Inverse Problems in Musical Instrument Modeling: A Structured Taxonomy and Review

RESUMO

Inverse problems arise in a wide range of applications in musical acoustics, including physics-based sound synthesis, musical instrument modeling, design, and optimization. However, these problems are inherently challenging due to their ill-conditioned nature and strong sensitivity to measurement noise. This paper presents a structured taxonomy and systematic review of inverse problems in musical instrument modeling, providing a unified framework for their classification and analysis. We categorize inverse problems in musical instrument modeling into ten distinct tasks: mechanical parameter estimation; geometric parameter estimation; loss estimation; boundary condition estimation; modal parameter estimation; excitation and articulatory parameter estimation; sound matching or model parameter fitting; instrument design and optimization; field reconstruction, characterization and separation; physical model identification and discovery.