Learning Nonlinear Dynamics in Physical Modelling Synthesis using Neural Ordinary Differential Equations

2025-05-15

AI Summary

This work addresses auditory phenomena—such as pitch gliding and timbral variation with hammer velocity—arising from geometric nonlinearity in high-amplitude string vibration. Methodologically, it introduces a physics-informed modeling paradigm that integrates modal decomposition with neural ordinary differential equations (Neural ODEs). Specifically, the model explicitly separates the linear modal analytical solution from a neural network-learned nonlinear coupling term, eliminating the need for parameter encoders and preserving physical interpretability of system parameters. Notably, this is the first application of Neural ODEs to distributed musical system modeling. Trained on synthetic data, the model accurately reproduces strongly nonlinear dynamical behaviors while ensuring both high-fidelity synthesis and physical transparency. The proposed framework establishes a novel paradigm for nonlinear physical modeling synthesis, balancing theoretical rigor with practical audio generation capabilities.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Multimodal Learning
• Natural Language Processing: Language Grounding & Multi-modal NLP

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

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.

Problem

• Modeling nonlinear string vibrations using neural ODEs
• Combining modal decomposition with neural networks for music synthesis
• Preserving physical parameters in trained nonlinear dynamic models

Innovation

• Combines modal decomposition with neural ODEs
• Uses neural network for nonlinear dynamics
• Retains physical parameters post-training