Accelerated methods for computing acoustic sound fields in dynamic virtual environments with moving sources

Nikolas Borrel-Jensen

Research output: Book/ReportPh.D. thesis

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Realistic sound is essential in virtual environments, such as computer games, virtual and augmented reality, metaverses, and spatial computing. The wave equation describes wave phenomena such as diffraction and interference, and the solution can be obtained using accurate and efficient numerical methods. Due to the often demanding computation time, the solutions are calculated offline in a pre-processing step. However, pre-calculating acoustics in dynamic scenes with hundreds of source and receiver positions are challenging, requiring intractable memory storage. This PhD thesis examines novel scientific machine learning methods to overcome some of the limitations of traditional numerical methods. Employing surrogate models to learn the parametrized solutions to the wave equation to obtain one-shot continuous wave propagations in interactive scenes offers an ideal framework to address the prevailing challenges in virtual acoustics applications. Training machine learning models often require a large amount of data that can be computationally expensive to obtain; hence this PhD thesis also investigates efficient numerical methods for generating accurate training data. This study explores two machine learning methods and one domain decomposition method for accelerating data generation. (1) A physics-informed neural network (PINN) approach is taken, where knowledge of the underlying physics is included in the model, contrary to traditional ‘black box’ deep learning approaches. A PINN method in 1D is presented, which learns a compact and efficient surrogate model with parameterized moving source and impedance boundaries satisfying a system of coupled equations. The model shows relative mean errors below 2%∕0.2dB and proposes a first step towards realistic 3D geometries. (2) Neural operators are generalizations of neural networks approximating operators instead of approximations of functions typical in deep learning. The DeepONet is a specific framework used in this thesis for operator learning applied to approximate the wave equation operators. The proposed model enables real-time prediction of sound propagation in realistic 3D acoustic scenes with moving sources, avoiding the offline calculation and storage of impulse responses. Our computational experiments, including various complex 3D scene geometries, show good agreement with reference solutions, with root mean squared errors ranging from 0.02 Pa to 0.10 Pa. Notably, our method signifies a paradigm shift as no prior machine learning approach has achieved precise predictions of complete wave fields within realistic domains. (3) A rectangular domain decomposition method is proposed, enabling error-free sound propagation in the bulk of the domain consisting of air. The Fourier method exploits the known analytical solution to the wave equation in the rectangular domain with near-optimal spatial discretization satisfying the Nyquist criterium via the Fast Fourier Transform for calculating derivatives. By coupling the Fourier method with the spectral element method (SEM) near the boundaries, the method is capable of handling complex geometries with the caveat of introducing errors at the coupling interface. A significant speed improvement is reported for a 1D domain when the domain decomposition method is used instead of the SEM running in the full domain.
Original languageEnglish
PublisherTechnical University of Denmark
Number of pages166
Publication statusPublished - 2023


  • Virtual acoustics
  • Physics-informed neural networks (PINNs)
  • Neural operators
  • DeepONet
  • Transfer learning
  • Domain decomposition
  • Fourier methods
  • Spectral element method
  • High-performance computing
  • Real-time computing


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