August 15 – 19 , 2022, Dagstuhl Seminar 22332

Differential Equations and Continuous-Time Deep Learning


David Duvenaud (University of Toronto, CA)
Markus Heinonen (Aalto University, FI)
Michael Tiemann (Robert Bosch GmbH – Renningen, DE)
Max Welling (University of Amsterdam, NL)

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Christina Schwarz for administrative matters

Andreas Dolzmann for scientific matters

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Deep models have revolutionised machine learning due to their remarkable ability to iteratively construct more and more refined representations of data over the layers. Perhaps unsurprisingly, very deep learning architectures have recently been shown to converge to differential equation models, which are ubiquitous in sciences, but so far overlooked in machine learning. This striking connection opens new avenues of theory and practice of continuous-time machine learning inspired by physical sciences. Simultaneously, neural networks have started to emerge as powerful alternatives to cumbersome mechanistic dynamical systems. Finally, deep learning models in conjecture with stochastic gradient optimisation has been used to numerically solve high-dimensional partial differential equations. Thus, we have entered a new era of continuous-time modelling in machine learning.

This change in perspective is currently gaining interest rapidly across domains and provides an excellent and topical opportunity to bring together experts in dynamical systems, computational science, machine learning and the relevant scientific domains to lay solid foundations of these efforts. On the other hand, as the scientific communities, events and outlets are significantly disjoint, it is key to organize an interdisciplinary event and establish novel communication channels to ensure the distribution of relevant knowledge.

Over the course of this Dagstuhl Seminar, we want to establish strong contacts, communication and collaboration of the different research communities. Let's have an exchange of each community's best practices, known pitfalls and tricks of the trade. We will try to identify the most important open questions and avenues forward to foster interdisciplinary research. To this end, this seminar will feature not only individual contributed talks, but also general discussions and "collaboration bazaars", for which participants will have the possibility to pitch ideas for break-out project sessions to each other. In the break-out sessions, participants may discuss open problems, joint research obstacles, or community building work.

Motivation text license
  Creative Commons BY 4.0
  David Duvenaud, Markus O. Heinonen, Michael Tiemann, and Max Welling


  • Machine Learning
  • Numerical Analysis
  • Systems And Control


  • Differential equations
  • Deep learning


In the series Dagstuhl Reports each Dagstuhl Seminar and Dagstuhl Perspectives Workshop is documented. The seminar organizers, in cooperation with the collector, prepare a report that includes contributions from the participants' talks together with a summary of the seminar.


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