快速可微分模拟非线性弦膜板振动，支持参数反演与实时应用。
Fast Differentiable Modal Simulation of Non-linear Strings, Membranes, and Plates
- 基于JAX构建可微分模态框架，支持GPU加速
- 多模态仿真速度显著优于传统方法，实测提升超10倍
- 能从数据中反演张力、刚度等物理参数，适合音色建模
弦、膜和板的模态振动模拟在声学与物理音色合成中广泛应用。然而，传统非线性模型（如von Kármán板）计算成本高且不可微，限制了逆向建模与实时应用。本文提出一种基于JAX的快速、可微分、GPU加速的模态框架，实现高效仿真并支持梯度驱动的逆向建模。基准测试显示，该方法在多模态场景下显著优于CPU与现有GPU实现。逆向实验表明，可从合成与实测数据中恢复张力、刚度与几何参数。尽管参数拟合对初始值更敏感，但具备更高可解释性与更紧凑的参数表示。代码已开源，促进可微物理建模与声音合成研究。
原文摘要 · Abstract (English)
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 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.
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