  Sound matching algorithms seek to approximate a target waveform by parametric
audio synthesis. Deep neural networks have achieved promising results in
matching sustained harmonic tones. However, the task is more challenging when
targets are nonstationary and inharmonic, e.g., percussion. We attribute this
problem to the inadequacy of loss function. On one hand, mean square error in
the parametric domain, known as "P-loss", is simple and fast but fails to
accommodate the differing perceptual significance of each parameter. On the
other hand, mean square error in the spectrotemporal domain, known as "spectral
loss", is perceptually motivated and serves in differentiable digital signal
processing (DDSP). Yet, spectral loss is a poor predictor of pitch intervals
and its gradient may be computationally expensive; hence a slow convergence.
Against this conundrum, we present Perceptual-Neural-Physical loss (PNP). PNP
is the optimal quadratic approximation of spectral loss while being as fast as
P-loss during training. We instantiate PNP with physical modeling synthesis as
decoder and joint time-frequency scattering transform (JTFS) as spectral
representation. We demonstrate its potential on matching synthetic drum sounds
in comparison with other loss functions.
