Learning Vocal-Tract Area and Radiation with a Physics-Informed Webster Model

2026-02-14

AI Summary

This work proposes a physics-informed neural network (PINN) approach to jointly estimate an interpretable vocal tract area function and open-end radiation coefficient from monophonic synthesized singing voice and its fundamental frequency trajectory. By embedding the time-domain Webster equation as a physical constraint during network training, this study introduces PINNs into the singing voice synthesis backend for the first time, enabling purely physics-driven parameter estimation. Experimental results demonstrate that the estimated parameters, when rendered through an independent Webster equation solver, accurately reproduce the spectral envelope, achieving performance comparable to a compact DDSP baseline. Furthermore, the method exhibits robustness under discretization, source perturbations, and pitch shifts of up to approximately 10%.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Natural Language Processing: Speech
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

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.

Problem

• vocal-tract area
• radiation coefficient
• Webster model
• singing-voice synthesis
• physics-informed

Innovation

• physics-informed neural network
• Webster equation
• vocal-tract area function
• singing voice synthesis
• radiation coefficient