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Approximation of Sound Propagation by Neural Networks
 Nguyen, Son Hai ; Bartl, Vojtěch (oponent) ; Herout, Adam (vedoucí práce)
Neural solvers have been increasingly explored to replace computationally expensive conventional numerical methods for solving PDEs. This work focuses on solving the time-independent Helmholtz equation for the transcranial ultrasound therapy. Using the convolutional neural networks requires the data to be sampled on a regular grid. In order to try to lift this restriction, we propose an iterative solver based on graph neural networks. Unlike Physics-informed neural networks, our model needs to be trained only once, and only a forward pass is required to obtain a new solution given input parameters. The model is trained using supervised learning, where the reference results are computed using the traditional solver k-Wave. Our results show the model's unroll stability despite being trained with only 8 unroll iterations. Despite the model being trained on the data with a single wave source, it can predict wavefields with multiple wave sources in much larger computational domains. Our model can produce a prediction for sub-pixel points with higher accuracy than linear interpolation. Additionally, our solution can predict the wavefield with downsampled Laplacian - only three samples per wavelength. We are unaware of any other existing method capable of working with such a sparse discretization.
Úplný záznam
Approximation of Sound Propagation by Neural Networks
 Nguyen, Son Hai ; Bartl, Vojtěch (oponent) ; Herout, Adam (vedoucí práce)
Neural solvers have been increasingly explored to replace computationally expensive conventional numerical methods for solving PDEs. This work focuses on solving the time-independent Helmholtz equation for the transcranial ultrasound therapy. Using the convolutional neural networks requires the data to be sampled on a regular grid. In order to try to lift this restriction, we propose an iterative solver based on graph neural networks. Unlike Physics-informed neural networks, our model needs to be trained only once, and only a forward pass is required to obtain a new solution given input parameters. The model is trained using supervised learning, where the reference results are computed using the traditional solver k-Wave. Our results show the model's unroll stability despite being trained with only 8 unroll iterations. Despite the model being trained on the data with a single wave source, it can predict wavefields with multiple wave sources in much larger computational domains. Our model can produce a prediction for sub-pixel points with higher accuracy than linear interpolation. Additionally, our solution can predict the wavefield with downsampled Laplacian - only three samples per wavelength. We are unaware of any other existing method capable of working with such a sparse discretization.
Úplný záznam

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