Physics-Informed Deep Learning for Nonlinear Friction Model of Bow-string Interaction

This study investigates the use of an unsupervised, physics-informed deep learning framework to model a one-degree-of-freedom mass-spring system subjected to a nonlinear friction bow force and governed by a set of ordinary differential equations. Specifically, it examines the application of Physics-Informed Neural Networks (PINNs) and Physics-Informed Deep Operator Networks (PI-DeepONets). Our findings demonstrate that PINNs successfully address the problem across different bow force scenarios, while PI-DeepONets perform well under low bow forces but encounter difficulties at higher forces. Additionally, we analyze the Hessian eigenvalue density and visualize the loss landscape. Overall, the presence of large Hessian eigenvalues and sharp minima indicates highly ill-conditioned optimization. These results underscore the promise of physics-informed deep learning for nonlinear modelling in musical acoustics, while also revealing the limitations of relying solely on physics-based approaches to capture complex nonlinearities. We demonstrate that PI-DeepONets, with their ability to generalize across varying parameters, are well-suited for sound synthesis. Furthermore, we demonstrate that the limitations of PI-DeepONets under higher forces can be mitigated by integrating observation data within a hybrid supervised-unsupervised framework. This suggests that a hybrid supervised-unsupervised DeepONets framework could be a promising direction for future practical applications.

Acoustic Field Reconstruction in Tubes via Physics-Informed Neural Networks

This study investigates the application of Physics-Informed Neural Networks (PINNs) to inverse problems in acoustic tube analysis, focusing on reconstructing acoustic fields from noisy and limited observation data. Specifically, we address scenarios where the radiation model is unknown, and pressure data is only available at the tube's radiation end. A PINNs framework is proposed to reconstruct the acoustic field, along with the PINN Fine-Tuning Method (PINN-FTM) and a traditional optimization method (TOM) for predicting radiation model coefficients. The results demonstrate that PINNs can effectively reconstruct the tube's acoustic field under noisy conditions, even with unknown radiation parameters. PINN-FTM outperforms TOM by delivering balanced and reliable predictions and exhibiting robust noise-tolerance capabilities.

Exploring the Acoustics of the Chinese Transverse Flute (dizi)

We investigate the acoustical characteristics of the Chinese transverse flute, the dizi, employing input impedance measurements, modeling and analysis. The input impedances for various fingerings of a bangdi in the key of F, a particular type of the dizi, are measured and compared to models using both the transfer matrix method and the Transfer Matrix Method with external Interaction (TMMI). In order to get more accurate modeling results, we provide specific transfer matrices for the unique components of the dizi, such as back end-holes, membrane hole and upstream branch. The matching volume length correction for holes drilled in a thick wall is also derived. Comparative analysis of modeling and measurement data validates the improved accuracy of TMMI, confirming the influence of radiated sound from closely spaced toneholes.