Virtual Analog Modeling of Distortion Circuits Using Neural Ordinary Differential Equations

Jan Wilczek; Alec Wright; Vesa Välimäki; Emanuël A.P. Habets

Virtual Analog Modeling of Distortion Circuits Using Neural Ordinary Differential Equations

Jan Wilczek, Alec Wright, Vesa Välimäki, Emanuël A.P. Habets

Audio Signal Processing

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

2 Citations (Scopus)

74 Downloads (Pure)

Abstract

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.

Original language	English
Title of host publication	Proceedings of the 25th International Conference on Digital Audio Effects (DAFx20in22)
Editors	Gianpaolo Evangelista, Nicki Holighaus
Place of Publication	Vienna, Austria
Publisher	DAFx
Pages	9-16
Number of pages	8
Edition	2022
ISBN (Electronic)	978-3-200-08599-2
Publication status	Published - 2022
MoE publication type	A4 Conference publication
Event	International Conference on Digital Audio Effects - University of Music and Performing Arts Vienna, Vienna, Austria Duration: 7 Sept 2022 → 9 Sept 2022 Conference number: 25 https://dafx2020.mdw.ac.at/DAFx20in22/ https://dafx2020.mdw.ac.at/DAFx20in22/index.html

Publication series

Name	Proceedings of the International Conference on Digital Audio Effects
ISSN (Print)	2413-6700
ISSN (Electronic)	2413-6689

Conference

Conference	International Conference on Digital Audio Effects
Abbreviated title	DAFx
Country/Territory	Austria
City	Vienna
Period	07/09/2022 → 09/09/2022
Internet address	https://dafx2020.mdw.ac.at/DAFx20in22/ https://dafx2020.mdw.ac.at/DAFx20in22/index.html

Access to Document

Wilczek_et alii_VIRTUAL ANALOG MODELING OF DISTORTION CIRCUITS USING NEURAL ORDINARY DIFFERENTIAL EQUATIONSFinal published version, 2.26 MBLicence: CC BY

https://dafx2020.mdw.ac.at/proceedings/papers/DAFx20in22_paper_12.pdfLicence: CC BY

Cite this

Wilczek, J., Wright, A., Välimäki, V., & Habets, E. A. P. (2022). Virtual Analog Modeling of Distortion Circuits Using Neural Ordinary Differential Equations. In G. Evangelista, & N. Holighaus (Eds.), Proceedings of the 25th International Conference on Digital Audio Effects (DAFx20in22) (2022 ed., pp. 9-16). Article 12 (Proceedings of the International Conference on Digital Audio Effects). DAFx . https://dafx2020.mdw.ac.at/proceedings/papers/DAFx20in22_paper_12.pdf

Wilczek, Jan ; Wright, Alec ; Välimäki, Vesa et al. / Virtual Analog Modeling of Distortion Circuits Using Neural Ordinary Differential Equations. Proceedings of the 25th International Conference on Digital Audio Effects (DAFx20in22). editor / Gianpaolo Evangelista ; Nicki Holighaus. 2022. ed. Vienna, Austria : DAFx , 2022. pp. 9-16 (Proceedings of the International Conference on Digital Audio Effects).

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title = "Virtual Analog Modeling of Distortion Circuits Using Neural Ordinary Differential Equations",

abstract = "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.",

author = "Jan Wilczek and Alec Wright and Vesa V{\"a}lim{\"a}ki and Habets, {Emanu{\"e}l A.P.}",

note = "Funding Information: ∗ This work was supported by a fellowship within the IFI programme of the German Academic Exchange Service (DAAD). † This research is part of the activities of the Nordic Sound and Music Computing Network—NordicSMC (NordForsk project no. 86892). ‡A joint institution of the Friedrich-Alexander-Universit{\"a}t Erlangen-N{\"u}rnberg (FAU) and Fraunhofer Institute for Integrated Circuits (IIS). Publisher Copyright: Copyright: {\textcopyright} 2022 Jan Wilczek et al.; International Conference on Digital Audio Effects, DAFx ; Conference date: 07-09-2022 Through 09-09-2022",

year = "2022",

language = "English",

series = "Proceedings of the International Conference on Digital Audio Effects",

publisher = "DAFx ",

pages = "9--16",

editor = "Gianpaolo Evangelista and Nicki Holighaus",

booktitle = "Proceedings of the 25th International Conference on Digital Audio Effects (DAFx20in22)",

address = "Austria",

edition = "2022",

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Wilczek, J, Wright, A, Välimäki, V & Habets, EAP 2022, Virtual Analog Modeling of Distortion Circuits Using Neural Ordinary Differential Equations. in G Evangelista & N Holighaus (eds), Proceedings of the 25th International Conference on Digital Audio Effects (DAFx20in22). 2022 edn, 12, Proceedings of the International Conference on Digital Audio Effects, DAFx , Vienna, Austria, pp. 9-16, International Conference on Digital Audio Effects, Vienna, Austria, 07/09/2022. <https://dafx2020.mdw.ac.at/proceedings/papers/DAFx20in22_paper_12.pdf>

Virtual Analog Modeling of Distortion Circuits Using Neural Ordinary Differential Equations. / Wilczek, Jan; Wright, Alec; Välimäki, Vesa et al.
Proceedings of the 25th International Conference on Digital Audio Effects (DAFx20in22). ed. / Gianpaolo Evangelista; Nicki Holighaus. 2022. ed. Vienna, Austria: DAFx , 2022. p. 9-16 12 (Proceedings of the International Conference on Digital Audio Effects).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

TY - GEN

T1 - Virtual Analog Modeling of Distortion Circuits Using Neural Ordinary Differential Equations

AU - Wilczek, Jan

AU - Wright, Alec

AU - Välimäki, Vesa

AU - Habets, Emanuël A.P.

N1 - Conference code: 25

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

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M3 - Conference article in proceedings

AN - SCOPUS:85138773865

T3 - Proceedings of the International Conference on Digital Audio Effects

SP - 9

EP - 16

BT - Proceedings of the 25th International Conference on Digital Audio Effects (DAFx20in22)

A2 - Evangelista, Gianpaolo

A2 - Holighaus, Nicki

PB - DAFx

CY - Vienna, Austria

T2 - International Conference on Digital Audio Effects

Y2 - 7 September 2022 through 9 September 2022

ER -

Wilczek J, Wright A, Välimäki V, Habets EAP. Virtual Analog Modeling of Distortion Circuits Using Neural Ordinary Differential Equations. In Evangelista G, Holighaus N, editors, Proceedings of the 25th International Conference on Digital Audio Effects (DAFx20in22). 2022 ed. Vienna, Austria: DAFx . 2022. p. 9-16. 12. (Proceedings of the International Conference on Digital Audio Effects).

Virtual Analog Modeling of Distortion Circuits Using Neural Ordinary Differential Equations

Abstract

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Conference

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NordicSMC: Nordic Sound and Music Computing Network

Aalto Acoustics Lab

Science-IT

Cite this

Virtual Analog Modeling of Distortion Circuits Using Neural Ordinary Differential Equations

Abstract

Publication series

Conference

Access to Document

Other files and links

Fingerprint

Projects

NordicSMC: Nordic Sound and Music Computing Network

Equipment

Aalto Acoustics Lab

Science-IT

Cite this