From 80ae881d181a962d5f5758b14442143080fb36f7 Mon Sep 17 00:00:00 2001 From: vchuravy Date: Fri, 7 Jun 2024 18:00:42 +0000 Subject: [PATCH] =?UTF-8?q?Deploying=20to=20gh-pages=20from=20@=20DJ4Earth?= =?UTF-8?q?/MPE24@f8a8b2ba5a4c8c036796d69fc6fcb82564e8e107=20=F0=9F=9A=80?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Burgers_tutorial/Project.toml | 10 + Burgers_tutorial/README.md | 10 + Burgers_tutorial/burgers_tutorial.html | 20 + Burgers_tutorial/burgers_tutorial.jl | 2201 ++++ Burgers_tutorial/burgers_tutorial.plutostate | Bin 0 -> 880726 bytes Burgers_tutorial/checkpointing.png | Bin 0 -> 51984 bytes .../ice_ocean_interaction.jl | 111 + .../ice_ocean_notebook_tutorial.html | 20 + .../ice_ocean_notebook_tutorial.jl | 536 + .../ice_ocean_notebook_tutorial.plutostate | Bin 0 -> 143168 bytes .../Data/PIG_Control_B_dJUICE.mat | Bin 0 -> 1040381 bytes .../Data/PIG_Control_drag_dJUICE.mat | Bin 0 -> 1158951 bytes 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mode 100644 index 0000000..a8ca8f8 --- /dev/null +++ b/Burgers_tutorial/Project.toml @@ -0,0 +1,10 @@ +[deps] +Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e" +CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba" +Checkpointing = "eb46d486-4f9c-4c3d-b445-a617f2a2f1ca" +Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9" +KernelAbstractions = "63c18a36-062a-441e-b654-da1e3ab1ce7c" +LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" +Parameters = "d96e819e-fc66-5662-9728-84c9c7592b0a" +Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" +Pluto = "c3e4b0f8-55cb-11ea-2926-15256bba5781" diff --git a/Burgers_tutorial/README.md b/Burgers_tutorial/README.md new file mode 100644 index 0000000..e021030 --- /dev/null +++ b/Burgers_tutorial/README.md @@ -0,0 +1,10 @@ +# README + +Start Pluto.jl +```julia +import Pluto +Pluto.run() +``` +and open `burgers_tutorial.jl` in the browser. + +Static html version of the notebook is available [here](https://dj4earth.github.io/MPE24/Burgers_tutorial/burgers_tutorial.html). diff --git a/Burgers_tutorial/burgers_tutorial.html b/Burgers_tutorial/burgers_tutorial.html new file mode 100644 index 0000000..c2d0b79 --- /dev/null +++ b/Burgers_tutorial/burgers_tutorial.html @@ -0,0 +1,20 @@ + + + + + + + + + + +
\ No newline at end of file diff --git a/Burgers_tutorial/burgers_tutorial.jl b/Burgers_tutorial/burgers_tutorial.jl new file mode 100644 index 0000000..abad8ad --- /dev/null +++ b/Burgers_tutorial/burgers_tutorial.jl @@ -0,0 +1,2201 @@ +### A Pluto.jl notebook ### +# v0.19.42 + +using Markdown +using InteractiveUtils + +# ╔═╡ bbe566f7-02b7-480b-bd63-d6c72aa1ac40 +begin +using KernelAbstractions +using Adapt +end + +# ╔═╡ ebd676b8-f98d-4384-a4c4-0f333c2804d2 +using CUDA + +# ╔═╡ bd0d9801-9d0d-4bee-beea-131439c262cc +using PlutoUI + +# ╔═╡ 06f23f52-0fcc-4707-b06c-80f4529b506d +using Enzyme + +# ╔═╡ cd9ef5ba-5e59-43ed-82d1-588dc7effefe +using Checkpointing + +# ╔═╡ a575949c-2368-11ef-2b2d-2fe3a2ffbae3 +md""" +# 2D Burgers Equations in a Nutshell + +## Governing equations + +```math +\begin{align} + \frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} &= \nu \nabla^2 u\\ + \frac{\partial v}{\partial t} + u \frac{\partial v}{\partial x} + v \frac{\partial v}{\partial y} &= \nu \nabla^2 v +\end{align} +``` +where $u$ and $v$ represent the $x$ and $y$ velocities of a fluid and $\nu$ is the viscosity coefficient. +""" + +# ╔═╡ db83cf1f-2946-4392-909f-ab96e4613260 +md""" +# Portable Implementation +[KernelAbstractions.jl](https://github.com/JuliaGPU/KernelAbstractions.jl) and [Adapt.jl](https://github.com/JuliaGPU/Adapt.jl) are used to write portable kernels, here the stencil. +""" + +# ╔═╡ d25fc2f9-7b5c-4a23-8c21-98322eff3bf0 +md""" +Too long of a package name... +""" + +# ╔═╡ b96ea551-35ef-4b87-989b-fe5e49e098cc +const KA = KernelAbstractions + +# ╔═╡ f3907dcf-e994-4449-ade0-ec7c6bf50c3f +md""" +We can load the CUDA Julia package even if our system does not have CUDA installed. +""" + +# ╔═╡ a4a001a4-cc83-4bd8-a0f6-a3645b9a241c +a = ones(10) + +# ╔═╡ 8ed9fa8a-6b5c-4658-a844-36afce6034aa +md""" +Move the array to the host CPU() architecture. +""" + +# ╔═╡ 85a78d65-4ac7-4057-afe1-1620df33ea6d +adapt(CPU(), a) + +# ╔═╡ 38ba9813-1cea-4e36-8729-bf401bf8ea72 +md""" +Let's do an element-wise addition. +""" + +# ╔═╡ 5ed89c14-d237-4aff-a999-90ed0093e266 +a .+ a + +# ╔═╡ dc5a47d7-9d6a-4c28-823e-4f76bd0a8eea +md""" +Enable the following cells only if you have a system with CUDA support. +""" + +# ╔═╡ 1d32785d-03d8-4309-aa19-f4031e371a29 +# ╠═╡ disabled = true +#=╠═╡ +cua = adapt(CUDABackend(), a) + ╠═╡ =# + +# ╔═╡ 95f79fd5-0017-4862-a27a-ad4a37c7fedd +md""" +Now we can do the sum on the GPU. +""" + +# ╔═╡ 127c3067-25b0-474b-993a-8b2db7c180a8 +# ╠═╡ disabled = true +#=╠═╡ +cua .+ cua + ╠═╡ =# + +# ╔═╡ cb27823a-dc0d-4953-8a9e-265ab0c7b7e0 +md""" +If the above lines worked, you've just run a CUDA kernel from Julia. +""" + +# ╔═╡ 0d88b56d-070c-403c-a17f-def34d87a335 +md""" +# Datastructures + +To implement Burgers we need a datastructure that stores + +* the field of the current timestep in two dimensions $u$ and $v$, +* the next field, +* grid points $n_x$ and $n_y$ in x and y direction, +* viscosity, $\mu$ +* discretization $dx$, $dy$, $dt$, +* number of timesteps, +* and architecture backend. +""" + +# ╔═╡ ddf67473-5f5f-44b2-bd40-415772f5aead +begin +mutable struct Burgers + nextu::AbstractMatrix + nextv::AbstractMatrix + lastu::AbstractMatrix + lastv::AbstractMatrix + nx::Int # Grid points in x direction + ny::Int # Grid points in y direction + μ::Float64 + dx::Float64 + dy::Float64 + dt::Float64 + tsteps::Int + backend::KA.Backend +end +function Burgers( + Nx::Int, + Ny::Int, + μ::Float64, + dx::Float64, + dy::Float64, + dt::Float64, + tsteps::Int, + backend=CPU(), +) + return Burgers( + adapt(backend,zeros(Nx, Ny)), + adapt(backend,zeros(Nx, Ny)), + adapt(backend,zeros(Nx, Ny)), + adapt(backend,zeros(Nx, Ny)), + Nx, + Ny, + μ, + dx, + dy, + dt, + tsteps, + backend, + ) +end +end + +# ╔═╡ feb5a4ce-f32e-4f72-94c9-a39460a6866e +md""" +# Functions and Methods +To discretize the system, we use a centered finite difference scheme in space and an explicit forward Euler scheme in time. + +## Stencil +We implement a kernel that computes $u_{t+1}, v_{t+1}$ with respect to $u_t$, $v_t$ at grid point $(i,j)$. This allows us to parallelize the kernel over the grid points. +""" + +# ╔═╡ d7df76fd-dbb3-43bd-a1a9-35b69cebcbcb +@kernel function stencil_kernel!