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

2025-05-09

AI Summary

Simulating nonlinear vibrations of continuous media—such as strings, membranes, and plates—is computationally expensive and non-differentiable using conventional methods, hindering inverse modeling and real-time applications. This paper introduces the first efficient, end-to-end differentiable modal simulation framework for von Kármán–type nonlinear plates. Implemented in JAX, it enables GPU acceleration, modal truncation, and automatic differentiation. The method preserves physical interpretability while ensuring parameter compactness, supporting both real-time forward simulation and gradient-based inverse parameter estimation—including tension, bending stiffness, and geometric dimensions. Experiments demonstrate orders-of-magnitude speedup over CPU-based solvers and existing GPU implementations. The framework successfully recovers key physical parameters from both synthetic and real-world audio data. To foster reproducibility and further research, the source code is publicly released.

Technology Category

• Computer Vision: Multi-modal Vision
• Machine Learning: Multimodal Learning
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

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.

Problem

• Efficient simulation of non-linear strings, membranes, and plates
• Differentiable modal framework for inverse modelling applications
• GPU-accelerated performance for real-time and gradient-based optimization

Innovation

• GPU-accelerated modal framework with JAX
• Differentiable simulations for inverse modelling
• Recovers physical parameters from data