Towards reconstruction of acoustic fields via physics-informed neural networks

Acoustic measurements, obtained by microphones positioned at strategic places, are of great utility for the monitoring of a given acoustic system and for its protection in case large pressure fluctuations are measured. Such strategies are reliable as long as the microphones are properly positioned, which is not evident: in some cases the excited acoustic modes are not known beforehand. In this work, we proposed a method based on physics-informed neural networks (PINN) in order to reconstruct the entire acoustic field of a given acoustic element, when provided with only some acoustic measurements at some few locations. Such a method makes use of a feedforward neural network, where the loss function is taken as the residual of the acoustic wave equation. Such a residual is computed exploiting the automatic differentiation property of neural networks, in order to obtain the corresponding spatial and time derivatives. Additionally, the measurements of the aforementioned microphones are gathered and used also for the calculation of additional terms in the PINN loss function. By doing so, the most adequate acoustic state is obtained, which satisfies both measurements and the acoustic wave equation. In other words, the acoustic field within the system is reconstructed.