Closing Remarks

Physics-based Audio: Models, Computation and Parameter Spaces

  • Physical modelling synthesis and audio effects—possible to run large models in real time now.
  • Some systems (in 3D) are still well out of real time for the time being.
  • Still: not dirt cheap like some procedural audio methods!
  • Specialised designs (passive) necessary to cope with strong nonlinear effects
  • For future “black box” modelling, some useful constraints appear: state size, as well as “passive” nature of recursive update.

Neural Networks for Physical Modelling Synthesis

  • Neural Ordinary Differential Equations (NODEs): Learning Continuous-Time Dynamics.
  • Physics-Informed Neural Networks (PINNs): Embedding Physics in the Loss.
  • Neural Operators: Learning Mappings Between Function Spaces.
  • Deep Koopman Operator: Finding Linear Representations for Non-Linear Systems.
  • Deep State Space Models (DSSMs): Structured Sequence Models for Audio.

Parameter Estimation in Physical Modeling

  • The gradient signal can hint at the direction to update
    • the parameter data point, or
    • the parameter distribution.
  • It is critical to have a good initial guess.
    • Can benefit from measured data, domain knowledge, etc.
  • In line with the future black-box modelling, hopefully can be used to estimate parameters of complex models.
    • Nonlinear simulators, sub-iterations in forward loop, etc.

Notices

  • Companion Paper will be available on arXiv soon!
    • Stay tuned for more updates:
      https://ismir-physical-modeling.github.io/
  • DAFx (International Conference on Digital Audio Effects)
    will be held in Boston, USA, in 2026!
    • Check out if you found this tutorial interesting!
      https://www.dafx.de/
    • Great opportunity to present your work on audio signal processing
      • Sound Synthesis, Virtual Analog, Audio Effects, Room Acoustics, …
  • Feel free to reach out to us for any questions or future collaborations!

Thank You!

Stefan Bilbao
Professor
University of Edinburgh

Rodrigo Diaz
Ph.D. Student
QMUL

Jin Woo Lee
Postdoctoral Assoc.
MIT