Physics Informed Neural Network for Head-Related Transfer Function Upsampling

Head-related transfer functions (HRTFs) capture the spatial and spectral features that a person uses to localize sound sources in space and thus are vital for creating an authentic virtual acoustic experience. However, practical HRTF measurement systems can only provide an incomplete measurement of a person's HRTFs, and this necessitates HRTF upsampling. This paper proposes a physics-informed neural network (PINN) method for HRTF upsampling. Unlike other upsampling methods which are based on the measured HRTFs only, the PINN method exploits the Helmholtz equation as additional information for constraining the upsampling process. This helps the PINN method to generate physically amiable upsamplings which generalize beyond the measured HRTFs. Furthermore, the width and the depth of the PINN are set according to the dimensionality of HRTFs under spherical harmonic (SH) decomposition and the Helmholtz equation. This makes the PINN have an appropriate level of expressiveness and thus does not suffer from under-fitting and over-fitting problems. Numerical experiments confirm the superior performance of the PINN method for HRTF upsampling in both interpolation and extrapolation scenarios over several datasets in comparison with the SH methods.