Learning Nonlinear Dynamics in Physical Modelling Synthesis using Neural Ordinary Differential Equations
This work addresses the challenge of accurately synthesizing perceptually important effects like pitch glides in musical systems, but it is incremental as it extends existing neural ODE methods to a specific domain.
The authors tackled the problem of modeling nonlinear dynamics in distributed musical systems, such as high-amplitude string vibrations, by combining modal decomposition with neural ordinary differential equations, and demonstrated that the model can reproduce the nonlinear dynamics using synthetic data for a nonlinear transverse string.
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.