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Rebuild advanced/02-advanced_ODE_solving.jmd #303

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76 changes: 38 additions & 38 deletions html/advanced/02-advanced_ODE_solving.html
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75 changes: 38 additions & 37 deletions markdown/advanced/02-advanced_ODE_solving.md
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Expand Up @@ -17,13 +17,13 @@ SDEs, DDEs, DAEs, etc.

For a detailed tutorial on how to optimize one's DifferentialEquations.jl code,
please see the
[Optimizing DiffEq Code tutorial](http://tutorials.juliadiffeq.org/html/introduction/03-optimizing_diffeq_code.html).
[Optimizing DiffEq Code tutorial](http://tutorials.sciml.ai/html/introduction/03-optimizing_diffeq_code.html).

### Choosing a Good Solver

Choosing a good solver is required for getting top notch speed. General
recommendations can be found on the solver page (for example, the
[ODE Solver Recommendations](https://docs.juliadiffeq.org/dev/solvers/ode_solve)).
[ODE Solver Recommendations](https://docs.sciml.ai/dev/solvers/ode_solve)).
The current recommendations can be simplified to a Rosenbrock method
(`Rosenbrock23` or `Rodas5`) for smaller (<50 ODEs) problems, ESDIRK methods
for slightly larger (`TRBDF2` or `KenCarp4` for <2000 ODEs), and Sundials
Expand All @@ -36,7 +36,7 @@ compare many solvers on many problems.

### Check Out the Speed FAQ

See [this FAQ](https://docs.juliadiffeq.org/latest/basics/faq/#faq_performance-1)
See [this FAQ](https://docs.sciml.ai/latest/basics/faq/#faq_performance-1)
for information on common pitfalls and how to improve performance.

### Setting Up Your Julia Installation for Speed
Expand Down Expand Up @@ -83,7 +83,7 @@ the linear algebra routines. Please see the package for the limitations.

When possible, use GPUs. If your ODE system is small and you need to solve it
with very many different parameters, see the
[ensembles interface](https://docs.juliadiffeq.org/dev/features/ensemble)
[ensembles interface](https://docs.sciml.ai/dev/features/ensemble)
and [DiffEqGPU.jl](https://github.com/JuliaDiffEq/DiffEqGPU.jl). If your problem
is large, consider using a [CuArray](https://github.com/JuliaGPU/CuArrays.jl)
for the state to allow for GPU-parallelism of the internal linear algebra.
Expand Down Expand Up @@ -158,9 +158,9 @@ using BenchmarkTools


````
310.245 μs (2779 allocations: 156.72 KiB)
324.317 μs (2780 allocations: 156.73 KiB)
retcode: Success
Interpolation: Automatic order switching interpolation
Interpolation: automatic order switching interpolation
t: 115-element Array{Float64,1}:
0.0
0.0014148468219250373
Expand Down Expand Up @@ -235,9 +235,9 @@ prob_jac = ODEProblem(f,[1.0,0.0,0.0],(0.0,1e5),(0.04,3e7,1e4))


````
235.800 μs (2312 allocations: 147.88 KiB)
239.289 μs (2313 allocations: 147.89 KiB)
retcode: Success
Interpolation: Automatic order switching interpolation
Interpolation: automatic order switching interpolation
t: 115-element Array{Float64,1}:
0.0
0.0014148468219250373
Expand Down Expand Up @@ -561,7 +561,7 @@ f = ODEFunction(brusselator_2d_loop;jac_prototype=jac_sparsity)


````
(::DiffEqBase.ODEFunction{true,typeof(Main.##WeaveSandBox#1647.brusselator_
(::DiffEqBase.ODEFunction{true,typeof(Main.##WeaveSandBox#1646.brusselator_
2d_loop),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing
,Nothing,SparseArrays.SparseMatrixCSC{Float64,Int64},SparseArrays.SparseMat
rixCSC{Float64,Int64},Nothing,Nothing,Nothing,Nothing,Nothing}) (generic fu
Expand Down Expand Up @@ -619,7 +619,7 @@ Now let's see how the version with sparsity compares to the version without:


````
16.903 s (6967 allocations: 70.11 MiB)
16.388 s (6968 allocations: 70.11 MiB)
````


Expand All @@ -630,7 +630,7 @@ Now let's see how the version with sparsity compares to the version without:


````
1.735 s (55514 allocations: 885.09 MiB)
1.742 s (55529 allocations: 885.09 MiB)
retcode: Success
Interpolation: 1st order linear
t: 2-element Array{Float64,1}:
Expand Down Expand Up @@ -704,7 +704,7 @@ prob_ode_brusselator_2d_sparse = ODEProblem(f,


````
1.731 s (18646 allocations: 881.06 MiB)
1.742 s (18659 allocations: 881.06 MiB)
retcode: Success
Interpolation: 1st order linear
t: 2-element Array{Float64,1}:
Expand Down Expand Up @@ -755,7 +755,7 @@ GMRES linear solver.


