Physics-informed machine learning model for prediction of ground reflected wave peak overpressure

The accurate prediction of peak overpressure of explosion shockwaves is significant in fields such as explosion hazard assessment and structural protection, where explosion shockwaves serve as typical destructive elements. Aiming at the problem of insufficient accuracy of the existing physical models for predicting the peak overpressure of ground reflected waves, two physics-informed machine learning models are constructed. The results demonstrate that the machine learning models, which incorporate physical information by predicting the deviation between the physical model and actual values and adding a physical loss term in the loss function, can accurately predict both the training and out-oftraining dataset. Compared to existing physical models, the average relative error in the predicted training domain is reduced from 17.459%-48.588% to 2%, and the proportion of average relative error less than 20% increased from 0% to 59.4% to more than 99%. In addition, the relative average error outside the prediction training set range is reduced from 14.496%-29.389% to 5%, and the proportion of relative average error less than 20% increased from 0% to 71.39% to more than 99%. The inclusion of a physical loss term enforcing monotonicity in the loss function effectively improves the extrapolation performance of machine learning. The findings of this study provide valuable reference for explosion hazard assessment and anti-explosion structural design in various fields.

Accurate and efficient remaining useful life prediction of batteries enabled by physics-informed machine learning

The safe and reliable operation of lithium-ion batteries necessitates the accurate prediction of remaining useful life(RUL).However,this task is challenging due to the diverse ageing mechanisms,various operating conditions,and limited measured signals.Although data-driven methods are perceived as a promising solution,they ignore intrinsic battery physics,leading to compromised accuracy,low efficiency,and low interpretability.In response,this study integrates domain knowledge into deep learning to enhance the RUL prediction performance.We demonstrate accurate RUL prediction using only a single charging curve.First,a generalisable physics-based model is developed to extract ageing-correlated parameters that can describe and explain battery degradation from battery charging data.The parameters inform a deep neural network(DNN)to predict RUL with high accuracy and efficiency.The trained model is validated under 3 types of batteries working under 7 conditions,considering fully charged and partially charged cases.Using data from one cycle only,the proposed method achieves a root mean squared error(RMSE)of 11.42 cycles and a mean absolute relative error(MARE)of 3.19%on average,which are over45%and 44%lower compared to the two state-of-the-art data-driven methods,respectively.Besides its accuracy,the proposed method also outperforms existing methods in terms of efficiency,input burden,and robustness.The inherent relationship between the model parameters and the battery degradation mechanism is further revealed,substantiating the intrinsic superiority of the proposed method.

An adaptive physics-informed deep learning method for pore pressure prediction using seismic data

Accurate prediction of formation pore pressure is essential to predict fluid flow and manage hydrocarbon production in petroleum engineering.Recent deep learning technique has been receiving more interest due to the great potential to deal with pore pressure prediction.However,most of the traditional deep learning models are less efficient to address generalization problems.To fill this technical gap,in this work,we developed a new adaptive physics-informed deep learning model with high generalization capability to predict pore pressure values directly from seismic data.Specifically,the new model,named CGP-NN,consists of a novel parametric features extraction approach(1DCPP),a stacked multilayer gated recurrent model(multilayer GRU),and an adaptive physics-informed loss function.Through machine training,the developed model can automatically select the optimal physical model to constrain the results for each pore pressure prediction.The CGP-NN model has the best generalization when the physicsrelated metricλ=0.5.A hybrid approach combining Eaton and Bowers methods is also proposed to build machine-learnable labels for solving the problem of few labels.To validate the developed model and methodology,a case study on a complex reservoir in Tarim Basin was further performed to demonstrate the high accuracy on the pore pressure prediction of new wells along with the strong generalization ability.The adaptive physics-informed deep learning approach presented here has potential application in the prediction of pore pressures coupled with multiple genesis mechanisms using seismic data.

Multi-scale physics-informed neural networks for solving high Reynolds number boundary layer flows based on matched asymptotic expansions

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.

Radiative heat transfer analysis of a concave porous fin under the local thermal non-equilibrium condition:application of the clique polynomial method and physics-informed neural networks

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.

