Space-time domain point neuron learning for sound field reconstruction

Physics Informed Neural Networks (PINNs) have been used in array signal processing allocations in recent years, where physical constraints such as governing partial differential equations (PDEs) and/or boundary conditions have been added to the usual data driven loss function. While these methods have helped to solve certain limitations, they also have several drawbacks such as being unable to approximate PDEs that have sharp gradients or strong non-linearities, not being able to move away from local optimums, and convergence to trivial solutions. Recently, we embedded the fundamental solution to the wave equation, the free space Green function, into the network architecture enabling the learned model to strictly satisfy the physical law of sound propagation. In the proposed network, the basic processing unit is called a point neuron whose weight and biases can be learned by back propagation. The physical meaning of point neuron is equivalent to point sources or plane wave sources, and the weight, location (biases) and distribution of equivalent sources can be updated while training. The proposed point neuron network can be implemented to model and estimate an arbitrary sound field purely based on microphone observations without a pre-existing dataset. Building on the concept of point neuron network, which is defined in space-frequency domain, the current work conceptualises the space-time domain sound field representation problem with the wave equation as a constraint.