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
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
The heat transfer through a concave permeable fin is analyzed by the local thermal non-equilibrium(LTNE)model.The governing dimensional temperature equations for the solid and fluid phases of the porous extended surfa...The heat transfer through a concave permeable fin is analyzed by the local thermal non-equilibrium(LTNE)model.The governing dimensional temperature equations for the solid and fluid phases of the porous extended surface are modeled,and then are nondimensionalized by suitable dimensionless terms.Further,the obtained nondimensional equations are solved by the clique polynomial method(CPM).The effects of several dimensionless parameters on the fin's thermal profiles are shown by graphical illustrations.Additionally,the current study implements deep neural structures to solve physics-governed coupled equations,and the best-suited hyperparameters are attained by comparison with various network combinations.The results of the CPM and physicsinformed neural network(PINN)exhibit good agreement,signifying that both methods effectively solve the thermal modeling problem.展开更多
Soft materials,with the sensitivity to various external stimuli,exhibit high flexibility and stretchability.Accurate prediction of their mechanical behaviors requires advanced hyperelastic constitutive models incorpor...Soft materials,with the sensitivity to various external stimuli,exhibit high flexibility and stretchability.Accurate prediction of their mechanical behaviors requires advanced hyperelastic constitutive models incorporating multiple parameters.However,identifying multiple parameters under complex deformations remains a challenge,especially with limited observed data.In this study,we develop a physics-informed neural network(PINN)framework to identify material parameters and predict mechanical fields,focusing on compressible Neo-Hookean materials and hydrogels.To improve accuracy,we utilize scaling techniques to normalize network outputs and material parameters.This framework effectively solves forward and inverse problems,extrapolating continuous mechanical fields from sparse boundary data and identifying unknown mechanical properties.We explore different approaches for imposing boundary conditions(BCs)to assess their impacts on accuracy.To enhance efficiency and generalization,we propose a transfer learning enhanced PINN(TL-PINN),allowing pre-trained networks to quickly adapt to new scenarios.The TL-PINN significantly reduces computational costs while maintaining accuracy.This work holds promise in addressing practical challenges in soft material science,and provides insights into soft material mechanics with state-of-the-art experimental methods.展开更多
Recently,numerous studies have demonstrated that the physics-informed neural network(PINN)can effectively and accurately resolve hyperelastic finite deformation problems.In this paper,a PINN framework for tackling hyp...Recently,numerous studies have demonstrated that the physics-informed neural network(PINN)can effectively and accurately resolve hyperelastic finite deformation problems.In this paper,a PINN framework for tackling hyperelastic-magnetic coupling problems is proposed.Since the solution space consists of two-phase domains,two separate networks are constructed to independently predict the solution for each phase region.In addition,a conscious point allocation strategy is incorporated to enhance the prediction precision of the PINN in regions characterized by sharp gradients.With the developed framework,the magnetic fields and deformation fields of magnetorheological elastomers(MREs)are solved under the control of hyperelastic-magnetic coupling equations.Illustrative examples are provided and contrasted with the reference results to validate the predictive accuracy of the proposed framework.Moreover,the advantages of the proposed framework in solving hyperelastic-magnetic coupling problems are validated,particularly in handling small data sets,as well as its ability in swiftly and precisely forecasting magnetostrictive motion.展开更多
A physics-informed neural network(PINN)is a powerful tool for solving differential equations in solid and fluid mechanics.However,it suffers from singularly perturbed boundary-layer problems in which there exist sharp...A physics-informed neural network(PINN)is a powerful tool for solving differential equations in solid and fluid mechanics.However,it suffers from singularly perturbed boundary-layer problems in which there exist sharp changes caused by a small perturbation parameter multiplying the highest-order derivatives.In this paper,we introduce Chien's composite expansion method into PINNs,and propose a novel architecture for the PINNs,namely,the Chien-PINN(C-PINN)method.This novel PINN method is validated by singularly perturbed differential equations,and successfully solves the wellknown thin plate bending problems.In particular,no cumbersome matching conditions are needed for the C-PINN method,compared with the previous studies based on matched asymptotic expansions.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