(lastu, nextu, lastv, nextv, dx, dy, dt, μ, nx, ny) + i, j = @index(Global, NTuple) + nextu[i+1, j+1] = + lastu[i+1, j+1] + + dt * ( + ( + -lastu[i+1, j+1] / (2 * dx) * (lastu[i+2, j+1] - lastu[i, j+1]) - + lastv[i+1, j+1] / (2 * dy) * (lastu[i+1, j+2] - lastu[i+1, j]) + ) + + μ * ( + (lastu[i+2, j+1] - 2 * lastu[i+1, j+1] + lastu[i, j+1]) / dx^2 + + (lastu[i+1, j+2] - 2 * lastu[i+1, j+1] + lastu[i+1, j]) / dy^2 + ) + ) + nextv[i+1, j+1] = + lastv[i+1, j+1] + + dt * ( + ( + -lastu[i+1, j+1] / (2 * dx) * (lastv[i+2, j+1] - lastv[i, j+1]) - + lastv[i+1, j+1] / (2 * dy) * (lastv[i+1, j+2] - lastv[i+1, j]) + ) + + μ * ( + (lastv[i+2, j+1] - 2 * lastv[i+1, j+1] + lastv[i, j+1]) / dx^2 + + (lastv[i+1, j+2] - 2 * lastv[i+1, j+1] + lastv[i+1, j]) / dy^2 + ) + ) +end + +# ╔═╡ dd62122a-89c0-471a-97c1-5f3d60b98f40 +md""" +## Boundary and Initial Conditions +The equation is solved on a square domain, $(x, y) \in [-L, L] \times [-L, L]$, with the initial velocities +```math + +u(0,x,y) = \exp\left(-x^2 - y^2 \right), \; \; \; \; v(0,x,y) = \exp\left(-x^2 - y^2\right). +``` +Here we use the domain $[-3,3] \times [-3,3]$. Again, we implement this as a kernel over all grid points. +""" + + +# ╔═╡ 0dc72edd-d11c-4f71-baee-a5c265b2d135 +@kernel function set_ic_kernel!(lastu, nextu, lastv, nextv, nx, ny) + i, j = @index(Global, NTuple) + lastu[i+1, j+1] = exp(-(-3.0 + i * 6.0 / (nx - 1))^2 - (-3.0 + j * 6.0 / (ny - 1))^2) + lastv[i+1, j+1] = exp(-(-3.0 + i * 6.0 / (nx - 1))^2 - (-3.0 + j * 6.0 / (ny - 1))^2) + nextu[i+1, j+1] = exp(-(-3.0 + i * 6.0 / (nx - 1))^2 - (-3.0 + j * 6.0 / (ny - 1))^2) + nextv[i+1, j+1] = exp(-(-3.0 + i * 6.0 / (nx - 1))^2 - (-3.0 + j * 6.0 / (ny - 1))^2) +end + +# ╔═╡ 75f0cbda-57f4-4232-93f8-a88ccd764d16 +md""" +We use Dirichlet conditions on all four boundaries +```math +u(t,x,-L) = u(t,x, L) = u(t,-L, y) = u(t,L, y) = 0, \\ +v(t,x,-L) = v(t,x, L) = v(t,-L, y) = v(t,L, y) = 0, . +``` +Here, we use the broadcast operator `.`. +""" + +# ╔═╡ 02e8e500-9785-436c-8e2c-d3455ab8eec3 +function set_bc!(burgers::Burgers) + (nx, ny) = (burgers.nx, burgers.ny) + burgers.lastu[1:1, 1:ny] .= 0.0 + burgers.lastv[1:1, 1:ny] .= 0.0 + burgers.lastu[nx:nx, 1:ny] .= 0.0 + burgers.lastv[nx:nx, 1:ny] .= 0.0 + burgers.lastu[1:nx, 1:1] .= 0.0 + burgers.lastv[1:nx, 1:1] .= 0.0 + burgers.lastu[1:nx, ny:ny] .= 0.0 + burgers.lastv[1:nx, ny:ny] .= 0.0 + return nothing +end + +# ╔═╡ 0e804a08-555d-46fc-bce0-7296b4a9a32c +md""" +## Time Loop +""" + +# ╔═╡ 69a5e411-7f1b-4f38-895d-c92a5fb152f7 +md""" +At each time $t_f$ we can compute the current kinetic energy. +```math + J = \frac{1}{N_x \cdot N_y} \sum_{j = 1}^{N_x} \sum_{k = 1}^{N_y} \left( u(t_f, x_j, y_k)^2+ v(t_f, x_j, y_k)^2 \right), +``` +We scale it by the number of grid points. +""" + + +# ╔═╡ a25e3d03-8eed-4a0b-9fd7-c5e30f9c8f1c +function energy(burgers::Burgers) + @inbounds lenergy = + sum(burgers.nextu[2:end-1, 2:end-1] .^ 2 .+ burgers.nextv[2:end-1, 2:end-1] .^ 2) / + (burgers.nx*burgers.ny) +end + +# ╔═╡ eabb6565-946f-4e00-a3ac-9ef33d05c594 +md""" +Finally, to get things moving we implement an `advance` method. +""" + +# ╔═╡ 664315e2-b4db-41ad-82d1-3039454fed1e +md""" +`advance` is then used in a time-stepping loop, which returns the final kinetic energy after $T$ timesteps. +""" + +# ╔═╡ 903d9b69-0e12-4591-8249-82b78a93d83e +md""" +## Kernel Launches + +Our implementation is done. The only missing piece is launching the kernels in a parallel way. KernelAbstractions.jl takes care of that. We need to provide the `backend` we want to launch on and the number of work items. For the `stencil_kernel!` and `set_ic_kernel!`, the number of work items are all of the inner grid points. The boundary conditions are untouched. +""" + +# ╔═╡ 12dfa763-b307-4f76-9a0d-5b24e6130da9 +md""" +How do we launch a kernel? + +stencil_kernel!(backend) +""" + +# ╔═╡ 64b6eca3-8b8a-470c-b496-8207d88fb99c +function stencil!(burgers::Burgers) + stencil_kernel!(burgers.backend)( + burgers.lastu, + burgers.nextu, + burgers.lastv, + burgers.nextv, + burgers.dx, + burgers.dy, + burgers.dt, + burgers.μ, + burgers.nx, + burgers.ny, + ndrange=(burgers.nx-2, burgers.ny-2), + ) + KA.synchronize(burgers.backend) +end + +# ╔═╡ 4b4f81f6-6ff0-430f-8a86-965d4a41044d +function advance!(burgers::Burgers) + stencil!(burgers) + copyto!(burgers.lastu, burgers.nextu) + copyto!(burgers.lastv, burgers.nextv) + return nothing +end + +# ╔═╡ 9c21cfa8-0db3-4d74-9465-75bf25b15a5b +function final_energy!(burgers::Burgers) + for i = 1:burgers.tsteps + advance!(burgers) + end + return energy(burgers) +end + +# ╔═╡ 96a54adb-015c-4243-a99d-9cda695f2a4d +function set_ic!(burgers::Burgers) + set_ic_kernel!