chore:

docs/src/index.md

@@ -9,6 +9,17 @@ TrixiEnzyme is not a registered Julia package, and it can be installed by runnin
 ] add https://github.com/junyixu/TrixiEnzyme.jl.git
 ```
 
+## Notes about Enzyme
+
+There's some issues with `Enzyme.make_zero!` right now for this use case, see https://github.com/EnzymeAD/Enzyme.jl/issues/1661
+One need to be careful with a vanilla closure outside Enzyme.
+If one writes to caches and expect to differentiate through them, then the closure should be duplicated for handling the derivative of those values.
+If you want to track derivatives through arrays that are enclosed, you have to duplicate the array to have shadow memory for its differentiation.
+if you want to track derivatives through arrays that are enclosed, you have to duplicate the array to have shadow memory for its differentiation
+So if you only have the original memory, you cannot do the differentiation since you don't have a place to store the extra values. In a simplified sense, a `Dual{Float64}` is 128 bits, `Float64` is 64 bits, so if you're writing to a buffer of 5 `Float64` numbers, you need 5*2*64 bits of space to keep a dual number, which you don't have
+So the best thing to do for a user would be to separate out the things that you need to track through, make them arguments to the function, and then simply Duplicate on those.
+This is how [TrixiEnzyme.jacobian_enzyme_forward](https://junyixu.github.io/TrixiEnzyme.jl/dev/api.html#TrixiEnzyme.jacobian_enzyme_forward) works.
+
 ## Configuring Batch Size
 
 To utilize `Enzyme.BatchDuplicated`, one can create a tuple containing duals (or shadows).
@@ -45,5 +56,5 @@ julia> @time jacobian_enzyme_forward(TrixiEnzyme.upwind!, x);
 ```
 
 Benchmark for a 401x401 Jacobian of `TrixiEnzyme.upwind!` (Lower is better):
-![upwind benchmark](../fig/upwind_benchmark.png)
+![upwind benchmark](./img/upwind_benchmark.png)
 `Enyme(@batch)` means applying `Polyester.@batch` to `middlebatches`.

src/jacobian.jl

@@ -1,5 +1,10 @@
 Enzyme.API.runtimeActivity!(true)
 
+```
+    jacobian_enzyme_forward_closure(semi::SemidiscretizationHyperbolic)
+
+Same as jacobian_enzyme_forward but with closure.
+```
 function jacobian_enzyme_forward_closure(semi)
     t0 = zero(real(semi))
     u_ode = compute_coefficients(t0, semi)
@@ -32,7 +37,14 @@ function jacobian_enzyme_forward_closure(semi)
     return dys
 end
 
+```
+    jacobian_enzyme_reverse_closure(semi::SemidiscretizationHyperbolic)
+
+Same as jacobian_enzyme_reverse but with closure
 
+!!! warning
+Enzyme.jl does not play well with Polyester.jl and there are no plans to fix this soon.
+```
 function jacobian_enzyme_reverse_closure(semi)
     t0 = zero(real(semi))
     u_ode = compute_coefficients(t0, semi)

test/SemiTest.jl

@@ -1,6 +1,7 @@
 module SemiTest
 using Test
 using TrixiEnzyme
+using TrixiEnzyme: LinearScalarAdvectionEquation1D, DGSEM, TreeMesh, SVector
 
 # %%
 # equation with a advection_velocity of `1`.