We present a physics-informed voiced backend renderer for singing-voice synthesis. Given synthetic single-channel audio and a fund-amental--frequency trajectory, we train a time-domain Webster model as a physics-informed neural network to estimate an interpretable vocal-tract area function and an open-end radiation coefficient. Training enforces partial differential equation and boundary consistency; a lightweight DDSP path is used only to stabilize learning, while inference is purely physics-based. On sustained vowels (/a/, /i/, /u/), parameters rendered by an independent finite-difference time-domain Webster solver reproduce spectral envelopes competitively with a compact DDSP baseline and remain stable under changes in discretization, moderate source variations, and about ten percent pitch shifts. The in-graph waveform remains breathier than the reference, motivating periodicity-aware objectives and explicit glottal priors in future work.