(burgers.backend)( + burgers.lastu, burgers.nextu, burgers.lastv, burgers.nextv, burgers.nx, burgers.ny, + ndrange=(burgers.nx-2, burgers.ny-2), + ) + KA.synchronize(burgers.backend) + return nothing +end + +# ╔═╡ e14d9a22-4d55-4e66-8a63-8fdccd0c6d27 +md""" +# Running the Burgers Model +We are ready to play with our Burgers model. Initially we use $100 \times 100$ grid points and only $10$ time steps. +""" + +# ╔═╡ 48b5e47b-e090-401d-ad7a-4898874b5117 +begin +Nx = 100 +Ny = 100 +tsteps = 10 +μ = 0.01 # # U * L / Re, nu +dx = 1e-1 +dy = 1e-1 +dt = 1e-3 # dt < 0.5 * dx^2 +end + +# ╔═╡ 3843e17d-7eb0-4b15-a1d8-ca7e0eaefd8d +md""" +The Burgers object is created, +""" + +# ╔═╡ de82b316-f8b9-479d-acac-dd18768e1e43 +burgers = Burgers(Nx, Ny, μ, dx, dy, dt, tsteps) + +# ╔═╡ 6b383ed1-80d0-4749-b1c2-44219bb7b7c2 +md""" +the boundary conditions are set, +""" + +# ╔═╡ 32aadddf-6220-4e3d-aae1-09d58e173b41 +set_ic!(burgers) + +# ╔═╡ 998c6c9b-9f30-4ad2-b1ae-089f53d1bb92 +md""" +and the boundary conditions are set. +""" + +# ╔═╡ c5feb1d9-4703-49a2-bedc-b996887f4d91 +set_bc!(burgers) + +# ╔═╡ c072dbfe-4866-4fd6-94b6-069c2deb29d5 +md""" +The initial energy is +""" + +# ╔═╡ 50c2b95a-9e72-48b9-879b-d31a70c0f6cb +ienergy = energy(burgers) + +# ╔═╡ 78e3b07f-f99a-4bfc-b42d-008c9417a14c +md""" +and the final energy is +""" + +# ╔═╡ 01549692-94ba-4119-b259-052be74fc4b0 +fenergy = final_energy!(burgers) + +# ╔═╡ c001200e-392e-4bd5-bf89-2b3b81e1a31f +md""" +# Plotting of Primal + +To get a nicely colored plot, we visualize the velocity magnitude $|v|^2 = u^2 + v^2$ at each point (x,y). +""" + +# ╔═╡ bc294229-2b02-4b19-8f1b-71348793b323 +function velocity_magnitude(burgers) + burgers.nextu[2:end-1, 2:end-1] .^ 2 + burgers.nextv[2:end-1, 2:end-1] .^ 2 +end + +# ╔═╡ f9f6b93f-74b4-49bb-91ed-71b14c87fb3a +begin +using Plots +color = :balance +surface( + range(-3, 3, length=burgers.nx-2), + range(-3, 3, length=burgers.ny-2), + velocity_magnitude(burgers);xlabel = "x", ylabel = "y", c = color, + legend=:none +) +end + +# ╔═╡ b8201b3f-5187-4fdd-86a2-feb4e1d4f05b +md""" +Let's crank up the resolution and number of timesteps. +""" + +# ╔═╡ a9814ad4-7c9b-4c25-8fa4-b1683ad9be82 +begin +burgers_hd = Burgers(1000, 1000, μ, 1e-2, 1e-2, dt, 1000) +set_ic!(burgers_hd) +set_bc!(burgers_hd) +final_energy!(burgers_hd) +surface( + range(-3, 3, length=burgers_hd.nx-2), + range(-3, 3, length=burgers_hd.ny-2), + velocity_magnitude(burgers_hd);xlabel = "x", ylabel = "y", c = color, + legend=:none +) +end + +# ╔═╡ 9f411195-2312-4385-924e-9bacecfd7fd2 +md""" +# Differentiating Burgers using Enzyme +""" + +# ╔═╡ 1eb06eee-fc1a-4074-ba20-661757996659 +md""" +Let's reset Burgers. +""" + +# ╔═╡ 7ff17e31-f755-4fc5-b66d-64965f92c6d7 +begin +set_bc!(burgers) +set_ic!(burgers) +end + +# ╔═╡ af620e89-c59b-4d69-89ca-020d5d958810 +md""" +Loading the tool 🔨 +""" + +# ╔═╡ 8112d5d6-151c-4b40-ac85-450786dff438 +begin +surface( + range(-3, 3, length=burgers.nx-2), + range(-3, 3, length=burgers.ny-2), + velocity_magnitude(burgers);xlabel = "x", ylabel = "y", c = color, + legend=:none +) +end + +# ╔═╡ f152117a-578c-451f-86ce-4acd1a669bfd +begin +dburgers = Enzyme.make_zero(deepcopy(burgers)) +autodiff(ReverseWithPrimal, final_energy!, Active, Duplicated(burgers, dburgers)) +end + +# ╔═╡ 33c47fe9-6326-47df-8539-3999297298a9 +begin +surface( + range(-3, 3, length=dburgers.nx-2), + range(-3, 3, length=dburgers.ny-2), + dburgers.lastu[2:end-1, 2:end-1] .^ 2 + dburgers.lastv[2:end-1, 2:end-1] .^ 2; + xlabel = "x", ylabel = "y", c = color, + legend=:none +) +end + +# ╔═╡ 3a4e997d-b002-4129-a69a-90bfe285f824 +md""" +## Checkpointing +Let's reset `burgers` and think. What happens if we differentiate `burgers_hd`? + +If we differentiate through the entire model, every state $u$ and $v$ needs to be stored for computing the adjoint. Enzyme automatically takes care of this. + +With $1,000$ time steps, $1,000 \times 1,000$ grid points and $4$ fields, this amounts to $4 \cdot 10^9 \cdot 8$ bytes, or 32 GB. + +Checkpointing is a technique for using recomputation to reduce memory load. It's a trade-off between memory requirement and runtime. +""" + +# ╔═╡ d90ca551-d0c9-4f6d-b061-82c978350d61 +md"""$(LocalResource("checkpointing.png"))""" + +# ╔═╡ 1cbdba02-e68a-4307-b19e-08a7f2848fd6 +md""" +Load the [Checkpointing.jl](https://github.com/Argonne-National-Laboratory/Checkpointing.jl) package. +""" + + +# ╔═╡ fd8cd500-0442-4006-9e25-5e51e0e61770 +md""" +The checkpointing scheme will be passed to the timestepping method as an additional argument. TODO +""" + +# ╔═╡ 6dabc190-b86e-47e7-ae4b-c00a4f83fdd7 +function final_energy_chk!(burgers::Burgers, scheme) + @checkpoint_struct scheme burgers for i = 1:burgers.tsteps + advance!(burgers) + end + return energy(burgers) +end + +# ╔═╡ d17ba6af-0ccc-4de5-9de5-9cefd4afa87c +md""" +We use the [Revolve](https://doi.org/10.1145/347837.347846) algorithm and set it up for `tsteps=10` timesteps and with a limit of 2 checkpoints. +""" + +# ╔═╡ 6989b054-e102-4349-bbb4-f45fabfa4d3e + revolve = Revolve{Burgers}(tsteps, 2; verbose = 1) + +# ╔═╡ 9092bf93-a2a5-46b5-9798-4adbadacf3f0 +md""" +Instead of $10$ forward steps, we now do $10$ extra forward steps, leading to an overhead of $20/10=2$. +TODO: fix overhead factor +""" + +# ╔═╡ c2bbb137-50f0-4a5e-b68e-e35b665e06e1 +md""" +Start the differentiation using Enzyme. The checkpointing scheme is passed as a Const or "non-active" variable. +""" + +# ╔═╡ 42a682f0-6fc4-44ae-9c3f-1434a69f5ff6 +begin + reset!(revolve) + autodiff(ReverseWithPrimal, final_energy_chk!, Active, Duplicated(burgers, dburgers), Const(revolve)) +end + +# ╔═╡ 3db86c1b-6a9a-4855-8385-a0c2a8f073b6 +md""" +The adjoint fields are stored in `dburgers` and store $du/dJ$, $dv/dJ$. We then compute the "adjoint velocity magnitude" $(dJ/du)^2 + (dJ/dv)^2$. +""" + +# ╔═╡ 5beb4b8b-2c08-440a-a275-12fba8bbd852 +surface( + range(-3, 3, length=burgers.nx-2), + range(-3, 3, length=burgers.ny-2), + dburgers.lastu[2:end-1, 2:end-1] .^ 2 + dburgers.lastv[2:end-1, 2:end-1] .^ 2; + xlabel = "x", ylabel = "y", c = color, + legend=:none +) + +# ╔═╡ caaef553-35cc-4984-9dcd-bc057bb93cf2 +md""" +Let's do the high-resolution example +""" + +# ╔═╡ b06b03fb-9be6-4077-8640-3a5dae4d7980 +begin +set_bc!