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.

Optimizing near-carbon-free nuclear energy systems:advances in reactor operation digital twin through hybrid machine learning algorithms for parameter identification and state estimation

Accurate and efficient online parameter identification and state estimation are crucial for leveraging digital twin simulations to optimize the operation of near-carbon-free nuclear energy systems.In previous studies,we developed a reactor operation digital twin(RODT).However,non-differentiabilities and discontinuities arise when employing machine learning-based surrogate forward models,challenging traditional gradient-based inverse methods and their variants.This study investigated deterministic and metaheuristic algorithms and developed hybrid algorithms to address these issues.An efficient modular RODT software framework that incorporates these methods into its post-evaluation module is presented for comprehensive comparison.The methods were rigorously assessed based on convergence profiles,stability with respect to noise,and computational performance.The numerical results show that the hybrid KNNLHS algorithm excels in real-time online applications,balancing accuracy and efficiency with a prediction error rate of only 1%and processing times of less than 0.1 s.Contrastingly,algorithms such as FSA,DE,and ADE,although slightly slower(approximately 1 s),demonstrated higher accuracy with a 0.3%relative L_2 error,which advances RODT methodologies to harness machine learning and system modeling for improved reactor monitoring,systematic diagnosis of off-normal events,and lifetime management strategies.The developed modular software and novel optimization methods presented offer pathways to realize the full potential of RODT for transforming energy engineering practices.

Regularization Method to the Parameter Identification of Interfacial Heat Transfer Coefficient and Properties during Casting Solidification

The accurate material physical properties, initial and boundary conditions are indispensable to the numerical simulation in the casting process, and they are related to the simulation accuracy directly. The inverse heat conduction method can be used to identify the mentioned above parameters based on the temperature measurement data. This paper presented a new inverse method according to Tikhonov regularization theory. A regularization functional was established and the regularization parameter was deduced, the Newton-Raphson iteration method was used to solve the equations. One detailed case was solved to identify the thermal conductivity and specific heat of sand mold and interfacial heat transfer coefficient (IHTC) at the meantime. This indicates that the regularization method is very efficient in decreasing the sensitivity to the temperature measurement data, overcoming the ill-posedness of the inverse heat conduction problem (IHCP) and improving the stability and accuracy of the results. As a general inverse method, it can be used to identify not only the material physical properties but also the initial and boundary conditions' parameters.

PARAMETER IDENTIFICATION OF DYNAMIC MODELS USING A BAYES APPROACH

The Bayesian method of statistical analysis has been applied to the parameter identification problem. A method is presented to identify parameters of dynamic models with the Bayes estimators of measurement frequencies. This is based on the solution of an inverse generalized evaluate problem. The stochastic nature of test data is considered and a normal distribution is used for the measurement frequencies. An additional feature is that the engineer's confidence in the measurement frequencies is quantified and incorporated into the identification procedure. A numerical example demonstrates the efficiency of the method.

PROPER APPLICATION OF A KIND OF MATRIX CON-STRUCTION METHOD IN PHYSICAL PARAMETER IDENTIFICATION OF DYNAMIC MODEL

The expressions of matrix construction by using the singular value decomposition (SVD) are applied to the physics parameter identification of dynamic model. Then, based upon to the characteristics of a kind of matrix construction method, the orders of the parameter identification model can be reduced. After reducing, the mathematics and physics correspondence relations between the subsystem and the original system are distinct. the condensation errors can be avoided. The numerical example shows the benefit of the presented methodology.

PARAMETER IDENTIFICATION IN FRACTIONAL DIFFERENTIAL EQUATIONS

This article investigates the fractional derivative order identification, the coefficient identification, and the source identification in the fractional diffusion problems. If 1 〈 α〈 2, we prove the unique determination of the fractional derivative order and the dif- fusion coefficient p（x） by fo u（0, s）ds, 0 〈 t 〈 T for one-dimensional fractional diffusion-wave equations. Besides, if 0 〈 α 〈 1, we show the unique determination of the source term f（x, y） by U（0, 0, t）, 0 〈 t 〈 T for two-dimensional fractional diffusion equations. Here, a denotes the fractional derivative order over t.

Analysis of a functionally graded piezothermoelastic hollow cylinder

A long thick-walled hollow cylinder of piezothermoelastic materials was studied in this work. The gradient prop- erty of the piezoelectric parameter g31 was taken into account. The theory of elasticity was applied to obtain the exact solutions of the cylinder subjected simultaneously to thermal and electric loadings. As an application, these solutions have been success- fully used to study the inverse problems of the material. For comparison, numerical results have been carried out for both graded and double-layered cylinders.

Reconstruction of a Heat Equation from One Point Observations

We are concerned with the reconstruction of the heat sink coefficient in a one-dimensional heat equation from the observations of solutions at the same point.This direct method which is based on spectral estimation and asymptotics techniques provides a fast algorithm and also an alternative to the Gelfand-Levitan theory or minimization procedures.

