Paper Archive

This study investigates the use of an unsupervised, physicsinformed deep learning framework to model a one-degree-offreedom 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.

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Estimating physical plate parameters from impulse responses is a challenging inverse problem. Task A of the first Digital Audio Effects Parameter Estimation Challenge requires the recovery of six identifiable parameters from displacement impulse responses. In this work, we propose a physics-inspired feature fusion network (PIFFN) that combines a pretrained convolutional backbone with a 15-dimensional physics-inspired feature vector computed from the impulse response. These physics-inspired features describe amplitude scale, temporal decay, and spectral structure without relying on modal-distribution priors. The proposed model is evaluated on the official validation set, achieving an overall normalized mean squared error of 0.00362. Compared with the official particle swarm optimization baseline and backbone-only model, PIFFN shows a clear performance improvement, demonstrating its effectiveness for plate parameter estimation.

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For physical modelling sound synthesis, many techniques are available; time-stepping methods (e.g., finite-difference time-domain (FDTD) methods) have an advantage of flexibility and generality in terms of the type of systems they can model. These methods do, however, lack the capability of easily handling smooth parameter changes while retaining optimal simulation quality and stability, something other techniques are better suited for. In this paper, we propose an efficient method to smoothly add and remove grid points from a FDTD simulation under sub-audio rate parameter variations. This allows for dynamic parameter changes in physical models of musical instruments. An instrument such as the trombone can now be modelled using FDTD methods, as well as physically impossible instruments where parameters such as e.g. material density or its geometry can be made time-varying. Results show that the method does not produce (visible) artifacts and stability analysis is ongoing.

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In this paper we explore extended techniques for a physical model of a bowed string instrument controlled using the metasaxophone.

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Distortion is a desirable effect for sound coloration in electric guitar amplifiers and effect processors. At high sound levels, particularly at low frequencies, the loudspeakers used in classic style cabinets are also a source of distortion. This paper presents a case study of measurements and digital modeling of a typical guitar loudspeaker as a real-time audio effect. It demonstrates the complexity of the driver behavior, which cannot be efficiently modeled in true physical detail. A model with linear transfer functions and static nonlinearity characteristics to approximate the measured behavior is derived based upon physical arguments. An efficient method to simulate radiation directivity is also proposed.

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This paper deals with the time-domain simulation of a simplified electro-mechanical piano. The physical model is composed of a hammer (nonlinear component), a cantilever beam (damped linear resonator) and a pickup (nonlinear transducer). In order to ensure stable simulations, a method is proposed, which preserves passivity, namely, the conservative and dissipative properties of the physical system. This issue is addressed in 3 steps. First, each physical component is described by a passive input-output system, which is recast in the port-Hamiltonian framework. In particular, a passive finite dimensional model of the Euler-Bernoulli beam is derived, based on a standard modal decomposition. Second, these components are connected, providing a nonlinear finite dimensional port-Hamiltonian system. Third, a numerical method is proposed, which preserves the power balance and passivity. Numerical results are presented and analyzed.

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Modal synthesis methods are a long-standing approach for modelling distributed musical systems. In some cases extensions are possible in order to handle geometric nonlinearities. One such case is the high-amplitude vibration of a string, where geometric nonlinear effects lead to perceptually important effects including pitch glides and a dependence of brightness on striking amplitude. A modal decomposition leads to a coupled nonlinear system of ordinary differential equations. Recent work in applied machine learning approaches (in particular neural ordinary differential equations) has been used to model lumped dynamic systems such as electronic circuits automatically from data. In this work, we examine how modal decomposition can be combined with neural ordinary differential equations for modelling distributed musical systems. The proposed model leverages the analytical solution for linear vibration of system’s modes and employs a neural network to account for nonlinear dynamic behaviour. Physical parameters of a system remain easily accessible after the training without the need for a parameter encoder in the network architecture. As an initial proof of concept, we generate synthetic data for a nonlinear transverse string and show that the model can be trained to reproduce the nonlinear dynamics of the system. Sound examples are presented.

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Artificial reverberation is usually introduced, as a digital audio effect, to give a sense of enclosing architectural space. In this paper we argue about the effectiveness and usefulness of diffusive reverberators in physically-inspired sound synthesis. Examples are given for the synthesis of textural sounds, as they emerge from solid mechanical interactions, as well as from aerodynamic and liquid phenomena.

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In this paper, we propose a parametric audio coding framework that combines the analysis and re-synthesis of electric bass guitar recordings. In particular, an existing synthesis algorithm that incorporates 11 playing techniques is extended by two calibration algorithms. Both the temporal and spectral decay parameters as well as the inharmonicity coefficient are set according to the fretboard position on the instrument. Listening tests show that there is still a gap in perceptual quality between real-world instrument recordings and the re-synthesized versions. Due to this gap, the perceived improvement due to the model calibration is only small. Second, the listening tests reveal that the plucking styles are more important towards realistic synthesis results than expression styles.

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This paper presents a musician-oriented modelling and simulation environment for designing physically modelled virtual instruments and interacting with them via a high performance haptic device. In particular, our system allows restoring the physical coupling between the user and the manipulated virtual instrument, a key factor for expressive playing of traditional acoustical instruments that is absent in the vast majority of computer-based musical systems. We first analyse the various uses of haptic devices in Computer Music, and introduce the various technologies involved in our system. We then present the modeller and simulation environments, and examples of musical virtual instruments created with this new environment.

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