Physics-informed optimization for a data-driven approach in landslide susceptibility evaluation

Landslide susceptibility mapping is an integral part of geological hazard analysis.Recently,the emphasis of many studies has been on data-driven models,notably those derived from machine learning,owing to their aptitude for tackling complex non-linear problems.However,the prevailing models often disregard qualitative research,leading to limited interpretability and mistakes in extracting negative samples,i.e.inaccurate non-landslide samples.In this study,Scoops 3D(a three-dimensional slope stability analysis tool)was utilized to conduct a qualitative assessment of slope stability in the Yunyang section of the Three Gorges Reservoir area.The depth of the bedrock was predicted utilizing a Convolutional Neural Network(CNN),incorporating local boreholes and building on the insights from prior research.The Random Forest(RF)algorithm was subsequently used to execute a data-driven landslide susceptibility analysis.The proposed methodology demonstrated a notable increase of 29.25%in the evaluation metric,the area under the receiver operating characteristic curve(ROC-AUC),outperforming the prevailing benchmark model.Furthermore,the landslide susceptibility map generated by the proposed model demonstrated superior interpretability.This result not only validates the effectiveness of amalgamating mathematical and mechanistic insights for such analyses,but it also carries substantial academic and practical implications.

MetaPINNs:Predicting soliton and rogue wave of nonlinear PDEs via the improved physics-informed neural networks based on meta-learned optimization

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.

Incorporating Lasso Regression to Physics-Informed Neural Network for Inverse PDE Problem

Partial Differential Equation(PDE)is among the most fundamental tools employed to model dynamic systems.Existing PDE modeling methods are typically derived from established knowledge and known phenomena,which are time-consuming and labor-intensive.Recently,discovering governing PDEs from collected actual data via Physics Informed Neural Networks(PINNs)provides a more efficient way to analyze fresh dynamic systems and establish PEDmodels.This study proposes Sequentially Threshold Least Squares-Lasso(STLasso),a module constructed by incorporating Lasso regression into the Sequentially Threshold Least Squares(STLS)algorithm,which can complete sparse regression of PDE coefficients with the constraints of l0 norm.It further introduces PINN-STLasso,a physics informed neural network combined with Lasso sparse regression,able to find underlying PDEs from data with reduced data requirements and better interpretability.In addition,this research conducts experiments on canonical inverse PDE problems and compares the results to several recent methods.The results demonstrated that the proposed PINN-STLasso outperforms other methods,achieving lower error rates even with less data.

TCAS-PINN:Physics-informed neural networks with a novel temporal causality-based adaptive sampling method

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.

Physics-informed deep learning for fringe pattern analysis

Recently,deep learning has yielded transformative success across optics and photonics,especially in optical metrology.Deep neural networks (DNNs) with a fully convolutional architecture (e.g.,U-Net and its derivatives) have been widely implemented in an end-to-end manner to accomplish various optical metrology tasks,such as fringe denoising,phase unwrapping,and fringe analysis.However,the task of training a DNN to accurately identify an image-to-image transform from massive input and output data pairs seems at best naive,as the physical laws governing the image formation or other domain expertise pertaining to the measurement have not yet been fully exploited in current deep learning practice.To this end,we introduce a physics-informed deep learning method for fringe pattern analysis (PI-FPA) to overcome this limit by integrating a lightweight DNN with a learning-enhanced Fourier transform profilometry (Le FTP) module.By parameterizing conventional phase retrieval methods,the Le FTP module embeds the prior knowledge in the network structure and the loss function to directly provide reliable phase results for new types of samples,while circumventing the requirement of collecting a large amount of high-quality data in supervised learning methods.Guided by the initial phase from Le FTP,the phase recovery ability of the lightweight DNN is enhanced to further improve the phase accuracy at a low computational cost compared with existing end-to-end networks.Experimental results demonstrate that PI-FPA enables more accurate and computationally efficient single-shot phase retrieval,exhibiting its excellent generalization to various unseen objects during training.The proposed PI-FPA presents that challenging issues in optical metrology can be potentially overcome through the synergy of physics-priors-based traditional tools and data-driven learning approaches,opening new avenues to achieve fast and accurate single-shot 3D imaging.

A transfer learning enhanced physics-informed neural network for parameter identification in soft materials

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.

Chien-physics-informed neural networks for solving singularly perturbed boundary-layer problems

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.

A physics-informed neural network for simulation of finite deformation in hyperelastic-magnetic coupling problems

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.

