Point Neuron Learning for broadband array processing

Whilst Physics Informed Neural Networks (PINNs) solve certain limitations of traditional networks, they also have several drawbacks including inability to approximate PDEs that have sharp gradients, strong non-linearities and convergence to trivial solutions. Recently, we proposed the point neuron network by embedding the free space Green function into the network architecture enabling the learned model to strictly satisfy the physical law of sound propagation. The physical meaning of point neurons is equivalent to point sources or plane wave sources, and the weight, location (biases) and distribution of equivalent sources can be updated while training. In this paper, we extend the point neuron learning network for broadband signals. The proposed point neuron network can be implemented efficiently with fewer network parameters to model and estimate an arbitrary broadband sound field based on microphone observations without a pre-existing data set. As an example application, we use the proposed network to estimate Room Transfer Functions at locations with no measurements.