(burgers_hd) +set_ic!(burgers_hd) +dburgers_hd = Enzyme.make_zero(deepcopy(burgers_hd)) +revolve_hd = Revolve{Burgers}(1000, 10; verbose = 1) +autodiff(ReverseWithPrimal, final_energy_chk!, Active, Duplicated(burgers_hd, dburgers_hd), Const(revolve_hd)) +end + +# ╔═╡ 9c5f3dbe-598c-4160-875f-51de499aba05 +surface( + range(-3, 3, length=burgers_hd.nx-2), + range(-3, 3, length=burgers_hd.ny-2), + dburgers_hd.lastu[2:end-1, 2:end-1] .^ 2 + dburgers_hd.lastv[2:end-1, 2:end-1] .^ 2; + xlabel = "x", ylabel = "y", c = color, + legend=:none, camera = (120, 30) +) + +# ╔═╡ 871a7d07-2417-4e73-a9b9-5d7916edb167 +md""" +We computed the adjoint field with checkpointing and Enzyme using only 10 checkpoints, or 40 fields and 305MB of storage, a factor of 100 less than 30GB. This leads to a slowdown of only around 3. For details see this [paper](https://doi.org/10.1007/978-3-031-36024-4_37). +""" + +# ╔═╡ fef27b29-d3f0-46d1-a054-fc01ef7b84ee +md""" +# Bonus and Outlook + +If you have a CUDA supported GPU you can run Burgers on a CUDA GPU. +""" + +# ╔═╡ 53e470c0-4f3b-4fc2-ad37-f2a4cd1d47c0 +# ╠═╡ disabled = true +#=╠═╡ +begin + cu_burgers = Burgers(1000, 1000, μ, 1e-2, 1e-2, dt, 1000, CUDABackend()) + set_ic!(cu_burgers) + set_bc!(cu_burgers) + final_energy!(cu_burgers) + # Transfer to host for plotting + nextu = adapt(CPU(), cu_burgers.nextu) + nextv = adapt(CPU(), cu_burgers.nextv) + + surface( + range(-3, 3, length=cu_burgers.nx-2), + range(-3, 3, length=cu_burgers.ny-2), + nextu[2:end-1, 2:end-1] .^ 2 .+ nextv[2:end-1, 2:end-1] .^2, + xlabel = "x", ylabel = "y", c = color, + legend=:none + ) +end + ╠═╡ =# + +# ╔═╡ afab0c0a-a85e-4c00-ad8b-b20897d65134 +md""" +Transparent support of Enzyme for GPUs using KernelAbstractions is in the making! 🐛🪲🪳 +""" + +# ╔═╡ 00000000-0000-0000-0000-000000000001 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zZt1DVT>+z%DbOo-Sv7v)I@O=O8O=tY_jRommK9FzudjVbLgyMoJ)~-q{v9R9C7Z*OH*NUW;11eC0V8r$O=LFXV8jv@(%plD@!OmFO4Crn literal 0 HcmV?d00001 diff --git a/ClimaIceOcean_tutorial/ice_ocean_interaction.jl b/ClimaIceOcean_tutorial/ice_ocean_interaction.jl new file mode 100644 index 0000000..4cd2d82 --- /dev/null +++ b/ClimaIceOcean_tutorial/ice_ocean_interaction.jl @@ -0,0 +1,111 @@ +using Oceananigans.Operators + +using Oceananigans.Architectures: architecture +using Oceananigans.BoundaryConditions: fill_halo_regions! +using Oceananigans.Models: AbstractModel +using Oceananigans.TimeSteppers: tick! +using Oceananigans.Utils: launch! + +using KernelAbstractions: @kernel, @index +using KernelAbstractions.Extras.LoopInfo: @unroll + +# Simulations interface +import Oceananigans: fields, prognostic_fields +import Oceananigans.Fields: set! +import Oceananigans.Architectures: AbstractArchitecture +import Oceananigans.Grids: architecture +import Oceananigans.Models: timestepper, NaNChecker +import Oceananigans.OutputWriters: default_included_properties +import Oceananigans.Simulations: reset!, initialize!, iteration +import Oceananigans.TimeSteppers: time_step!, update_state!, time +import Oceananigans.Utils: prettytime + +function ice_ocean_latent_heat!(ice_model, ocean_model, Δt) + ρₒ = 1024 # ocean_density + cₒ = 3991 # ocean_heat_capacity + Qₒ = ice_model.external_heat_fluxes.bottom + Tₒ = ocean_model.tracers.T + Sₒ = 30 #ocean.model.tracers.S . NOOOOOO YOU NEED SALT! + hᵢ = ice_model.ice_thickness + + liquidus = ice_model.phase_transitions.liquidus + grid = ocean_model.grid + arch = architecture(grid) + + launch!(arch, grid, :xy, _compute_ice_ocean_latent_heat!, + Qₒ, grid, hᵢ, Tₒ, Sₒ, liquidus, ρₒ, cₒ, Δt) + + return nothing +end + +@kernel function _compute_ice_ocean_latent_heat!(latent_heat, + grid, + ice_thickness, + ocean_temperature, + ocean_salinity, + liquidus, + ρₒ, cₒ, Δt) + + i, j = @index(Global, NTuple) + + Nz = size(grid, 3) + Qₒ = latent_heat + hᵢ = ice_thickness + Tₒ = ocean_temperature + Sₒ = ocean_salinity + + δQ = zero(grid) + icy_cell = @inbounds hᵢ[i, j, 1] > 0 # make ice bath approximation then + + @unroll for k = Nz:-1:1 + @inbounds begin + # Various quantities + Δz = Δzᶜᶜᶜ(i, j, k, grid) + Tᴺ = Tₒ[i, j, k] + Sᴺ = Sₒ[i, j, k] + end + + # Melting / freezing temperature at the surface of the ocean + Tₘ = melting_temperature(liquidus, Sᴺ) + + # Conditions for non-zero ice-ocean flux: + # - the ocean is below the freezing temperature, causing formation of ice. + freezing = Tᴺ < Tₘ + + # - We are at the surface and the cell is covered by ice. + icy_surface_cell = (k == Nz) & icy_cell + + # When there is a non-zero ice-ocean flux, we will instantaneously adjust the + # temperature of the grid cells accordingly. + adjust_temperature = freezing | icy_surface_cell + + # Compute change in ocean heat energy. + # + # - When Tᴺ < Tₘ, we heat the ocean back to melting temperature by extracting heat from the ice, + # assuming that the heat flux (which is carried by nascent ice crystals called frazil ice) floats + # instantaneously to the surface. + # + # - When Tᴺ > Tₘ and we are in a surface cell covered by ice, we assume equilibrium + # and cool the ocean by injecting excess heat into the ice. + # + δEₒ = adjust_temperature * ρₒ * cₒ * (Tₘ - Tᴺ) + + # Perform temperature adjustment + @inline Tₒ[i, j, k] = ifelse(adjust_temperature, Tₘ, Tᴺ) + + # Compute the heat flux from ocean into ice. + # + # A positive value δQ > 0 implies that the ocean is cooled; ie heat + # is fluxing upwards, into the ice. This occurs when applying the + # ice bath equilibrium condition to cool down a warm ocean (δEₒ < 0). + # + # A negative value δQ < 0 implies that heat is fluxed from the ice into + # the ocean, cooling the ice and heating the ocean (δEₒ > 0). This occurs when + # frazil ice is formed within the ocean. + + δQ -= δEₒ * Δz / Δt + end + + # Store ice-ocean flux + @inbounds Qₒ[i, j, 1] = δQ +end diff --git a/ClimaIceOcean_tutorial/ice_ocean_notebook_tutorial.html b/ClimaIceOcean_tutorial/ice_ocean_notebook_tutorial.html new file mode 100644 index 0000000..7fd73dd --- /dev/null +++ b/ClimaIceOcean_tutorial/ice_ocean_notebook_tutorial.html @@ -0,0 +1,20 @@ + + + + + + + + + + +

