Bayesian Neural Ordinary Differential Equations

This paper shows how to train this object and the results we are currently getting. There's a full set of tutorials in the DiffEqFlux.jl documentation:

- Bayesian Neural ODEs with NUTS (https://diffeqflux.sciml.ai/dev/examples/BayesianNODE_NUTS/)

- Bayesian Neural ODEs with Stochastic Langevin Gradient Descent (https://diffeqflux.sciml.ai/dev/examples/BayesianNODE_SGLD/)

- General usage of the differential equation solvers (ODEs, SDEs, DDEs) in the Turing probabilistic programming language (https://turing.ml/dev/tutorials/10-bayesiandiffeq/)

- More demonstrations of ODEs, SDEs, and DDEs estimated by Turing + DifferentialEquations.jl in a way that you can swap in neural networks (https://github.com/TuringLang/TuringTutorials/blob/master/10...)

Our focus is more on the model discovery and scientific machine learning aspects, but we did throw an MNIST portion in there for good measure. The results are still early but everything is usable today.

If you're interested, you might want to check out the LAFI 2021 conference