Any examples applying Physics Informed Neural Networks to ODEs?

Specific Domains Machine Learning
1

I recently have been involved in PINNs and their applications. While I understand the mathematics of NNs, ODE solvers, PDEs, etc… I have very little experience in implementing them and in Julia especially. Does anyone have any examples/blog posts of applying PINNs to ODE systems? For what its worth, my research is in mathematical biology and the ODE systems I mostly work with are compartmental models (i.e. SIR/SEIR models).

An example of what I am looking for is this LinkedIn video/post by Mustafa K.

2

ODEs are just one dimensional PDEs. The documentation of NeuralPDE has quite a few examples of this:

https://docs.sciml.ai/NeuralPDE/dev/tutorials/ode/
https://docs.sciml.ai/NeuralPDE/dev/tutorials/param_estim/
https://docs.sciml.ai/NeuralPDE/dev/manual/ode/

Note that we are changing the loss in these docs examples to make it more robust: Docs modifications to use QuadratureTraining instead of GridTraining by sdesai1287 · Pull Request #729 · SciML/NeuralPDE.jl · GitHub