A neural network for predicting with the diffusion equation: a case study of long rooms

The diffusion equation model with a constant diffusion coefficient underestimates the sound pressure level and reverberation time when elongated rooms are considered in room acoustics. In fact, for these types of rooms, it has been established that the diffusion coefficient is spatially variable and depends on the acoustics properties of the surfaces. This study presents a novel method for estimating the spatially dependent diffusion coefficient of the diffusion equation model for the case study of long rooms using an artificial neural network. The network is trained to relate the dimensions of the room, the absorption coefficients of the surfaces and the 3D source and receiver positions to the corresponding diffusion coefficient using supervised learning. The databases are generated using the sound particle tracing approach (SPPS) and Fick’s law. Results show that the neural network model, with the appropriate considerations and architecture, can quickly recover the space-varying diffusion coefficients over the room based only on the model’s inputs (geometries, properties of the room, and source positions). When the predicted diffusion coefficients of the neural network are used
in the diffusion equation, the sound pressure level and reverberation time of the room can be accurately predicted.