# Physical Modeling using Recurrent Neural Networks with Fast Convolutional Layers

arXiv: https://arxiv.org/abs/2204.10125 · HTML: https://mlsanity.com/paper/2204.10125/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 35 references that are in the map.
- First posted on arXiv 21 Apr 2022.

## Builds on (most cited first, 7 of 7)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1801.01236/) (2018)
- [Deep Learning for Tube Amplifier Emulation](https://mlsanity.com/paper/1811.00334/) (2018)
- [wav2shape: Hearing the Shape of a Drum Machine](https://mlsanity.com/paper/2007.10299/) (2020)

## Built on by (most cited first, 9 of 9)

- [Modelling black-box audio effects with time-varying feature modulation](https://mlsanity.com/paper/2211.00497/) (2022)
- [Learning to Highlight Audio by Watching Movies](https://mlsanity.com/paper/2505.12154/) (2025)
- [Differentiable Modal Synthesis for Physical Modeling of Planar String Sound and Motion Simulation](https://mlsanity.com/paper/2407.05516/) (2024)
- [Towards Efficient Modelling of String Dynamics: A Comparison of State Space and Koopman based Deep Learning Methods](https://mlsanity.com/paper/2408.16650/) (2024)
- [Fast Differentiable Modal Simulation of Non-linear Strings, Membranes, and Plates](https://mlsanity.com/paper/2505.05940/) (2025)
- [Learning Nonlinear Dynamics in Physical Modelling Synthesis using Neural Ordinary Differential Equations](https://mlsanity.com/paper/2505.10511/) (2025)
- [Conditional Flow Matching for Visually-Guided Acoustic Highlighting](https://mlsanity.com/paper/2602.03762/) (2026)
- [Stable Differentiable Modal Synthesis for Learning Nonlinear Dynamics](https://mlsanity.com/paper/2601.10453/) (2026)
- [Identifying the nonlinear string dynamics with port-Hamiltonian neural networks](https://mlsanity.com/paper/2605.12785/) (2026)

## Abstract (arXiv)

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.