# Fast Differentiable Modal Simulation of Non-linear Strings, Membranes, and Plates

arXiv: https://arxiv.org/abs/2505.05940 · HTML: https://mlsanity.com/paper/2505.05940/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 31 references that are in the map.
- First posted on arXiv 9 May 2025.

## Builds on (most cited first, 9 of 9)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [I'm Sorry for Your Loss: Spectrally-Based Audio Distances Are Bad at Pitch](https://mlsanity.com/paper/2012.04572/) (2020)
- [Physical Modeling using Recurrent Neural Networks with Fast Convolutional Layers](https://mlsanity.com/paper/2204.10125/) (2022)
- [RealImpact: A Dataset of Impact Sound Fields for Real Objects](https://mlsanity.com/paper/2306.09944/) (2023)
- [Unsupervised Harmonic Parameter Estimation Using Differentiable DSP and Spectral Optimal Transport](https://mlsanity.com/paper/2312.14507/) (2023)
- [DiffSound: Differentiable Modal Sound Rendering and Inverse Rendering for Diverse Inference Tasks](https://mlsanity.com/paper/2409.13486/) (2024)
- [Rigid-Body Sound Synthesis with Differentiable Modal Resonators](https://mlsanity.com/paper/2210.15306/) (2022)
- [Differentiable Modal Synthesis for Physical Modeling of Planar String Sound and Motion Simulation](https://mlsanity.com/paper/2407.05516/) (2024)
- [Towards Efficient Modelling of String Dynamics: A Comparison of State Space and Koopman based Deep Learning Methods](https://mlsanity.com/paper/2408.16650/) (2024)

## Built on by (most cited first, 3 of 3)

- [Stable Differentiable Modal Synthesis for Learning Nonlinear Dynamics](https://mlsanity.com/paper/2601.10453/) (2026)
- [Identifying the nonlinear string dynamics with port-Hamiltonian neural networks](https://mlsanity.com/paper/2605.12785/) (2026)
- [Simulation-Based Plate-Reverb Parameter Estimation from a Single Impulse Response](https://mlsanity.com/paper/2608.00656/) (2026)

## Abstract (arXiv)

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 K'arm'an 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 gradient-based 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 other methods, 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.