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
Prognosis of bearing is critical to improve the safety,reliability,and availability of machinery systems,which provides the health condition assessment and determines how long the machine would work before failure occ...Prognosis of bearing is critical to improve the safety,reliability,and availability of machinery systems,which provides the health condition assessment and determines how long the machine would work before failure occurs by predicting the remaining useful life(RUL).In order to overcome the drawback of pure data-driven methods and predict RUL accurately,a novel physics-informed deep neural network,named degradation consistency recurrent neural network,is proposed for RUL prediction by integrating the natural degradation knowledge of mechanical components.The degradation is monotonic over the whole life of bearings,which is characterized by temperature signals.To incorporate the knowledge of monotonic degradation,a positive increment recurrence relationship is introduced to keep the monotonicity.Thus,the proposed model is relatively well understood and capable to keep the learning process consistent with physical degradation.The effectiveness and merit of the RUL prediction using the proposed method are demonstrated through vibration signals collected from a set of run-to-failure tests.展开更多
Physics-informed neural networks(PINNs)are proved methods that are effective in solving some strongly nonlinear partial differential equations(PDEs),e.g.,Navier-Stokes equations,with a small amount of boundary or inte...Physics-informed neural networks(PINNs)are proved methods that are effective in solving some strongly nonlinear partial differential equations(PDEs),e.g.,Navier-Stokes equations,with a small amount of boundary or interior data.However,the feasibility of applying PINNs to the flow at moderate or high Reynolds numbers has rarely been reported.The present paper proposes an artificial viscosity(AV)-based PINN for solving the forward and inverse flow problems.Specifically,the AV used in PINNs is inspired by the entropy viscosity method developed in conventional computational fluid dynamics(CFD)to stabilize the simulation of flow at high Reynolds numbers.The newly developed PINN is used to solve the forward problem of the two-dimensional steady cavity flow at Re=1000 and the inverse problem derived from two-dimensional film boiling.The results show that the AV augmented PINN can solve both problems with good accuracy and substantially reduce the inference errors in the forward problem.展开更多
Physics-informed deep learning has drawn tremendous interest in recent years to solve computational physics problems,whose basic concept is to embed physical laws to constrain/inform neural networks,with the need of l...Physics-informed deep learning has drawn tremendous interest in recent years to solve computational physics problems,whose basic concept is to embed physical laws to constrain/inform neural networks,with the need of less data for training a reliable model.This can be achieved by incorporating the residual of physics equations into the loss function.Through minimizing the loss function,the network could approximate the solution.In this paper,we propose a mixed-variable scheme of physics-informed neural network(PINN)for fluid dynamics and apply it to simulate steady and transient laminar flows at low Reynolds numbers.A parametric study indicates that the mixed-variable scheme can improve the PINN trainability and the solution accuracy.The predicted velocity and pressure fields by the proposed PINN approach are also compared with the reference numerical solutions.Simulation results demonstrate great potential of the proposed PINN for fluid flow simulation with a high accuracy.展开更多
Accurate dynamics modeling is crucial for the safety and control offixed-wing aircraft under perturbation(e.g.icing/fault).In this work,we propose a physics-informed Neural Ordinary Differential Equation(PI-NODE)-base...Accurate dynamics modeling is crucial for the safety and control offixed-wing aircraft under perturbation(e.g.icing/fault).In this work,we propose a physics-informed Neural Ordinary Differential Equation(PI-NODE)-based scheme for aircraft dynamics modeling under icing/fault.First,icing accumulation and control surface faults are considered and injected into the nominal(clean)aircraft dynamics model.Second,the physics knowledge of aircraft dynamics modeling is divided into kinematics and kinetics.The former is universally applicable and borrows directly from the nominal aircraft.The latter kinetics knowledge,which hinges on external forces and moments,is inaccurate and challenging under icing/fault.To address this issue,we employ Neural ODE to compensate for the residual between the aircraft dynamics under icing/fault and the nominal(clean)condition,resulting in a naturally continuous-time modeling approach.In experiments,we benchmark the proposed PI-NODE against three baseline methods in a dedicated flight scenario.Comparative studies validate the higher accuracy and improve the generalization ability of the proposed PI-NODE for aircraft dynamics modeling under icing/fault.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
