRG/2019/001581)。
文摘With the explosive growth of computational resources and data generation,deep machine learning has been successfully employed in various applications.One important and emerging scientific application of deep learning involves solving differential equations.Here,physics-informed neural networks(PINNs)are developed to solve the differential equations associated with a specific scientific problem.As such,algorithms for solving the differential equations by embedding their initial and boundary conditions in the cost function of the artificial neural networks using algorithmic differentiation must also be developed.In this study,various PINNs are adopted to estimate the stresses in the tablets and the interphase of a single lap joint.The proposed model is represented by two fourth-order non-homogeneous coupled partial differential equations,with the axial stresses in the upper and lower tablets adopted as the dependent variables.The axial stresses are a function of the tablet length,which presents the independent variable.Therefore,the axial stresses in the tablets are estimated by solving the coupled partial differential equations when subjected to the boundary conditions,whereas the remaining stress components are expressed in terms of axial stresses.The results obtained using the developed methodology are validated using the results obtained via MAPLE software.
基金funded by the Cora Topolewski Cardiac Research Fund at the Children’s Hospital of Philadelphia(CHOP)the Pediatric Valve Center Frontier Program at CHOP+4 种基金the Additional Ventures Single Ventricle Research Fund Expansion Awardthe National Institutes of Health(USA)supported by the program(Nos.NHLBI T32 HL007915 and NIH R01 HL153166)supported by the program(No.NIH R01 HL153166)supported by the U.S.Department of Energy(No.DE-SC0022953)。
文摘Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions.However,material identification is a challenging task,especially when the characteristic of the material is highly nonlinear in nature,as is common in biological tissue.In this work,we identify unknown material properties in continuum solid mechanics via physics-informed neural networks(PINNs).To improve the accuracy and efficiency of PINNs,we develop efficient strategies to nonuniformly sample observational data.We also investigate different approaches to enforce Dirichlet-type boundary conditions(BCs)as soft or hard constraints.Finally,we apply the proposed methods to a diverse set of time-dependent and time-independent solid mechanic examples that span linear elastic and hyperelastic material space.The estimated material parameters achieve relative errors of less than 1%.As such,this work is relevant to diverse applications,including optimizing structural integrity and developing novel materials.
文摘This paper proposes a physics-informed neural network(PINN)framework to analyze the nonlinear buckling behavior of a three-dimensional(3D)FG porous,slender beam resting on a Winkler-Pasternak foundation.PINNs need much less training data to obtain high accuracy using a straightforward network.The powerful tool used in this work can handle any class of PDEs.We use the deep learning platform TensorFlow and DeepXDE library to design our network.In this study,the PINNs framework takes information from the governing differential equations of the beam system and the data from boundary conditions and outputs the critical nonlinear buckling load.The mathematical model is developed using Hamilton’s principle,considering geometry’s nonlinearity.The accuracy of the modeling framework is carefully examined by applying it to various boundary condition cases as well as the physical parameters such as 3D FG indexes on the nonlinear mechanical behaviors.Finally,the PINNs results are validated with those extracted from the generalized differential quadrature method(GDQM).It is found that the proposed PINN framework can characterize the nonlinear buckling behavior of 3D FG porous,slender beams with satisfactory accuracy.Furthermore,PINN is presented to accurately predict the nonlinear buckling behavior of the beam up to 71 times faster than the numerical method.
