Physics-Informed Neural Networks for Modal Wave Field Predictions in 3D Room Acoustics
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Abstract
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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This Zenodo record is a permanently preserved version of a PREreview. You can view the complete PREreview at https://prereview.org/reviews/14588713.
This manuscript investigates the use of neural networks for the wave propagation problems. There are a few points that could be addressed.
Throughout the paper, the wavelength is kept constant as 1/2 and the domain length is 1. This is a constrained way of investigating the wave propagation as there are only two waves in one direction, as such the wave dispersion, pollution, reflection effects etc. can be monitored properly. Imagine that we have a music hall and a cello player plays a note A at 440 Hz. The wavelength will then be ~0.78 m and the room length would correspond to ~1.6 meters. If the first octave A note is played, then we would be in a room that is less than 1 m3 in volume. …
This Zenodo record is a permanently preserved version of a PREreview. You can view the complete PREreview at https://prereview.org/reviews/14588713.
This manuscript investigates the use of neural networks for the wave propagation problems. There are a few points that could be addressed.
Throughout the paper, the wavelength is kept constant as 1/2 and the domain length is 1. This is a constrained way of investigating the wave propagation as there are only two waves in one direction, as such the wave dispersion, pollution, reflection effects etc. can be monitored properly. Imagine that we have a music hall and a cello player plays a note A at 440 Hz. The wavelength will then be ~0.78 m and the room length would correspond to ~1.6 meters. If the first octave A note is played, then we would be in a room that is less than 1 m3 in volume. This is not a proper setting for the investigation of room acoustics problems.
The manuscript places a large focus on the parameter s (sharpness); though, it is rather demonstrating in general that the model does not properly work, reporting error values around 98% - 99%! The only case that seems to have non-erratic results is that when the case approaches the classical Helmholtz problem for large values of s. What is the benefit of publishing erroneous simulations? It would be more appropriate to omit the related sections where s is smaller than 1.
The manuscript proposes to apply the Fourier feature extraction method in Section 4.5. However, equation (23) is just an alternative way of rewriting the analytical solution given by Eq. (5). The training data (X, y) pairs are generated in the current method according to the analytical solution or the FEM solution. For the case s = Inf, between the first layer and the output layer, the neural network is practically being trained for the value pairs p(x) = p(x). Would one practically need to perform a computational simulation for this case?
The essence of neural networks (NN) and artificial intelligence is that one develops a model that is subsequently able to predict some unseen cases. In the current paper, can the trained NN be used for any other cases? For example, if the acoustic source is re-positioned to x=0.4, y=0.5, z=0.5, can we make reliable predictions? Alternatively, if the driving frequency (hence the wavenumber) is changed by a factor of 10 %, or the boundary condition on some part of the domain is modified, can the NN model deliver accurate results?
Competing interests
The author declares that they have no competing interests.
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