传统的数值求解方法面临维数灾难和效率与精度平衡问题,而基于数据驱动的神经网络求解方法又存在训练量冗余和不可解释性问题。针对此问题,物理信息神经网络(Physical Information Neural Networks,PINNs)关注了训练数据中隐含的物理先...传统的数值求解方法面临维数灾难和效率与精度平衡问题,而基于数据驱动的神经网络求解方法又存在训练量冗余和不可解释性问题。针对此问题,物理信息神经网络(Physical Information Neural Networks,PINNs)关注了训练数据中隐含的物理先验知识,融合了神经网络拟合复杂变量的能力,赋予了传统神经网络所缺乏的物理可解释性。应用该算法模型,提出了一种基于PINN的Burgers方程求解模型,该算法模型在训练中施加物理信息约束,因此能用少量的训练样本学习预测到分布在时空域上的偏微分方程模型。实验结果表明,在1+1维Burgers方程算例下,所提方法相比于经典的机器学习算法能有效捕抓到方程的变化并进行精确模拟,相比于有限差分法,可以大幅度缩短模拟时间。通过对不同的网络参数进行比较实验,所提方法在10%的噪声破坏下能产生合理的识别准确度,网络逼近方程的待定系数误差在0.001以内。展开更多
The electron-phonon interaction can reveal the microscopic mechanism of heat transfer in metals.The two-step heat conduction considering electron-phonon interaction has become an effective theoretical model for extrem...The electron-phonon interaction can reveal the microscopic mechanism of heat transfer in metals.The two-step heat conduction considering electron-phonon interaction has become an effective theoretical model for extreme environments,such as micro-scale and ultrafast processes.In this work,the two-step heat transfer model is further extended by considering the Burgers heat conduction model with the secondorder heat flux rate for electrons.Then,a novel generalized electron-phonon coupling thermoelasticity is proposed with the Burgers electronic heat transfer.Then,the problem of one-dimensional semi-infinite copper strip subject to a thermal shock at one side is studied by the Burgers two-step(BTS)model.The thermoelastic analytical solutions are systematically derived in the Laplace domain,and the numerical Laplace inversion method is adopted to obtain the transient responses.The new model is compared with the parabolic two-step(PTS)model and the hyperbolic two-step(HTS)model.The results show that in ultrafast heating,the BTS model has the same wave front jump as the HTS model.The present model has the faster wave speed,and predicts the bigger disturbed regions than the HTS model.More deeply,all two-step models also have the faster wave speeds than one-step models.This work may benefit the theoretical modeling of ultrafast heating of metals.展开更多
The Time Fractional Burger equation was solved in this study using the Mabel software and the Variational Iteration approach. where a number of instances of the Time Fractional Burger Equation were handled using this ...The Time Fractional Burger equation was solved in this study using the Mabel software and the Variational Iteration approach. where a number of instances of the Time Fractional Burger Equation were handled using this technique. Tables and images were used to present the collected numerical results. The difference between the exact and numerical solutions demonstrates the effectiveness of the Mabel program’s solution, as well as the accuracy and closeness of the results this method produced. It also demonstrates the Mabel program’s ability to quickly and effectively produce the numerical solution.展开更多
In this paper, the Adomian decomposition method was used to solve the Time Fractional Burger equation using Mabel program. This method was applied to a number of examples of the Time Fractional Burger Equation. The ob...In this paper, the Adomian decomposition method was used to solve the Time Fractional Burger equation using Mabel program. This method was applied to a number of examples of the Time Fractional Burger Equation. The obtained numerical results were presented in the form of tables and graphics. The difference between the exact solutions and the numerical solutions shows us the effectiveness of the solution using the Mabel program and that this method gave accurate results and was close to the exact solution, in addition to its ability to obtain the numerical solution quickly and efficiently using the Mabel program.展开更多
文摘传统的数值求解方法面临维数灾难和效率与精度平衡问题,而基于数据驱动的神经网络求解方法又存在训练量冗余和不可解释性问题。针对此问题,物理信息神经网络(Physical Information Neural Networks,PINNs)关注了训练数据中隐含的物理先验知识,融合了神经网络拟合复杂变量的能力,赋予了传统神经网络所缺乏的物理可解释性。应用该算法模型,提出了一种基于PINN的Burgers方程求解模型,该算法模型在训练中施加物理信息约束,因此能用少量的训练样本学习预测到分布在时空域上的偏微分方程模型。实验结果表明,在1+1维Burgers方程算例下,所提方法相比于经典的机器学习算法能有效捕抓到方程的变化并进行精确模拟,相比于有限差分法,可以大幅度缩短模拟时间。通过对不同的网络参数进行比较实验,所提方法在10%的噪声破坏下能产生合理的识别准确度,网络逼近方程的待定系数误差在0.001以内。
基金Project supported by the Fundamental Research Funds for the Central Universities of China(Nos.D5000230066 and D5000210117)the Natural Science Basic Research Plan in Shaanxi Province of China(No.2022JQ-358)。
文摘The electron-phonon interaction can reveal the microscopic mechanism of heat transfer in metals.The two-step heat conduction considering electron-phonon interaction has become an effective theoretical model for extreme environments,such as micro-scale and ultrafast processes.In this work,the two-step heat transfer model is further extended by considering the Burgers heat conduction model with the secondorder heat flux rate for electrons.Then,a novel generalized electron-phonon coupling thermoelasticity is proposed with the Burgers electronic heat transfer.Then,the problem of one-dimensional semi-infinite copper strip subject to a thermal shock at one side is studied by the Burgers two-step(BTS)model.The thermoelastic analytical solutions are systematically derived in the Laplace domain,and the numerical Laplace inversion method is adopted to obtain the transient responses.The new model is compared with the parabolic two-step(PTS)model and the hyperbolic two-step(HTS)model.The results show that in ultrafast heating,the BTS model has the same wave front jump as the HTS model.The present model has the faster wave speed,and predicts the bigger disturbed regions than the HTS model.More deeply,all two-step models also have the faster wave speeds than one-step models.This work may benefit the theoretical modeling of ultrafast heating of metals.
文摘The Time Fractional Burger equation was solved in this study using the Mabel software and the Variational Iteration approach. where a number of instances of the Time Fractional Burger Equation were handled using this technique. Tables and images were used to present the collected numerical results. The difference between the exact and numerical solutions demonstrates the effectiveness of the Mabel program’s solution, as well as the accuracy and closeness of the results this method produced. It also demonstrates the Mabel program’s ability to quickly and effectively produce the numerical solution.
文摘In this paper, the Adomian decomposition method was used to solve the Time Fractional Burger equation using Mabel program. This method was applied to a number of examples of the Time Fractional Burger Equation. The obtained numerical results were presented in the form of tables and graphics. The difference between the exact solutions and the numerical solutions shows us the effectiveness of the solution using the Mabel program and that this method gave accurate results and was close to the exact solution, in addition to its ability to obtain the numerical solution quickly and efficiently using the Mabel program.