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This talk was part of SciMLCon 2022! For more information, check out https://scimlcon.org/2022/. For more information on the SciML Open Source Software Organization for Scientific Machine Learning, check out https://sciml.ai/. Universal Differential Equations with Gaussian Processes | Steffen Ridderbusch | SciMLCon 2022 Abstract: In this talk we demonstrate using Gaussian Prosses as a basis for Universal Differential Equations, instead of Neural Networks. As GPs, given the right underlying kernel, are also Universal Approximators, the combination promises to be similarly powerful and allows additionally for some quantification of the model uncertainty. This work connects the SciML and the JuliaGaussianProcesses ecosystems and enables interesting further research. Description: Neural Networks are Universal Approximators, which have proven themselves to be powerful, but they can struggle with uncertainty quantification and extrapolation. Here, we show that Gaussian Processes can be combined with ODE models in a very similar manner, serving not as a replacement but as an alternative that may be more suitable in some contexts. This approach opens exciting new research opportunities into uncertainty propagation through general ODE solvers, and incorporation of additional knowledge. Initial work on this has been presented at CDC’21 (https://arxiv.org/abs/2011.05364). For more info on the Julia Programming Language, follow us on Twitter: / julialanguage and consider sponsoring us on GitHub: https://github.com/sponsors/JuliaLang 00:00 Welcome! 00:10 Help us add time stamps or captions to this video! See the description for details. Want to help add timestamps to our YouTube videos to help with discoverability? Find out more here: https://github.com/JuliaCommunity/You... Interested in improving the auto generated captions? Get involved here: https://github.com/JuliaCommunity/You...