A hybrid physics-informed data-driven neural network for CO_(2) storage in depleted shale reservoirs

To reduce CO_(2) emissions in response to global climate change,shale reservoirs could be ideal candidates for long-term carbon geo-sequestration involving multi-scale transport processes.However,most current CO_(2) sequestration models do not adequately consider multiple transport mechanisms.Moreover,the evaluation of CO_(2) storage processes usually involves laborious and time-consuming numerical simulations unsuitable for practical prediction and decision-making.In this paper,an integrated model involving gas diffusion,adsorption,dissolution,slip flow,and Darcy flow is proposed to accurately characterize CO_(2) storage in depleted shale reservoirs,supporting the establishment of a training database.On this basis,a hybrid physics-informed data-driven neural network(HPDNN)is developed as a deep learning surrogate for prediction and inversion.By incorporating multiple sources of scientific knowledge,the HPDNN can be configured with limited simulation resources,significantly accelerating the forward and inversion processes.Furthermore,the HPDNN can more intelligently predict injection performance,precisely perform reservoir parameter inversion,and reasonably evaluate the CO_(2) storage capacity under complicated scenarios.The validation and test results demonstrate that the HPDNN can ensure high accuracy and strong robustness across an extensive applicability range when dealing with field data with multiple noise sources.This study has tremendous potential to replace traditional modeling tools for predicting and making decisions about CO_(2) storage projects in depleted shale reservoirs.

采用STAMP-24Model的多组织事故分析

安全生产事故往往由多组织交互、多因素耦合造成,事故原因涉及多个组织。为预防和遏制多组织生产安全事故的发生,基于系统理论事故建模与过程模型(Systems-Theory Accident Modeling and Process,STAMP)、24Model,构建一种用于多组织事故分析的方法,并以青岛石油爆炸事故为例进行事故原因分析。结果显示:STAMP-24Model可以分组织,分层次且有效、全面、详细地分析涉及多个组织的事故原因,探究多组织之间的交互关系;对事故进行动态演化分析,可得到各组织不安全动作耦合关系与形成的事故失效链及管控失效路径,进而为预防多组织事故提供思路和参考。

基于改进24Model-ISM-SNA建筑工人不安全行为关联路径研究

建筑施工现场环境复杂,为有效控制不安全行为发生,基于行为安全“2-4”模型对360份具有代表性的建筑安全事故调查报告进行分析,提取出22个不安全行为的主要影响因素。利用灰色关联分析方法(GRA)改进的集成ISM-SNA模型,将不安全行为风险因素划分为表层、过渡层与深层,然后对风险因素进行可视化分析、中心度分析及凝聚子群分析,揭示了各致因因素间的关联关系和传导路径。结果表明,建筑工人不安全行为影响因素可划分成7级3阶的多级递阶结构,安全意识、现场监管、外部环境是建筑工人不安全行为的关键影响因素,同时现场监管和隐患排查到位能有效降低不安全行为的发生。

基于24Model-D-ISM的地铁站火灾疏散影响因素研究

为预防地铁站火灾事故,深入了解地铁站火灾人员疏散影响因素间的内在联系与层次结构,基于第6版“2-4”模型(24Model)分析63起地铁站火灾疏散事故,充分考虑各个因素之间的交互作用,提取19个影响地铁站人员疏散的关键因素,建立地铁站火灾人员疏散影响因素指标体系;采用算子客观赋权法(C-OWA)改进决策试验与评价实验法(DEMATEL),确定地铁站火灾人员疏散的重要影响因素;在此基础上,采用解释结构模型(ISM)分析各个因素间的层次结构及相互作用路径,构建地铁站火灾人员疏散影响因素的多级递阶结构模型。研究结果表明:疏散引导、恐慌从众行为、人员拥挤为地铁站火灾人员疏散的关键影响因素;地铁站火灾人员疏散受表层因素、中间层因素、深层因素共同作用的影响,其中,疏散教育与培训、设施维护与检查、疏散预案等因素是根源影响因素,重视根源影响因素的改善有利于从本质上预防和控制事故的发生。

Physics-informed neural network approach for heat generation rate estimation of lithium-ion battery under various driving conditions

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.

Physics-informed neural networks with residual/gradient-based adaptive sampling methods for solving partial differential equations with sharp solutions

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.

Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics

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.