Neural network based approach for solving problems in plane wave duct acoustics

TL;DR

This paper presents a neural network approach for solving differential equations in plane wave duct acoustics, addressing high-frequency challenges and demonstrating good agreement with analytical solutions.

Contribution

It introduces a formulation that overcomes the vanishing gradient problem in frequency domain acoustics and incorporates boundary conditions directly into the neural network model.

Findings

The neural network accurately predicts acoustic fields in duct problems.

Transfer learning effectively computes particle velocity from pressure fields.

The method remains robust with different activation functions and collocation points.

Abstract

Neural networks have emerged as a tool for solving differential equations in many branches of engineering and science. But their progress in frequency domain acoustics is limited by the vanishing gradient problem that occurs at higher frequencies. This paper discusses a formulation that can address this issue. The problem of solving the governing differential equation along with the boundary conditions is posed as an unconstrained optimization problem. The acoustic field is approximated to the output of a neural network which is constructed in such a way that it always satisfies the boundary conditions. The applicability of the formulation is demonstrated on popular problems in plane wave acoustic theory. The predicted solution from the neural network formulation is compared with those obtained from the analytical solution. A good agreement is observed between the two solutions. The method of transfer learning to calculate the particle velocity from the existing acoustic pressure field is demonstrated with and without mean flow effects. The sensitivity of the training process to the choice of the activation function and the number of collocation points is studied.