Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or partial differential equations, using established techniques. Recent work has applied the techniques of machine-learning to construct such models automatically from data for the case of systems which have lumped states described by scalar values, such as electrical circuits. In this work, we examine how similar techniques are able to construct models of systems which have spatially distributed rather than lumped states. We describe several novel recurrent neural network structures, and show how they can be thought of as an extension of modal techniques. As a proof of concept, we generate synthetic data for three physical systems and show that the proposed network structures can be trained with this data to reproduce the behavior of these systems.
翻译:在音乐信号处理文献中,音响、机械和电气系统的分立时间建模是一个突出的主题。这些模型主要通过使用既定技术,从普通或部分差异方程式的数学模型分离而产生。最近的工作应用了机器学习技术,从数据中自动建立这种模型,这些系统用电路等缩放值描述的星标值来建立。在这项工作中,我们研究了类似技术如何能够建立空间分布而不是断层状态的系统模型。我们描述了几个新的经常神经网络结构,并展示了如何将它们视为模式技术的延伸。作为概念的证明,我们为三个物理系统生成了合成数据,并表明可以用这些数据对拟议的网络结构进行培训,以便复制这些系统的行为。