Physics-informed deep learning has recently emerged as an effective tool for leveraging both observational data and available physical laws.Physics-informed neural networks(PINNs)and deep operator networks(DeepONets)a...Physics-informed deep learning has recently emerged as an effective tool for leveraging both observational data and available physical laws.Physics-informed neural networks(PINNs)and deep operator networks(DeepONets)are two such models.The former encodes the physical laws via the automatic differentiation,while the latter learns the hidden physics from data.Generally,the noisy and limited observational data as well as the over-parameterization in neural networks(NNs)result in uncertainty in predictions from deep learning models.In paper“MENG,X.,YANG,L.,MAO,Z.,FERRANDIS,J.D.,and KARNIADAKIS,G.E.Learning functional priors and posteriors from data and physics.Journal of Computational Physics,457,111073(2022)”,a Bayesian framework based on the generative adversarial networks(GANs)has been proposed as a unified model to quantify uncertainties in predictions of PINNs as well as DeepONets.Specifically,the proposed approach in“MENG,X.,YANG,L.,MAO,Z.,FERRANDIS,J.D.,and KARNIADAKIS,G.E.Learning functional priors and posteriors from data and physics.Journal of Computational Physics,457,111073(2022)”has two stages:(i)prior learning,and(ii)posterior estimation.At the first stage,the GANs are utilized to learn a functional prior either from a prescribed function distribution,e.g.,the Gaussian process,or from historical data and available physics.At the second stage,the Hamiltonian Monte Carlo(HMC)method is utilized to estimate the posterior in the latent space of GANs.However,the vanilla HMC does not support the mini-batch training,which limits its applications in problems with big data.In the present work,we propose to use the normalizing flow(NF)models in the context of variational inference(VI),which naturally enables the mini-batch training,as the alternative to HMC for posterior estimation in the latent space of GANs.A series of numerical experiments,including a nonlinear differential equation problem and a 100-dimensional(100D)Darcy problem,are conducted to demonstrate that the NFs with full-/mini-batch training are able to achieve similar accuracy as the“gold rule”HMC.Moreover,the mini-batch training of NF makes it a promising tool for quantifying uncertainty in solving the high-dimensional partial differential equation(PDE)problems with big data.展开更多
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.
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funding this work through Small Research Project under grant number RGP.1/141/45。
文摘The heat transfer through a concave permeable fin is analyzed by the local thermal non-equilibrium(LTNE)model.The governing dimensional temperature equations for the solid and fluid phases of the porous extended surface are modeled,and then are nondimensionalized by suitable dimensionless terms.Further,the obtained nondimensional equations are solved by the clique polynomial method(CPM).The effects of several dimensionless parameters on the fin's thermal profiles are shown by graphical illustrations.Additionally,the current study implements deep neural structures to solve physics-governed coupled equations,and the best-suited hyperparameters are attained by comparison with various network combinations.The results of the CPM and physicsinformed neural network(PINN)exhibit good agreement,signifying that both methods effectively solve the thermal modeling problem.
基金supported by the National Natural Science Foundation of China(Nos.12172273 and 11820101001)。
文摘Soft materials,with the sensitivity to various external stimuli,exhibit high flexibility and stretchability.Accurate prediction of their mechanical behaviors requires advanced hyperelastic constitutive models incorporating multiple parameters.However,identifying multiple parameters under complex deformations remains a challenge,especially with limited observed data.In this study,we develop a physics-informed neural network(PINN)framework to identify material parameters and predict mechanical fields,focusing on compressible Neo-Hookean materials and hydrogels.To improve accuracy,we utilize scaling techniques to normalize network outputs and material parameters.This framework effectively solves forward and inverse problems,extrapolating continuous mechanical fields from sparse boundary data and identifying unknown mechanical properties.We explore different approaches for imposing boundary conditions(BCs)to assess their impacts on accuracy.To enhance efficiency and generalization,we propose a transfer learning enhanced PINN(TL-PINN),allowing pre-trained networks to quickly adapt to new scenarios.The TL-PINN significantly reduces computational costs while maintaining accuracy.This work holds promise in addressing practical challenges in soft material science,and provides insights into soft material mechanics with state-of-the-art experimental methods.
