# Virtual Analog Modeling of Distortion Circuits Using Neural Ordinary Differential Equations

arXiv: https://arxiv.org/abs/2205.01897 · HTML: https://mlsanity.com/paper/2205.01897/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 31 references that are in the map.
- First posted on arXiv 4 May 2022.

## Builds on (most cited first, 6 of 6)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [A disciplined approach to neural network hyper-parameters: Part 1 -- learning rate, batch size, momentum, and weight decay](https://mlsanity.com/paper/1803.09820/) (2018)
- [Perceptual Loss Function for Neural Modelling of Audio Systems](https://mlsanity.com/paper/1911.08922/) (2019)

## Built on by (most cited first, 2 of 2)

- [Comparative Study of State-based Neural Networks for Virtual Analog Audio Effects Modeling](https://mlsanity.com/paper/2405.04124/) (2024)
- [Learning Nonlinear Dynamics in Physical Modelling Synthesis using Neural Ordinary Differential Equations](https://mlsanity.com/paper/2505.10511/) (2025)

## Abstract (arXiv)

Recent research in deep learning has shown that neural networks can learn differential equations governing dynamical systems. In this paper, we adapt this concept to Virtual Analog (VA) modeling to learn the ordinary differential equations (ODEs) governing the first-order and the second-order diode clipper. The proposed models achieve performance comparable to state-of-the-art recurrent neural networks (RNNs) albeit using fewer parameters. We show that this approach does not require oversampling and allows to increase the sampling rate after the training has completed, which results in increased accuracy. Using a sophisticated numerical solver allows to increase the accuracy at the cost of slower processing. ODEs learned this way do not require closed forms but are still physically interpretable.