Fast Differentiable Modal Simulation of Non-Linear Strings, Membranes, and Plates
Modal methods for simulating vibrations of strings, membranes, and plates are widely used in acoustics and physically
informed audio synthesis. However, traditional implementations,
particularly for non-linear models like the von Kármán plate, are
computationally demanding and lack differentiability, limiting inverse modelling and real-time applications. We introduce a fast,
differentiable, GPU-accelerated modal framework built with the
JAX library, providing efficient simulations and enabling gradientbased inverse modelling.
Benchmarks show that our approach
significantly outperforms CPU and GPU-based implementations,
particularly for simulations with many modes. Inverse modelling
experiments demonstrate that our approach can recover physical
parameters, including tension, stiffness, and geometry, from both
synthetic and experimental data. Although fitting physical parameters is more sensitive to initialisation compared to methods that
fit abstract spectral parameters, it provides greater interpretability
and more compact parameterisation. The code is released as open
source to support future research and applications in differentiable
physical modelling and sound synthesis.