Predicting the Propagation of Acoustic Waves using Deep Convolutional Neural Networks

Abstract

A novel approach for numerically propagating acoustic waves in two-dimensional quiescent media has been developed through a fully convolutional multi-scale neural network. This datadriven method managed to produce accurate results for long simulation times with a database of Lattice Boltzmann temporal simulations of propagating Gaussian Pulses, even in the case of initial conditions unseen during training time, such as the plane wave configuration or the two initial Gaussian pulses of opposed amplitudes. Two different choices of optimization objectives are compared, resulting in an improved prediction accuracy when adding the spatial gradient difference error to the traditional mean squared error loss function. Further accuracy gains are observed when performing an a posteriori correction on the neural network prediction based on the conservation of acoustic energy, indicating the benefit of including physical information in data-driven methods. Nomenclature= Gaussian pulse half-width 0

A generic deep learning framework for propagation and scattering of acoustic waves in quiescent flows

“…Such a space-time operator can be learned through a highly non-linear neural network regressor. For high-dimensional databases, such as the ones encountered in Computational Aeroacoustics or Computational Fluid Dynamics, the use of convolutional networks is an efficient solution to simultaneously learn the spatial and time integration, as shown in earlier works [6,7,10]. The main advantage with respect to traditional numerical schemes is two-fold: in comparison with explicit schemes, such as Euler or Runge-Kutta integrators, the learned surrogate is not constrained by the classical time-stepping stability constraints [5,13].…”

“…As in [6], a LBM code is used to generate the data for the optimization of the network on the training dataset. Such a dataset, employed to feed inputs into the neural network and compare its outputs with supervised references, is decribed in the following section.…”

“…3a), each direction being discretized with = 200. Similar to the dataset used in [6], the wave sources are composed of a random number of Gaussian pulses which are used as initial conditions for the density field, namely:…”

“…A recent work by the authors [5,6] developed an alternative method to replicate, at lower cost, a high-fidelity numerical code for the propagation of acoustic waves using a surrogate model: instead of resolving the discretized propagation equations, a neural network was trained with examples of high-fidelity direct Lattice-Boltzmann (LBM) simulations, resulting in a data-driven convolutional neural network for acoustic wave propagation. It was found that such an approach managed to reproduce wave propagation in simple academic cases of 2D quiescent closed domains with reflecting walls.…”

“…The work focuses on two mains aspects: (i) the ability of the trained neural network to perform in various physics regimes dependent on the choice of boundary conditions, some of which differ significantly from the ones present in the chosen database, (ii) the practical choices for pre-and post-processing the data when predicting in the auto-regressive loop. In particular, two types of data normalization are compared, along with a modified Energy Preserving Correction, which was introduced in [6]. The latter intends to improve the conservation of acoustic energy over the temporal neural network predictions, and thus improving significantly its long-term predictions.…”