基于邻域保留投影的工作模态参数识别

针对拉普拉斯特征映射和等距离映射算法识别弱非线性特征模态精度低的缺点,提出一种利用邻域保留投影算法的工作模态参数识别方法。该方法利用局部线性特征寻找结构位移响应数据的低维嵌入数据,低维嵌入数据与模态坐标响应矩阵相对应;利用单自由度识别技术从模态响应矩阵中识别出结构的模态固有频率;再用最小二乘广义逆估计变换矩阵,变换矩阵与模态振型矩阵相对应。该方法能够保留数据的局部线性特征,从而识别弱非线性模态。通过三维圆柱壳仿真数据集的识别结果表明,相比拉普拉斯特征映射和等距离映射算法,邻域保留投影算法能够更有效地识别出弱非线性特征模态的参数,平均识别精度更高。

Identification of the Material Parameters of Laminated Plates

A scheme is developed to identify the material parameters of laminated plates using mathematical optimization and measured eigenfrequencies of the object. The object function of the optimization is defined as the difference between the measured frequencies and the computed frequencies of the laminated plates. The sensitivity of the structural eigenvalue with respect to the material parameters is analyzed. A numerical example is presented to show the feasibility of the scheme.

MULTIPLE PARAMETERS IDENTIFICATION PROBLEMS IN RESISTIVITY WELL-LOGGING

In petroleum exploitation, the main aim of resistivity well-logging is to determine the resistivity of the layers by measuring the potential on the electrodes. This mathematical problem can be described as an inverse problem for the elliptic equivalued surface boundary value problem. In this paper, the author gets the expression of the derivative functions of the potential on the electrodes with respect to the resistivity of the layers. This allows us to solve the identification problem of the resistivity of the layers.

抛物型方程的演化参数识别方法

给出了一种利用演化计算方法求解微分方程中的参数识别类型反问题的方法。该方法把参数识别问题转化为泛函的优化问题用演化算法来求解 ,指定待定参数的函数类形式 ,用遗传算法 (GeneticAlgorithms)来演化待求参数的最优估计值 ,并将该方法运用于线性扩散方程和拟线性对流扩散反方程反问题的数值模拟中。

用演化算法求解抛物型方程扩散系数的识别问题

基于演化算法给出了一类求解参数识别反问题的一般方法 .该方法表明只要找到好的、求解相应的正问题的数值方法 ,演化算法就可以用于求解此类反问题 .设计有效的求解反问题的演化算法的关键是寻找一种适合反问题的解空间的编码表示形式、适当的适应值函数形式以及有效的计算正问题的数值方法 .该文结合演化算法、传统的求解反问题的迭代方法和正则化技术 ,设计了一类求解参数识别反问题的方法 .为验证此类方法 ,将其用于求解一维扩散方程的扩散系数的识别问题 ,得到了较好的数值结果 。

河流水质多参数识别反问题的演化算法

给出了利用演化计算方法求解河流水质多参数反问题的一种新方法。该方法把参数识别反问题转化为优化问题用演化方法求解。它的特点在于:从多个初始点开始寻优,并借助交叉和变异算子来获得水质参数的全局最优解。数据模拟结果表明,该方法具有很高的精度,收敛速度快,且编程简单,易于计算机实现,值得在实际工作中采用。

识别混凝土重力坝弹性模量的一种新方法

采用改进的遗传算法 ,根据混凝土重力坝的水位位移分量识别坝体和基础的弹性模量 .算例表明这种方法是可行的 ,具有较强的抗噪音能力 ,没有求解病态方程的困难 ,且具有全局收敛性 。

基于灵敏度的热传导辨识问题求解方法

本文采用灵敏度分析和优化方法求解热传导参数辨识问题。根据测量点已知温度值 ,将测量点的计算温度值与测量温度值之差平方和作为优化问题的目标函数 ,将待识别的热传导参数作为设计变量 ,极小化目标函数得到设计变量最优值就是真实的识别参数值。优化问题采用序列线性规划算法求解 ,基于温度场灵敏度分析构造线性规划问题。数值计算结果表明 ,本文方法求解热传导参数辨识这类反问题的效率和精度很高。

基于贝叶斯推理的标准k-ε湍流模型参数识别

为了降低湍流模型湍流参数不确定性给工程湍流问题求解带来数值误差,以后台阶流动为例研究了适用范围很广的k-ε湍流模型的参数识别问题。针对模型和实验数据的不确定性而采用了贝叶斯概率反演方法,该方法集成了有限单元法的正向计算和Metropolis-Hastings抽样算法的反向计算,从而给出在流速测量值已知的条件下标准k-ε湍流模型参数的后验概率分布。算例计算表明,采用参数识别后的参数值进行计算比传统推荐值有效地降低了数值误差。

一种基于神经网络的结构参数识别方法

提出了一种基于神经网络的结构参数识别方法，该方法以残余力向量作为结构参数识别的网络输入⒚针对训练样本在数据空间分布不均匀的问题，采用 Ｇ Ｓ Ｌ变换对训练样本数据进行预处理。

基于改进模拟退火算法反演水文地质参数

水文地质参数的反演是一个复杂的非线性优化问题,针对标准模拟退火算法收敛速度慢的缺陷,提出了反演水文地质参数的改进模拟退火算法。采取了设置内阀值、增加约束条件和记忆功能等措施,以提高标准模拟退火算法的收敛速度。实例分析结果表明,改进模拟退火算法在水文地质参数反演和含水层隔水边界的识别问题中不仅是可行的,而且求解精度较高。同时,结合实例的结果分析并给出了影响算法收敛性能的几个因素。