\ No newline at end of file diff --git a/ClimaIceOcean_tutorial/ice_ocean_notebook_tutorial.jl b/ClimaIceOcean_tutorial/ice_ocean_notebook_tutorial.jl new file mode 100644 index 0000000..863d02d --- /dev/null +++ b/ClimaIceOcean_tutorial/ice_ocean_notebook_tutorial.jl @@ -0,0 +1,536 @@ +### A Pluto.jl notebook ### +# v0.19.42 + +using Markdown +using InteractiveUtils + +# ╔═╡ 9afd85ee-b9de-4629-b9a8-3ce6ea0f10db +begin + import Pkg + # activate a temporary environment + Pkg.activate(mktempdir()) + Pkg.add([ + Pkg.PackageSpec(name="ClimaSeaIce", rev="jlk9/mutable-slabseaicemodel"), + Pkg.PackageSpec(name="Enzyme", version="0.12.8"), + Pkg.PackageSpec(name="KernelAbstractions", version="0.9.19"), + Pkg.PackageSpec(name="Oceananigans", rev="jlk9/stabilize-tuple-in-permute-boundary-conditions"), + Pkg.PackageSpec(name="GLMakie") + ]) + + using Oceananigans + using Oceananigans.TurbulenceClosures: with_tracers + using Oceananigans.BoundaryConditions: fill_halo_regions! + using Oceananigans.Fields: ZeroField, ConstantField + using Oceananigans.Models.HydrostaticFreeSurfaceModels: tracernames + + using Enzyme + using LinearAlgebra + + using ClimaSeaIce + using ClimaSeaIce: melting_temperature + using ClimaSeaIce.HeatBoundaryConditions: RadiativeEmission, IceWaterThermalEquilibrium + + using KernelAbstractions + + using GLMakie + + include("./ice_ocean_interaction.jl") + + Enzyme.API.runtimeActivity!(true) + Enzyme.API.looseTypeAnalysis!(true) + Enzyme.EnzymeRules.inactive_type(::Type{<:Oceananigans.Grids.AbstractGrid}) = true + Enzyme.EnzymeRules.inactive_type(::Type{<:Oceananigans.Clock}) = true +end + +# ╔═╡ 92d7f11a-6a68-4d2e-9a5f-ee0798528c43 +md"# Ocean Sea-Ice Inverse Problem" + +# ╔═╡ 32388534-3ac7-497d-a933-086100ff0c20 +md"As a (very!) simplified model, suppose we have a circlular floe of ice floating on top of a body of water. The water has a steady horizontal current represented by functions $u$ and $v$, and its initial temperature $T$ varies depending on depth and horizontal location. Both diffusion and advection will affect the water's temperature, which will in turn cause temperature changes and encourage growth or melt in the ice. + +We'll implement this model using two Julia packages: `Oceananigans.jl` for ocean-flavored fluid dynamics, and `ClimaSeaIce.jl` for ice thermodynamics and dynamics. Both of these packages are designed for use with GPUs in mind, but for this tutorial we will only use CPUs since our problem will be fairly small. Both of these packages were written by scientists at the Climate Modeling Alliance (CliMA: https://clima.caltech.edu), and thus use very similar conventions. + +To differentiate this model, we'll use `Enzyme`, a tool that performs automatic differentiation (AD) of code. `Enzyme` operates at the LLVM level (low-level virtual machine), which makes it usable for several programming languages. Here we'll use its Julia bindings, from the package `Enzyme.jl`. + +The following block activates an environment using Oceananigans, ClimaSeaIce, and Enzyme - for this tutorial we'll use specific versions of each. You might also see references in the output to `KernelAbstractions.jl`, a library for writing code kernels that can be run on the CPU or GPU (both Oceananigans and ClimaSeaIce use this) as well as a file named `ice_ocean_interaction.jl`, which includes a helper function that implements energy transfer between water and ice." + +# ╔═╡ 3adeeda5-7db4-4d38-a0c4-2adee41c14e8 +md"### Step 1: Set up ocean and sea ice grid + +Both Oceananigans and ClimaSeaIce feature a `struct` called `grid`, which discretizes the model domain and stores some important information: +- The hardware architecture our model is running on (CPU or GPU). +- The coordinate system of our grid (we're using rectilinear coordinates). +- The spatial dimensions of our grid. +- The resolution in each dimension. +- The topology of the domain boundaries, i.e. whether boundaries are bounded or periodic. + +Our ocean grid will have three dimensions labeled $x$, $y$, and $z$. Our ice grid will only have $x$ and $y$ coordinates, since our ice occupies only a single spatial layer on top of the ocean." + +# ╔═╡ 071a8881-0be3-4052-9c28-bc76057b6b5a +begin + # Here we will set some important model parameters. First we specify the architecture: + arch = Oceananigans.CPU() + + # Next we set the spatial resolution of the problem. We'll keep this low so it can be run locally: + Nx = Ny = 16 + Nz = 16 + + # Here we set the horizontal and vertical distances of the problem: + x = y = (-π, π) + z = (-1.0, 0) + topology = (Bounded, Bounded, Bounded) + + # Here we specify the grid - the spatial discretization of our model: + grid = RectilinearGrid(arch, + size=(Nx, Ny, Nz); + x, y, z, topology) + + # And here we set up the ice grid. Note that is is flat in the z-direction since all ice is at the surface: + ice_grid = RectilinearGrid(arch, + size = (Nx, Ny), + topology = (topology[1], topology[2], Flat), + x = x, + y = y) +end + +# ╔═╡ 9637e4af-6176-490d-9c96-c2d3b2a7b32d +md"Here we can see key information for both our ocean grid (labelled just `grid`) and our ice grid. Note the ocean grid is of size 8 $\times$ 8 $\times$ 16, while the ice grid is of size 8 $\times$ 8 $\times$ 1. We set the domain the be $[-\pi,\pi] \times [-\pi,\pi] \times [-0.5, 0.5]$, but any spatial coordinates can be used. All domain boundaries are either bounded or flat (in the case of the ice vertical