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CITATION.bib

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@@ -16,7 +16,7 @@ @article{DBLP:journals/corr/abs-1902-02376
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journal = {CoRR},
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volume = {abs/1902.02376},
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year = {2019},
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url = {http://arxiv.org/abs/1902.02376},
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url = {https://arxiv.org/abs/1902.02376},
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archivePrefix = {arXiv},
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eprint = {1902.02376},
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timestamp = {Tue, 21 May 2019 18:03:36 +0200},
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journal = {CoRR},
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volume = {abs/1811.01457},
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year = {2018},
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url = {http://arxiv.org/abs/1811.01457},
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url = {https://arxiv.org/abs/1811.01457},
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archivePrefix = {arXiv},
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eprint = {1811.01457},
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timestamp = {Thu, 22 Nov 2018 17:58:30 +0100},

README.md

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DiffEqFlux.jl fuses the world of differential equations with machine learning
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by helping users put diffeq solvers into neural networks. This package utilizes
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[DifferentialEquations.jl](http://docs.sciml.ai/DiffEqDocs/stable/),
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[Flux.jl](https://docs.sciml.ai/Flux.jl/stable/) and [Lux.jl](https://docs.sciml.ai/Lux/stable/) as its building blocks to support research in
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[Scientific Machine Learning](http://www.stochasticlifestyle.com/the-essential-tools-of-scientific-machine-learning-scientific-ml/),
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[DifferentialEquations.jl](https://docs.sciml.ai/DiffEqDocs/stable/),
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[Flux.jl](https://docs.sciml.ai/Flux/stable/) and [Lux.jl](https://docs.sciml.ai/Lux/stable/) as its building blocks to support research in
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[Scientific Machine Learning](https://www.stochasticlifestyle.com/the-essential-tools-of-scientific-machine-learning-scientific-ml/),
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specifically neural differential equations and universal differential equations,
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to add physical information into traditional machine learning.
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[the release blog post](https://julialang.org/blog/2019/01/fluxdiffeq).
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Additional demonstrations, like neural
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PDEs and neural jump SDEs, can be found
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[in this blog post](http://www.stochasticlifestyle.com/neural-jump-sdes-jump-diffusions-and-neural-pdes/)
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[in this blog post](https://www.stochasticlifestyle.com/neural-jump-sdes-jump-diffusions-and-neural-pdes/)
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(among many others!).
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Do not limit yourself to the current neuralization. With this package, you can

docs/src/examples/neural_ode.md

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commented out the plotting). You can easily incorporate the procedure below to
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set up custom optimization problems. For more information on the usage of
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[Optimization.jl](https://github.com/SciML/Optimization.jl), please consult
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[this](http://docs.sciml.ai/Optimization/stable/) documentation.
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[this](https://docs.sciml.ai/Optimization/stable/) documentation.
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The `x` and `p` variables in the optimization function are different than
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`x` and `p` above. The optimization function runs over the space of parameters of

docs/src/examples/neural_sde.md

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```
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For our dataset we will use DifferentialEquations.jl's [parallel ensemble
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interface](http://docs.juliadiffeq.org/dev/features/ensemble.html) to generate
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interface](https://docs.sciml.ai/DiffEqDocs/stable/features/ensemble/) to generate
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data from the average of 10,000 runs of the SDE:
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```@example nsde

docs/src/index.md

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# DiffEqFlux: High Level Pre-Built Architectures for Implicit Deep Learning
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# DiffEqFlux: High Level Pre-Built Architectures for Implicit Deep Learning
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DiffEqFlux.jl is an implicit deep learning library built using the SciML ecosystem. It is
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a high level interface that pulls together all of the tools with heuristics
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The approach of this package is the easy and efficient training of
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[Universal Differential Equations](https://arxiv.org/abs/2001.04385).
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DiffEqFlux.jl provides architectures which match the interfaces of
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machine learning libraries such as [Flux.jl](https://fluxml.ai/)
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and [Lux.jl](http://lux.csail.mit.edu/dev/)
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machine learning libraries such as [Flux.jl](https://docs.sciml.ai/Flux/stable/)
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and [Lux.jl](https://docs.sciml.ai/Lux/stable/)
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to make it easy to build continuous-time machine learning layers
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into larger machine learning applications.
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</details>
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```
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```@raw html
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You can also download the
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You can also download the
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<a href="
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```
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```@eval
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```
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```@raw html
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">project</a> file.
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```
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```

src/hnn.jl

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To obtain the gradients to train this network, ReverseDiff.gradient is supposed to
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be used. This prevents the usage of `DiffEqFlux.sciml_train` or `Flux.train`. Follow
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this [tutorial](https://diffeqflux.sciml.ai/dev/examples/hamiltonian_nn/) to see how
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this [tutorial](https://docs.sciml.ai/DiffEqFlux/stable/examples/hamiltonian_nn/) to see how
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to define a training loop to circumvent this issue.
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```julia

src/neural_de.jl

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- `alg`: The algorithm used to solve the ODE. Defaults to `nothing`, i.e. the
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default algorithm from DifferentialEquations.jl. This method requires an
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implicit ODE solver compatible with singular mass matrices. Consult the
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[DAE solvers](https://diffeq.sciml.ai/latest/solvers/dae_solve/) documentation for more details.
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[DAE solvers](https://docs.sciml.ai/DiffEqDocs/stable/solvers/dae_solve/) documentation for more details.
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- `sensealg`: The choice of differentiation algorthm used in the backpropogation.
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Defaults to an adjoint method, and with `FastChain` it defaults to utilizing
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a tape-compiled ReverseDiff vector-Jacobian product for extra efficiency. Seee

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