基金supported by the National Natural Science Foundation of China(Nos.12072105 and 11932006)。
文摘Recently,numerous studies have demonstrated that the physics-informed neural network(PINN)can effectively and accurately resolve hyperelastic finite deformation problems.In this paper,a PINN framework for tackling hyperelastic-magnetic coupling problems is proposed.Since the solution space consists of two-phase domains,two separate networks are constructed to independently predict the solution for each phase region.In addition,a conscious point allocation strategy is incorporated to enhance the prediction precision of the PINN in regions characterized by sharp gradients.With the developed framework,the magnetic fields and deformation fields of magnetorheological elastomers(MREs)are solved under the control of hyperelastic-magnetic coupling equations.Illustrative examples are provided and contrasted with the reference results to validate the predictive accuracy of the proposed framework.Moreover,the advantages of the proposed framework in solving hyperelastic-magnetic coupling problems are validated,particularly in handling small data sets,as well as its ability in swiftly and precisely forecasting magnetostrictive motion.
基金Project supported by the National Natural Science Foundation of China Basic Science Center Program for“Multiscale Problems in Nonlinear Mechanics”(No.11988102)the National Natural Science Foundation of China(No.12202451)。
文摘A physics-informed neural network(PINN)is a powerful tool for solving differential equations in solid and fluid mechanics.However,it suffers from singularly perturbed boundary-layer problems in which there exist sharp changes caused by a small perturbation parameter multiplying the highest-order derivatives.In this paper,we introduce Chien's composite expansion method into PINNs,and propose a novel architecture for the PINNs,namely,the Chien-PINN(C-PINN)method.This novel PINN method is validated by singularly perturbed differential equations,and successfully solves the wellknown thin plate bending problems.In particular,no cumbersome matching conditions are needed for the C-PINN method,compared with the previous studies based on matched asymptotic expansions.
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.
基金support in part by China Postdoctoral Science Foundation (No.2021M702634)National Science Foundation of China (No.52175116).
文摘Prognosis of bearing is critical to improve the safety,reliability,and availability of machinery systems,which provides the health condition assessment and determines how long the machine would work before failure occurs by predicting the remaining useful life(RUL).In order to overcome the drawback of pure data-driven methods and predict RUL accurately,a novel physics-informed deep neural network,named degradation consistency recurrent neural network,is proposed for RUL prediction by integrating the natural degradation knowledge of mechanical components.The degradation is monotonic over the whole life of bearings,which is characterized by temperature signals.To incorporate the knowledge of monotonic degradation,a positive increment recurrence relationship is introduced to keep the monotonicity.Thus,the proposed model is relatively well understood and capable to keep the learning process consistent with physical degradation.The effectiveness and merit of the RUL prediction using the proposed method are demonstrated through vibration signals collected from a set of run-to-failure tests.
基金Project supported by the Fundamental Research Funds for the Central Universities of China(No.DUT21RC(3)063)the National Natural Science Foundation of China(No.51720105007)the Baidu Foundation(No.ghfund202202014542)。
文摘Physics-informed neural networks(PINNs)are proved methods that are effective in solving some strongly nonlinear partial differential equations(PDEs),e.g.,Navier-Stokes equations,with a small amount of boundary or interior data.However,the feasibility of applying PINNs to the flow at moderate or high Reynolds numbers has rarely been reported.The present paper proposes an artificial viscosity(AV)-based PINN for solving the forward and inverse flow problems.Specifically,the AV used in PINNs is inspired by the entropy viscosity method developed in conventional computational fluid dynamics(CFD)to stabilize the simulation of flow at high Reynolds numbers.The newly developed PINN is used to solve the forward problem of the two-dimensional steady cavity flow at Re=1000 and the inverse problem derived from two-dimensional film boiling.The results show that the AV augmented PINN can solve both problems with good accuracy and substantially reduce the inference errors in the forward problem.