dimension)." + +# ╔═╡ 31ea7ca7-9e45-4722-9282-a636823f9a4e +@show grid + +# ╔═╡ a30d3476-fe00-4e2c-a786-8673a64bc8cf +@show ice_grid + +# ╔═╡ 1819e8b4-2902-4d43-95ea-e2748513ba6b +md"### Step 2: Set up ocean and sea ice model objects + +With our grids set up, we can now focus on the other aspects of the model. Our ocean model needs a diffusivity to handle the temperature tracer diffusing through the water - we'll use a vertical scalar diffusivity for this. We label this choice `diffusion`. + +We also need a velocity field for our water body. Here we'll use a time-invariant function, showing the water flows at a consistent speed and direction over time. We name our $x$-direction velocity `u` and our $y$-direction velocity `v`. We also isolate the ocean surface velocities with the `view` function so they can interact with the ice (`view` doesn't create a new instance of the array in its argument - it gives you an additional reference to that array that only tracks the slice passed to it). + +For the ice, we need variables to represent heat and salt flux, as well as the boundary condition of the bottom with the water. We're simplifying this model by assuming the water has a constant salinity everywhere, but Oceananigans has the ability to track salinity as a tracer like temperature. + +(One non-physical limitation of this model is a lack of ice advection - in other words, the ocean velocity will not directly make the ice above it move. Ice dynamics are still a work in progress in ClimaSeaIce. However, the ocean velocity does advect the ocean temperature, which in turn affects the ice through thermodynamics.) + +Note that all of these variables use our `grid` or `ice_grid` objects, to determine the resolution they need and architecture on which they are represented." + +# ╔═╡ 1853ac7c-b18a-43df-86a9-1f5195b19fda +begin + # Then we set a maximal diffusivity and diffusion type: + const maximum_diffusivity = 100 + diffusion = VerticalScalarDiffusivity(κ=0.1) + + # For this problem we'll have a constant-values velocity field - the water will flow at a + # constant speed and direction over time. We have to assign the proper velocity values to + # every point in our grid: + u = XFaceField(grid) + v = YFaceField(grid) + + U = 40 + u₀(x, y, z) = - U * cos(x + π/4) * sin(y) + v₀(x, y, z) = + U * 0.5 + + set!(u, u₀) + set!(v, v₀) + fill_halo_regions!(u) + fill_halo_regions!(v) + + ice_ocean_heat_flux = Field{Center, Center, Nothing}(ice_grid) + top_ocean_heat_flux = Qᵀ = Field{Center, Center, Nothing}(ice_grid) + top_salt_flux = Qˢ = Field{Center, Center, Nothing}(ice_grid) + + bottom_bc = IceWaterThermalEquilibrium(ConstantField(30)) + + ocean_surface_velocities = (u = view(u, :, :, Nz), #interior(u, :, :, Nz), + v = view(v, :, :, Nz), #interior(v, :, :, Nz), + w = ZeroField()) +end + +# ╔═╡ dd2b04b7-d35d-42ad-8887-206da0576688 +md"#### With our required variables initialized, we can now create our ocean and ice `models`! + +Our ocean `model` uses the hydrostatic approximation - hence we construct a `HydrostaticFreeSurfaceModel`. In addition to supplying the diffusivity and velocity fields above, we also add a tracer `T` to represent our temperature, and the WENO advection scheme to describe how temperature is moved by the ocean velocity field. Since we're assuming a constant salinity in our water, we won't track salinity as an additional tracer. + +Our ice `model` is a simple slab model with only one layer (it's often referred to as a zero-layer model, since most other ice models represent internal temperature or energy). In addition to the fluxes above, we also supply a starting salinity, internal heat flux, and top heat flux and boundary condition." + +# ╔═╡ a3efa97e-467b-43a2-87db-8c3bdc251d25 +ocean_model = HydrostaticFreeSurfaceModel(; grid, + tracer_advection = WENO(), + tracers = :T, + buoyancy = nothing, + velocities = PrescribedVelocityFields(; u, v), + closure = diffusion) + +# ╔═╡ 63f3f573-d12f-4c22-aeec-275c33750ab9 +ice_model = SlabSeaIceModel(ice_grid; + velocities = ocean_surface_velocities, + advection = nothing, + ice_consolidation_thickness = 0.05, + ice_salinity = 4, + internal_heat_flux = ConductiveFlux(conductivity=2), + top_heat_flux = ConstantField(0), # W m⁻² + top_heat_boundary_condition = PrescribedTemperature(-10), + bottom_heat_boundary_condition = bottom_bc, + bottom_heat_flux = ice_ocean_heat_flux) + +# ╔═╡ f8194371-97d4-45f4-8441-309bc535302c +md"### Step 3: Obtain the (fictional) real data values + +Now we have functioning ocean and sea ice `models`. Suppose we have the final temperature distribution and ice thickness, and wish to use these to reconstruct the initial ocean temperature. In a real project, we might have measured temperature and thickness data to use for our inverse problem. For this tutorial, we'll instead generate synthetic data values using a function called `ice_ocean_data`. For this function we'll run our ocean and ice `models` forward a number of time steps (called $n_{\text{max}}$) to produce our data values. At each step we call the `time_step!` function for both `ocean_model` and `ice_model`, along with an additional function called `ice_ocean_latent_heat!` that handles the energy exchange between the ice and water, plus resulting temperature changes in the water. + +Note: `time_step!` is a general-purpose function implemented in both Oceananigans and ClimaSeaIce that automatically runs every model component that changes in a time step. In our case it handles tracer (temperature) advection and diffusion when `ocean_model` is the argument, and changes in ice thickness when `ice_model` is the argument (energy fluxes from `ice_ocean_latent_heat!