````
135.205 s (3643100 allocations: 238.68 MiB)
136.948 s (3643102 allocations: 238.68 MiB)
````


Expand All @@ -766,7 +766,7 @@ GMRES linear solver.


````
6.504 s (2475960 allocations: 110.74 MiB)
6.511 s (2475962 allocations: 110.74 MiB)
retcode: Success
Interpolation: 1st order linear
t: 2-element Array{Float64,1}:
Expand Down Expand Up @@ -798,7 +798,7 @@ u: 2-element Array{Array{Float64,3},1}:


For more information on linear solver choices, see the
[linear solver documentation](https://docs.juliadiffeq.org/dev/features/linear_nonlinear).
[linear solver documentation](https://docs.sciml.ai/dev/features/linear_nonlinear).

On this problem, handling the sparsity correctly seemed to give much more of a
speedup than going to a Krylov approach, but that can be dependent on the problem
Expand All @@ -817,10 +817,10 @@ Jv = JacVecOperator(brusselator_2d_loop,u0,p,0.0)


````
DiffEqOperators.JacVecOperator{Float64,typeof(Main.##WeaveSandBox#1647.brus
DiffEqOperators.JacVecOperator{Float64,typeof(Main.##WeaveSandBox#1646.brus
selator_2d_loop),Array{ForwardDiff.Dual{DiffEqOperators.JacVecTag,Float64,1
},3},Array{ForwardDiff.Dual{DiffEqOperators.JacVecTag,Float64,1},3},Array{F
loat64,3},NTuple{4,Float64},Float64,Bool}(Main.##WeaveSandBox#1647.brussela
loat64,3},NTuple{4,Float64},Float64,Bool}(Main.##WeaveSandBox#1646.brussela
tor_2d_loop, ForwardDiff.Dual{DiffEqOperators.JacVecTag,Float64,1}[Dual{Dif
fEqOperators.JacVecTag}(0.0,0.0) Dual{DiffEqOperators.JacVecTag}(0.12134432
813715873,0.12134432813715873) … Dual{DiffEqOperators.JacVecTag}(0.12134432
Expand Down Expand Up @@ -901,7 +901,7 @@ prob_ode_brusselator_2d_jacfree = ODEProblem(f,u0,(0.,11.5),p)


````
4.723 s (4160636 allocations: 2.31 GiB)
4.715 s (4160638 allocations: 2.31 GiB)
retcode: Success
Interpolation: 1st order linear
t: 2-element Array{Float64,1}:
Expand Down Expand Up @@ -934,7 +934,7 @@ u: 2-element Array{Array{Float64,3},1}:

### Adding a Preconditioner

The [linear solver documentation](https://docs.juliadiffeq.org/latest/features/linear_nonlinear/#iterativesolvers-jl-1)
The [linear solver documentation](https://docs.sciml.ai/latest/features/linear_nonlinear/#iterativesolvers-jl-1)
shows how you can add a preconditioner to the GMRES. For example, you can
use packages like [AlgebraicMultigrid.jl](https://github.com/JuliaLinearAlgebra/AlgebraicMultigrid.jl)
to add an algebraic multigrid (AMG) or [IncompleteLU.jl](https://github.com/haampie/IncompleteLU.jl)
Expand All @@ -948,7 +948,7 @@ pc = aspreconditioner(ruge_stuben(jac_sparsity))


````
392.980 ms (28395 allocations: 32.79 MiB)
354.730 ms (28397 allocations: 32.79 MiB)
retcode: Success
Interpolation: 1st order linear
t: 2-element Array{Float64,1}:
Expand Down Expand Up @@ -1006,7 +1006,7 @@ be given (otherwise it will default to attempting an LU-decomposition).
While much of the setup makes the transition to using Sundials automatic, there
are some differences between the pure Julia implementations and the Sundials
implementations which must be taken note of. These are all detailed in the
[Sundials solver documentation](https://docs.juliadiffeq.org/latest/solvers/ode_solve/#ode_solve_sundials-1),
[Sundials solver documentation](https://docs.sciml.ai/latest/solvers/ode_solve/#ode_solve_sundials-1),
but here we will highlight the main details which one should make note of.

Defining a sparse matrix and a Jacobian for Sundials works just like any other
Expand All @@ -1025,7 +1025,7 @@ using Sundials


````
23.746 s (51627 allocations: 3.20 MiB)
20.861 s (51627 allocations: 3.20 MiB)
````


Expand All @@ -1037,7 +1037,7 @@ using Sundials


````
331.856 ms (51827 allocations: 3.06 MiB)
332.648 ms (51827 allocations: 3.06 MiB)
retcode: Success
Interpolation: 1st order linear
t: 2-element Array{Float64,1}:
Expand Down Expand Up @@ -1069,7 +1069,7 @@ u: 2-element Array{Array{Float64,3},1}:


Details for setting up a preconditioner with Sundials can be found at the
[Sundials solver page](https://docs.juliadiffeq.org/latest/solvers/ode_solve/#ode_solve_sundials-1).
[Sundials solver page](https://docs.sciml.ai/latest/solvers/ode_solve/#ode_solve_sundials-1).

