Neural SDEs as Infinite-Dimensional GANs

Patrick Kidger, James Foster, Xuechen Li, Harald Oberhauser, Terry Lyons

Research output: Chapter or section in a book/report/conference proceedingChapter in a published conference proceeding

34 Citations (SciVal)


Stochastic differential equations (SDEs) are a staple of mathematical modelling of temporal dynamics. However, a fundamental limitation has been that such models have typically been relatively inflexible, which recent work introducing Neural SDEs has sought to solve. Here, we show that the current classical approach to fitting SDEs may be approached as a special case of (Wasserstein) GANs, and in doing so the neural and classical regimes may be brought together. The input noise is Brownian motion, the output samples are time-evolving paths produced by a numerical solver, and by parameterising a discriminator as a Neural Controlled Differential Equation (CDE), we obtain Neural SDEs as (in modern machine learning parlance) continuous-time generative time series models. Unlike previous work on this problem, this is a direct extension of the classical approach without reference to either prespecified statistics or density functions. Arbitrary drift and diffusions are admissible, so as the Wasserstein loss has a unique global minima, in the infinite data limit \textit{any} SDE may be learnt.
Original languageEnglish
Title of host publicationProceedings of the 38th International Conference on Machine Learning
Number of pages11
Publication statusPublished - 24 Jul 2021
Externally publishedYes
EventThirty-eighth International Conference on Machine Learning - Virutal only
Duration: 18 Jul 202124 Jul 2021
Conference number: 38

Publication series

NameProceedings of Machine Learning Research
ISSN (Electronic)2640-3498


ConferenceThirty-eighth International Conference on Machine Learning
Abbreviated titleICML
Internet address


Dive into the research topics of 'Neural SDEs as Infinite-Dimensional GANs'. Together they form a unique fingerprint.

Cite this