A perceptual evaluation of numerical errors in acoustic FEM simulation for sound quality applications

Pulvirenti, Giorgio; Totaro, Nicolas; Parizet, Étienne

doi:10.1016/j.apacoust.2023.109295

Cited by 1 publication

(1 citation statement)

References 39 publications

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“…PINN has its unique application background, mainly replacing numerical methods such as finite difference method (FDM), FEM and finite volume method (FVM). These traditional computational methods have clear principles, rapid convergence and mature error analysis 24,25 . Combining the design ideas of PINN with FEM and incorporating the valuable parts of FEM into the PINN design is a promising approach.…”

Section: Introductionmentioning

confidence: 99%

M‐PINN: A mesh‐based physics‐informed neural network for linear elastic problems in solid mechanics

Wang,

Liu,

Wang

et al. 2024

Numerical Meth Engineering

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Physics‐informed neural networks (PINNs) have emerged as a promising approach for solving a wide range of numerical problems. Nevertheless, conventional PINNs frequently face challenges in model convergence and stability when optimizing complex loss functions containing complex gradients. In this study, a new mesh‐based PINN method, called M‐PINN, is proposed drawing the ideas of the finite element method (FEM). By partitioning the solution domain into several subdomains and incorporating finite element data distribution constraints to the prior estimates of the predicted data distribution of PINN on the solution domain, the M‐PINN approach effectively reduces the optimization difficulty of conventional PINNs. Moreover, it is sometimes difficult to directly obtain precise boundary conditions in some practical applications. This method can be used to solve PINN problems with unknown boundary conditions, thus having wider applicability. In this study, the efficiency of M‐PINN was demonstrated through a standard 2D linear elastic solid mechanics simulation experiment, and its applicability was investigated in depth. The results indicate that the M‐PINN method outperforms traditional PINN and exhibits superior applicability and convergence, especially in cases involving unknown boundary conditions.

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Section: Introductionmentioning

confidence: 99%