  Head-related transfer function (HRTF) capture the information that a person
uses to localize sound sources in space, and thus is crucial for creating
personalized virtual acoustic experiences. However, practical HRTF measurement
systems may only measure a person's HRTFs sparsely, and this necessitates HRTF
upsampling. This paper proposes a physics-informed neural network (PINN) method
for HRTF upsampling. The PINN exploits the Helmholtz equation, the governing
equation of acoustic wave propagation, for regularizing the upsampling process.
This helps the generation of physically valid upsamplings which generalize
beyond the measured HRTF. Furthermore, the size (width and depth) of the PINN
is set according to the Helmholtz equation and its solutions, the spherical
harmonics (SHs). This makes the PINN have an appropriate level of expressive
power and thus does not suffer from the over-fitting problem. Since the PINN is
designed independent of any specific HRTF dataset, it offers more
generalizability compared to pure data-driven methods. Numerical experiments
confirm the better performance of the PINN method for HRTF upsampling in both
interpolation and extrapolation scenarios in comparison with the SH method and
the HRTF field method.
