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Physics-Informed Neural Networks for Modal Wave Field Predictions in 3D Room Acoustics

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Preprints.org
DOI
10.20944/preprints202411.1848.v1

The capabilities of Physics-Informed Neural Networks (PINNs) to solve the Helmholtz equation in a simplified three-dimensional room are investigated. From a simulation point of view, it is interesting since room acoustic simulations often lack information from the applied absorbing material in the low-frequency range. This study extends previous findings toward modeling the 3D sound field with PINNs in an excitation case using DeepXDE with the backend PyTorch. The neural network is memory-efficiently optimized by mini-batch stochastic gradient descent with periodic resampling after 100 iterations. A detailed hyperparameter study is conducted regarding the network shape, activation functions, and deep learning backends (PyTorch, TensorFlow 1, TensorFlow 2). We address the computational challenges of realistic sound excitation in a confined area. The accuracy of the PINN results is assessed by a Finite Element Method (FEM) solution computed with openCFS. For distributed sources, it was shown that the PINNs converge to the solution, with deviations occurring in the range of a relative error of 0.28%. With feature engineering and including the dispersion relation of the wave into the neural network input via transformation, the trainable parameters were reduced to a fraction (around 5%) compared to the standard PINN formulation while yielding a higher accuracy of 1.54% compared to 1.99%.

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