Thesis Details

Approximation of Sound Propagation by Neural Networks

Master's Thesis Student: Nguyen Son Hai Academic Year: 2021/2022 Supervisor: Herout Adam, prof. Ing., Ph.D.
Czech title
Aproximace šíření ultrazvuku pomocí neuronových sítí

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.


neural solver, Helmholtz equation, graph neural networks, approximation of sound propagation, iterative model, PDE, partial differential equation, machine learning

Degree Programme
defended, grade A
20 June 2022
Zemčík Pavel, prof. Dr. Ing. (DCGM FIT BUT), předseda
Beran Vítězslav, Ing., Ph.D. (DCGM FIT BUT), člen
Čadík Martin, doc. Ing., Ph.D. (DCGM FIT BUT), člen
Juránek Roman, Ing., Ph.D. (DCGM FIT BUT), člen
Křivka Zbyněk, Ing., Ph.D. (DIFS FIT BUT), člen
Milet Tomáš, Ing., Ph.D. (DCGM FIT BUT), člen
NGUYEN, Son. Approximation of Sound Propagation by Neural Networks. Brno, 2022. Master's Thesis. Brno University of Technology, Faculty of Information Technology. 2022-06-20. Supervised by Herout Adam. Available from:
    author = "Hai Son Nguyen",
    type = "Master's thesis",
    title = "Approximation of Sound Propagation by Neural Networks",
    school = "Brno University of Technology, Faculty of Information Technology",
    year = 2022,
    location = "Brno, CZ",
    language = "english",
    url = ""
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