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Pre-built implicit layer architectures with O(1) backprop, GPUs, and stiff+non-stiff DE solvers, demonstrating scientific machine learning (SciML) and physics-informed machine learning methods

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This is a follow up to https://github.com/SciML/DiffEqFlux.jl/issues/344 but with an example that actually uses the parameters input: ```julia import DifferentialEquations: Tsit5 import DiffEqFlux: FastDense, initial_params, ODEProblem, solve import Zygote x_dim...

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Implementing https://arxiv.org/abs/2006.00104 to complement the FFJORD layers. Pinging the authors @lruthotto @donken in case they are interested.

https://arxiv.org/pdf/2003.04630.pdf

https://arxiv.org/pdf/2006.06033.pdf from @cfinlay would be interesting to add as a layer in contrast to the FFJORD layer. It could train using the differentiable adaptive Monte Carlo from https://github.com/SciML/Quadrature.jl and then...

I ran the [CNF example](https://diffeqflux.sciml.ai/dev/examples/normalizing_flows/). `@time` repeatedly gives memory allocations around 50GB. Given that the example looks simplistic, I had expected to see much lower numbers. Is that number in...

The docs for DifferentialEquations.jl include a nice FAQ section with performance tips [here](https://docs.sciml.ai/stable/basics/faq/). Is there anything like that for common performance pitfalls for `sciml_train` specifically? I'm struggling to get good...

Here's a chunk of code that one could add to the UDE tutorial. This code illustrates four things. 1. Minibatches in the loss function 2. Dynamic Composition of layers to...

Basic inspiration: neuralODE is NOT explicitly mini-batch aware. you can kludge it right now, but this kludge won't scale because it's not mini-batch aware. SO introduce mini-batch smartness into neuralODE....

@ChrisRackauckas This MFGnet.jl package is significant in applying Lagrangian methods to MFG and therefore lessening the curse of dimensionality in this class of problems (dimension from 2 to 100 in...

Apologies if this is a very basic question: before all the changes in the ```DiffEqFlux.jl``` library one could specify different adjoint methods (in the ```solve``` call to the neural ODE)...