Generalized conditional symmetry enhanced physics-informed neural network and application to the forward and inverse problems of nonlinear diffusion equations

Zhang, Zhiyong; Zhang, Hui; Liu, Ye; Li, Jie-Ying; Liu, Cheng-Bao

doi:10.1016/j.chaos.2023.113169

Cited by 13 publications

(2 citation statements)

References 29 publications

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“…Secondly, the PINN is relatively efficient in handling high-dimensional problems, avoiding the dimensionality catastrophe that plagues traditional numerical methods [33]. Finally, the PINN can combine known actual data to solve inverse problems, such as identifying material parameters and unknown boundary conditions [34][35][36][37][38]. Cai [39] used the PINN to obtain temperature and velocity distributions under unknown thermal boundary conditions, a task that is typically challenging for conventional numerical techniques.…”

Section: Introductionmentioning

confidence: 99%

Physics-Informed Neural Network (PINN) for Solving Frictional Contact Temperature and Inversely Evaluating Relevant Input Parameters

Xia,

Meng

2024

Lubricants

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Ensuring precise prediction, monitoring, and control of frictional contact temperature is imperative for the design and operation of advanced equipment. Currently, the measurement of frictional contact temperature remains a formidable challenge, while the accuracy of simulation results from conventional numerical methods remains uncertain. In this study, a PINN model that incorporates physical information, such as partial differential equation (PDE) and boundary conditions, into neural networks is proposed to solve forward and inverse problems of frictional contact temperature. Compared to the traditional numerical calculation method, the preprocessing of the PINN is more convenient. Another noteworthy characteristic of the PINN is that it can combine data to obtain a more accurate temperature field and solve inverse problems to identify some unknown parameters. The experimental results substantiate that the PINN effectively resolves the forward problems of frictional contact temperature when provided with known input conditions. Additionally, the PINN demonstrates its ability to accurately predict the friction temperature field with an unknown input parameter, which is achieved by incorporating a limited quantity of easily measurable actual temperature data. The PINN can also be employed for the inverse identification of unknown parameters. Finally, the PINN exhibits potential in solving inverse problems associated with frictional contact temperature, even when multiple input parameters are unknown.

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Section: Introductionmentioning

confidence: 99%

Physics-Informed Neural Network (PINN) for Solving Frictional Contact Temperature and Inversely Evaluating Relevant Input Parameters

Xia,

Meng

2024

Lubricants

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“…In general, the inverse problems of diffusion equations are ill-posed, that is, their solution does not fulfill the requirement of the aforementioned conditions in the presence of a tiny disturbance to the input data. To overcome such difficulties, a variety of methods have been proposed [6][7][8][9][10][11][12]. To date, considerable efforts have been devoted to formulating accurate and efficient methods of inverse diffusion problems.…”

Section: Introductionmentioning

confidence: 99%

Combination of Multigrid with Constraint Data for Inverse Problem of Nonlinear Diffusion Equation

Liu

Ouyang

Guo³

et al. 2023

Mathematics

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This paper delves into a rapid and accurate numerical solution for the inverse problem of the nonlinear diffusion equation in the context of multiphase porous media flow. For the realization of this, the combination of the multigrid method with constraint data is utilized and investigated. Additionally, to address the ill-posedness of the inverse problem, the Tikhonov regularization is incorporated. Numerical results demonstrate the computational performance of this method. The proposed combination strategy displays remarkable capabilities in reducing noise, avoiding local minima, and accelerating convergence. Moreover, this combination method performs better than any one method used alone.

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A study of mechanism-data hybrid-driven method for multibody system via physics-informed neural network

Song,

Wang,

Peng

et al. 2024

Acta Mech. Sin.

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Generalized conditional symmetry enhanced physics-informed neural network and application to the forward and inverse problems of nonlinear diffusion equations

Cited by 13 publications

References 29 publications

Physics-Informed Neural Network (PINN) for Solving Frictional Contact Temperature and Inversely Evaluating Relevant Input Parameters

Physics-Informed Neural Network (PINN) for Solving Frictional Contact Temperature and Inversely Evaluating Relevant Input Parameters

Combination of Multigrid with Constraint Data for Inverse Problem of Nonlinear Diffusion Equation

A study of mechanism-data hybrid-driven method for multibody system via physics-informed neural network

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