swilliamson7
commented
2 years ago Adding to this, the way I learned how to run the barotropic gyre model in Oceananigans is through the steps
mkdir blah_20220707 cd blah_20220707 wget https://julialang-s3.julialang.org/bin/linux/x64/1.7/julia-1.7.3-linux-x86_64.tar.gz (or whatever version of Julia you need, Mac/PC)
tar -xzvf julia-1.7.3-linux-x86_64.tar.gz
git clone https://github.com/CliMA/Oceananigans.jl.git
cd Oceananigans.jl/
export JULIA_DEPOT_PATH=pwd/.julia
../julia-1.7.3/bin/julia --project=@. -e 'using Pkg;Pkg.instantiate()' ../julia-1.7.3/bin/julia --project=@.
include("validation/barotropic_gyre/barotropic_gyre.jl")
All of the setup for the model exists in that script "barotropic_gyre.jl"
NoraLoose
glwagner
vchuravy
heimbach
As of right now, the steps to get to an adjoint-able barotropic gyre model are
1) Create a "forward step" function. Right now the barotropic gyre model in Oceananigans takes in some initial inputs, and then just runs the model forward in its entirety to return the fields $u,$ $v,$ and $\eta$ at the end, if understood correctly. Ideally, we would instead take just one forward step: $$f(\mathbf{u}(t), \mathbf{v}(t), \mathbf{\eta}(t)) = (\mathbf{u}(t + \Delta t), \mathbf{v}(t + \Delta t), \mathbf{\eta}(t + \Delta t) )$$ (not trying to say $f$ returns a vector, just returns the fields at the next time step.)
2) Once we have that forward function, we first want to apply Enzyme to see if it works. This shouldn't be difficult at this point (hopefully). This step will also let us see if there are issues with Enzyme + Oceananigans that would need to be worked out.
3) Then we can run a trial sensitivity analysis. Namely, per Patrick's suggestion we can choose the cost function $$J(\mathbf{u}(t_f), \mathbf{v}(t_f)) = \mathbf{u}^2(t_f) + \mathbf{v}^2(tf) = \sum{j, k} u{jk}^2 + v{jk}^2$$ (i.e. we sum $u^2 + v^2$ at every point on the grid and add them all together.) Then we can ask what happens to this quantity if we change the initial $u$ field a little bit. This will just be running the "adjoint equations" step-by-step backwards.