` are also factored in for time stepping with ice). It will automatically handle other model components as additional complexity is added (such as equations of state, coriolis force, or velocity advection in an ocean `model`). If you want to run ice and ocean `models` at a higher level you can also create a `simulation` struct in either Oceananigans or ClimaSeaIce and call the `run!` function, which will simply call `time_step!` for a specified number of iterations. However, `simulations` are not yet compatible with Enzyme, so for now we have to call `time_step!` directly. + + +The function `ice_ocean_data` produces both the initial temperature distribution of the water (what we aim to invert for) as well as the final water temperature distribution and initial and final ice thickness (what we are given for the inverse problem). We also have helper functions to set the initial water diffusivity, water temperature, and ice thickness." + +# ╔═╡ fc39f605-9635-402d-b60a-1c8c15a82c89 +begin + # Set the initial ice thickness: + function hᵢ(x, y) + if sqrt(x^2 + y^2) < π / 3 + return 0.05 #0.05 + 0.01 * rand() + else + return 0 + end + end + + set!(ice_model, h=hᵢ) + + # Sets the initial diffusivity: + function set_diffusivity!(ocean_model, diffusivity) + closure = VerticalScalarDiffusivity(; κ=diffusivity) + names = tuple(:T) # tracernames(model.tracers) + closure = with_tracers(names, closure) + ocean_model.closure = closure + return nothing + end + + # This produces an initial data distribution: + function set_initial_temps!(ocean_model) + amplitude = Ref(1) + width = 0.1 + #Tᵢ(x, y, z) = amplitude[] * exp(-z^2 / (2width^2) - (x^2 + y^2) / 0.05) + Tᵢ(x, y, z) = amplitude[] * exp(-z^2 / (2width^2)) * sin((x^2 + y^2) / 0.05) + + set!(ocean_model, T=Tᵢ) + + return nothing + end + + # Generates the "real" data from a stable diffusion run: + function ice_ocean_data(ocean_model, ice_model, diffusivity, n_max) + + set_diffusivity!(ocean_model, diffusivity) + set_initial_temps!(ocean_model) + + # Do time-stepping + Nx, Ny, Nz = size(ocean_model.grid) + κ_max = maximum_diffusivity + Δz = 2π / Nz + Δt = 1e-1 * Δz^2 / κ_max + @show Δt + + ocean_model.clock.time = 0 + ocean_model.clock.iteration = 0 + + # Running one time step to "stabilize" model fields: + for n = 1:1 + time_step!(ice_model, Δt) + ice_ocean_latent_heat!(ice_model, ocean_model, Δt) + time_step!(ocean_model, Δt; euler=true) + end + + T₀ = deepcopy(ocean_model.tracers.T) + h₀ = deepcopy(ice_model.ice_thickness) + + for n = 1:n_max + time_step!(ice_model, Δt) + ice_ocean_latent_heat!(ice_model, ocean_model, Δt) + time_step!(ocean_model, Δt; euler=true) + + #@show n + #@show ocean_model.tracers.T + #@show ice_model.ice_thickness + end + + # Compute scalar metric + Tₙ = deepcopy(ocean_model.tracers.T) + hₙ = deepcopy(ice_model.ice_thickness) + + return T₀, Tₙ, h₀, hₙ + end +end + +# ╔═╡ 62b3adee-63b0-4f05-b304-d1d8b0d40ef9 +md"Let's set diffusivity $\kappa = 1$ and our number of forward time steps $n_{\text{max}} = 10$:" + +# ╔═╡ 7cc53014-2395-4357-bbbb-d2d7eff59e20 +begin + κ = 1 + n_max = 100 +end + +# ╔═╡ 0b04432b-0e5d-4d99-9808-0a1ad7765f72 +md"Then we can call `ice_ocean_data` and get the true initial water temperature and ice thickness $T_0$ and $h_0$, as well as the true final temperature and thickness $T_n$ and $h_n$. We can use the `@show` macro on each of these fields to see their shapes (which should align with their corresponding grids) and some statistics, and also plot them." + +# ╔═╡ 045b79be-be33-4f17-b142-5f5b82c9e1f1 +T₀, Tₙ, h₀, hₙ = ice_ocean_data(ocean_model, ice_model, κ, n_max) + +# ╔═╡ 023737b6-401f-4ebf-8295-a2d783400a40 +md"Here we plot the initial temperature along the surface and a cross section through the depth. Note how it fluctuates in circles near the surface and becomes constant at greater depths." + +# ╔═╡ 042ee0ec-58b2-470d-84f5-302c87a88281 +begin + @show T₀ + xpoints = xnodes(grid, Center()) + ypoints = ynodes(grid, Center()) + zpoints = znodes(grid, Center()) + + figsize = (1000, 500) + temp_color_range = (-3, 3) + + fig = Figure(size=figsize) + + axTtop = Axis(fig[1, 1], xlabel="x (m)", ylabel="y (m)", title="Initial water surface Temperature") + axTside = Axis(fig[1, 2], xlabel="x (m)", ylabel="z (m)", title="Initial water depth temperature (cross-section)") + Colorbar(fig[1, 3], limits = temp_color_range, colormap = :bluesreds, + label = "Temperature (⚪ C)") + + heatmap!(axTtop, xpoints, ypoints, T₀.data[1:Nx,1:Ny,Nz], colormap=:bluesreds, colorrange = temp_color_range) + heatmap!(axTside, xpoints, zpoints, T₀.data[1:Nx,Int(Ny/2),1:Nz], colormap=:bluesreds, colorrange = temp_color_range) + + fig +end + +# ╔═╡ aa51161a-f1b6-4389-a9f8-b5c3ac1bc63e +md"These are the same plots for the final temperature. We can see how the current distorted the temperature field via advection, and how the colder water at the middle of the surface started to diffuse." + +# ╔═╡ d6e9261a-5455-4bdf-86cd-dc52d70411fa +begin + @show Tₙ + + fign = Figure(size=figsize) + + axTntop = Axis(fign[1, 1], xlabel="x (m)", ylabel="y (m)", title="Final water surface Temperature") + axTnside = Axis(fign[1, 2], xlabel="x (m)", ylabel="z (m)", title="Final water depth temperature (cross-section)") + Colorbar(fign[1, 3], limits = temp_color_range, colormap = :bluesreds, + label = "Temperature (⚪ C)") + + heatmap!(axTntop, xpoints, ypoints, Tₙ.data[1:Nx,1:Ny,Nz], colormap=:bluesreds, colorrange = temp_color_range) + heatmap!(axTnside, xpoints, zpoints, Tₙ.data[1:Nx,Int(Ny/2),1:Nz], colormap=:bluesreds, colorrange = temp_color_range) + + fign +end + +# ╔═╡ 39555d5c-b20e-4058-a0d0-846723560fbb +md"Lastly, we have plots of the initial and final ice thickness. There's a little melt along the egdes of the ice flow:" + +# ╔═╡ 843067f7-034f-4483-bcec-0b99af8b0862 +begin + @show h₀, hₙ + + figh = Figure(size=figsize) + ice_color_range = (0, 0.05) + + axH0 = Axis(figh[1, 1], xlabel="x (m)", ylabel="y (m)", title="Initial ice thickness") + axHn = Axis(figh[1, 2], xlabel="x (m)", ylabel="y (m)", title="Final ice thickness") + Colorbar(figh[1, 3], limits = ice_color_range, colormap = :grays, + label = "Ice thickness (m)") + + + heatmap!