## Handling Mass Matrices

Expand Down Expand Up @@ -1126,17 +1126,18 @@ plot(sol, xscale=:log10, tspan=(1e-6, 1e5), layout=(3,1))

Note that if your mass matrix is singular, i.e. your system is a DAE, then you
need to make sure you choose
[a solver that is compatible with DAEs](https://docs.juliadiffeq.org/latest/solvers/dae_solve/#dae_solve_full-1)
[a solver that is compatible with DAEs](https://docs.sciml.ai/latest/solvers/dae_solve/#dae_solve_full-1)


## Appendix

This tutorial is part of the DiffEqTutorials.jl repository, found at: <https://github.com/JuliaDiffEq/DiffEqTutorials.jl>
This tutorial is part of the SciMLTutorials.jl repository, found at: <https://github.com/SciML/SciMLTutorials.jl>.
For more information on doing scientific machine learning (SciML) with open source software, check out <https://sciml.ai/>.

To locally run this tutorial, do the following commands:
```
using DiffEqTutorials
DiffEqTutorials.weave_file("advanced","02-advanced_ODE_solving.jmd")
using SciMLTutorials
SciMLTutorials.weave_file("advanced","02-advanced_ODE_solving.jmd")
```

Computer Information:
Expand All @@ -1150,10 +1151,10 @@ Platform Info:
LIBM: libopenlibm
LLVM: libLLVM-8.0.1 (ORCJIT, skylake)
Environment:
JULIA_LOAD_PATH = /builds/JuliaGPU/DiffEqTutorials.jl:
JULIA_DEPOT_PATH = /builds/JuliaGPU/DiffEqTutorials.jl/.julia
JULIA_CUDA_MEMORY_LIMIT = 2147483648
JULIA_PROJECT = @.
JULIA_NUM_THREADS = 4
JULIA_NUM_THREADS = 8

```

Expand All @@ -1165,17 +1166,17 @@ Status `/builds/JuliaGPU/DiffEqTutorials.jl/tutorials/advanced/Project.toml`
[6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf] BenchmarkTools 0.5.0
[be33ccc6-a3ff-5ff2-a52e-74243cff1e17] CUDAnative 3.2.0
[3a865a2d-5b23-5a0f-bc46-62713ec82fae] CuArrays 2.2.2
[9fdde737-9c7f-55bf-ade8-46b3f136cc48] DiffEqOperators 4.10.0
[9fdde737-9c7f-55bf-ade8-46b3f136cc48] DiffEqOperators 4.12.0
[0c46a032-eb83-5123-abaf-570d42b7fbaa] DifferentialEquations 6.15.0
[587475ba-b771-5e3f-ad9e-33799f191a9c] Flux 0.10.4
[961ee093-0014-501f-94e3-6117800e7a78] ModelingToolkit 3.11.0
[2774e3e8-f4cf-5e23-947b-6d7e65073b56] NLsolve 4.4.0
[961ee093-0014-501f-94e3-6117800e7a78] ModelingToolkit 3.16.0
[2774e3e8-f4cf-5e23-947b-6d7e65073b56] NLsolve 4.4.1
[8faf48c0-8b73-11e9-0e63-2155955bfa4d] NeuralNetDiffEq 1.6.0
[1dea7af3-3e70-54e6-95c3-0bf5283fa5ed] OrdinaryDiffEq 5.41.0
[91a5bcdd-55d7-5caf-9e0b-520d859cae80] Plots 1.5.2
[47a9eef4-7e08-11e9-0b38-333d64bd3804] SparseDiffTools 1.9.0
[1dea7af3-3e70-54e6-95c3-0bf5283fa5ed] OrdinaryDiffEq 5.42.2
[91a5bcdd-55d7-5caf-9e0b-520d859cae80] Plots 1.5.9
[47a9eef4-7e08-11e9-0b38-333d64bd3804] SparseDiffTools 1.9.1
[684fba80-ace3-11e9-3d08-3bc7ed6f96df] SparsityDetection 0.3.3
[789caeaf-c7a9-5a7d-9973-96adeb23e2a0] StochasticDiffEq 6.24.0
[789caeaf-c7a9-5a7d-9973-96adeb23e2a0] StochasticDiffEq 6.25.0
[c3572dad-4567-51f8-b174-8c6c989267f4] Sundials 4.2.5
[37e2e46d-f89d-539d-b4ee-838fcccc9c8e] LinearAlgebra
[2f01184e-e22b-5df5-ae63-d93ebab69eaf] SparseArrays
Expand Down
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