Physics-Informed Learning of Neural Scattering Fields Towards Measurement-Free Mesh-To-HRTF Estimation

This paper describes neural simulation of the scattered pressure field from a plane wave around a scattering object in both continuous 2D and 3D domains. This task has typically been treated as a regression problem that aims to train a physics-informed neural network (PINN) using pressure measurements at discrete positions. This approach, however, needs to train the whole network for each incident wave direction. To address this, we propose a measurement-free simulator based on a PINN purely driven by the Helmholtz equation with the Robin boundary condition and the Sommerfeld radiation condition with the aid of the perfectly matched layer (PML) framework. More specifically, we design a physics-informed scattering hypernetwork (PHISK) that can generalize to incident waves from any direction via low-rank adaptation (LoRA) of a PINN trained for a specific configuration. The experiment shows that the proposed method accurately simulated sound scattering around various objects, adapting to unseen incident wave directions with minimal performance loss, and realized reasonable simulation of head-related transfer functions (HRTFs) from complex mesh data of a human head.