文摘Physics-informed deep learning has drawn tremendous interest in recent years to solve computational physics problems,whose basic concept is to embed physical laws to constrain/inform neural networks,with the need of less data for training a reliable model.This can be achieved by incorporating the residual of physics equations into the loss function.Through minimizing the loss function,the network could approximate the solution.In this paper,we propose a mixed-variable scheme of physics-informed neural network(PINN)for fluid dynamics and apply it to simulate steady and transient laminar flows at low Reynolds numbers.A parametric study indicates that the mixed-variable scheme can improve the PINN trainability and the solution accuracy.The predicted velocity and pressure fields by the proposed PINN approach are also compared with the reference numerical solutions.Simulation results demonstrate great potential of the proposed PINN for fluid flow simulation with a high accuracy.
基金sponsored by the Shanghai Sailing Program under Grant No.20YF1402500the Shanghai Natural Science Fund under Grant No.22ZR1404500.
文摘Accurate dynamics modeling is crucial for the safety and control offixed-wing aircraft under perturbation(e.g.icing/fault).In this work,we propose a physics-informed Neural Ordinary Differential Equation(PI-NODE)-based scheme for aircraft dynamics modeling under icing/fault.First,icing accumulation and control surface faults are considered and injected into the nominal(clean)aircraft dynamics model.Second,the physics knowledge of aircraft dynamics modeling is divided into kinematics and kinetics.The former is universally applicable and borrows directly from the nominal aircraft.The latter kinetics knowledge,which hinges on external forces and moments,is inaccurate and challenging under icing/fault.To address this issue,we employ Neural ODE to compensate for the residual between the aircraft dynamics under icing/fault and the nominal(clean)condition,resulting in a naturally continuous-time modeling approach.In experiments,we benchmark the proposed PI-NODE against three baseline methods in a dedicated flight scenario.Comparative studies validate the higher accuracy and improve the generalization ability of the proposed PI-NODE for aircraft dynamics modeling under icing/fault.
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Project supported by the National Natural Science Foundation of China(No.12201229)。
文摘Physics-informed deep learning has recently emerged as an effective tool for leveraging both observational data and available physical laws.Physics-informed neural networks(PINNs)and deep operator networks(DeepONets)are two such models.The former encodes the physical laws via the automatic differentiation,while the latter learns the hidden physics from data.Generally,the noisy and limited observational data as well as the over-parameterization in neural networks(NNs)result in uncertainty in predictions from deep learning models.In paper“MENG,X.,YANG,L.,MAO,Z.,FERRANDIS,J.D.,and KARNIADAKIS,G.E.Learning functional priors and posteriors from data and physics.Journal of Computational Physics,457,111073(2022)”,a Bayesian framework based on the generative adversarial networks(GANs)has been proposed as a unified model to quantify uncertainties in predictions of PINNs as well as DeepONets.Specifically,the proposed approach in“MENG,X.,YANG,L.,MAO,Z.,FERRANDIS,J.D.,and KARNIADAKIS,G.E.Learning functional priors and posteriors from data and physics.Journal of Computational Physics,457,111073(2022)”has two stages:(i)prior learning,and(ii)posterior estimation.At the first stage,the GANs are utilized to learn a functional prior either from a prescribed function distribution,e.g.,the Gaussian process,or from historical data and available physics.At the second stage,the Hamiltonian Monte Carlo(HMC)method is utilized to estimate the posterior in the latent space of GANs.However,the vanilla HMC does not support the mini-batch training,which limits its applications in problems with big data.In the present work,we propose to use the normalizing flow(NF)models in the context of variational inference(VI),which naturally enables the mini-batch training,as the alternative to HMC for posterior estimation in the latent space of GANs.A series of numerical experiments,including a nonlinear differential equation problem and a 100-dimensional(100D)Darcy problem,are conducted to demonstrate that the NFs with full-/mini-batch training are able to achieve similar accuracy as the“gold rule”HMC.Moreover,the mini-batch training of NF makes it a promising tool for quantifying uncertainty in solving the high-dimensional partial differential equation(PDE)problems with big data.