(axH0, xpoints, ypoints, h₀.data[1:Nx,1:Ny], colormap=:grays, colorrange = ice_color_range) + heatmap!(axHn, xpoints, ypoints, hₙ.data[1:Nx,1:Ny], colormap=:grays, colorrange = ice_color_range) + + figh +end + +# ╔═╡ 76727025-342d-4cec-b632-e66e2b655ff1 +md"### Step 4: Run the forward model + +With our `model` structs and intial data, we can now run the actual ice-ocean model for an inverse problem. The names here are a little confusing, but this forward model will use our ocean and ice `model` objects - all of our required data is stored in these two objects. Similar to in `ice_ocean_data`, here we run the forward model a total of $n_\text{max}$ time steps, calling the `time_step!` for both `ocean_model` and `ice_model`, along with `ice_ocean_latent_heat!`. + +Given some initial guess for our temperature distribution, we will run the model forward the set number of time steps and compare our computed final ocean temperature and ice thickness with the synthetic temperature and thickness from `ice_ocean_data`. Note that we provide diffusivity and initial ice thickness $h_i$ as function arguments, too. If we want to invert for these parameters in addition to or instead of the initial temperature, we can. + +For the comparison, we're creating a function $J$ that's the combined mean squared error of our final ocean temperatures and ice thicknesses. Smaller $J$ implies that we have a better initial guess of $T_i$, since it produces similar data to our synthetic results $T_n$ and $h_n$." + +# ╔═╡ 66bef546-fe87-4d73-b6b5-9a305bff3765 +begin + function set_initial_condition!(ocean_model, Tᵢ) + set!(ocean_model, T=Tᵢ) + return nothing + end + + # cᵢ is the proposed initial condition, cₙ is the actual data collected + # at the final time step: + function ice_ocean_model(ocean_model, ice_model, diffusivity, n_max, Tᵢ, Tₙ, hᵢ, hₙ) + set_diffusivity!(ocean_model, diffusivity) + set_initial_condition!(ocean_model, Tᵢ) + set!(ice_model, h=hᵢ) + + # Run the forward model: + Nx, Ny, Nz = size(ocean_model.grid) + κ_max = maximum_diffusivity + Δz = 2π / Nz + Δt = 1e-1 * Δz^2 / κ_max + + ocean_model.clock.time = 0 + ocean_model.clock.iteration = 0 + + for n = 1:n_max + time_step!(ice_model, Δt) + ice_ocean_latent_heat!(ice_model, ocean_model, Δt) + time_step!(ocean_model, Δt; euler=true) + end + + T = ocean_model.tracers.T + h = ice_model.ice_thickness + # Compute the misfit of our forward model run with the true data Tₙ: + J = 0.0 + ## + for i = 1:Nx, j = 1:Ny, k = 1:Nz + J += (T[i, j, k] - Tₙ[i, j, k])^2 + end + ## + ## + for i = 1:Nx, j = 1:Ny + J += (h[i, j] - hₙ[i, j])^2 + end + ## + return J::Float64 + end +end + +# ╔═╡ b5d3f15a-aafe-43c0-8c09-ca8e6c6cbc13 +md"### Step 5: Set up the inverse problem parameters + +So now we have data for the ocean temperature and ice thickness after $n_\text{max}$ time steps, respectively called $T_n$ and $h_n$. We have a forward model defined by the function `ice_ocean_model`, utilizing the `model` structs from Oceananigans and ClimaSeaIce. We have a parameter we wish to invert for - the initial ocean temperature $T_i$ (we also have the 'true' ocean temperature $T_0$ used to generate our synthetic data, but in a real inverse problem we wouldn't already have that). And lastly, our forward model produces an output $J$ that measures its accuracy relative to $T_n$ and $h_n$. $J$ might be referred to as a misfit or loss function. + +The next steps are to set up and run the inverse problem. We start with an initial guess for the starting temperature $T_i$. We call `ice_ocean_model` with this guess as an argument to produce $J$. A classic way to improve our guess for $T_i$ is by a method called gradient descent: if we somehow have the gradient for $J$ in terms of $T_i$, then we can adjust our guess for $T_i$ in the negative direction of the gradient to get an improved guess, + +$$[T_i]_{n+1} = [T_i]_n - \gamma \nabla J\left([T_i]_n\right),$$ + +which will often produce a better approximation of $T_i$. The learning rate $\gamma$ determines the size of the step we take at each iteration of gradient descent - smaller steps require more iterations, but bigger steps run the risk of 'overshooting` and producing a new guess that performs worse than expected. Fortunately, we can choose an optimal $\gamma$ for our model and inverse problem. + +The main challenge with this optimization is actually acquiring the gradient $\nabla J\left([T_i]_n\right)$. But this is made trivial with the use of Enzyme! If we supply enzyme with a zero-valued array that matches the size and typing of $T_i$, we can automatically generate its numerical derivative. + +First, let's set an initial guess for $T_i$ - a constant array of value -1 seems reasonable, assuming we know the average value of the actual $T_0$ is somewhat close to that. We'll also set $\gamma = 0.2$ and our total number of gradient descent steps to 80:" + +# ╔═╡ e0b647ee-827f-4bce-9b0c-244b7e55af75 +begin + + Tᵢ = -1.0 .+ zeros(size(ocean_model.tracers.T)) + + set!(ice_model, h=h₀) + + learning_rate = 0.2 + max_steps = 80 +end + +# ╔═╡ 44400683-d766-4fe1-b53b-03f5d2f60776 +heatmap(xpoints, ypoints, Tᵢ[1:Nx,1:Ny,Nz], colormap=:bluesreds, colorrange = (-5, 5)) + +# ╔═╡ b7abbc43-4af1-4d20-9d01-14b28dc63cc0 +md"### Step 6: Run the inverse problem + +We'll run the inverse problem in a for-loop with `max_steps` iterations. In each iteration we have to create shadows of our forward model arguments, which store their derivative information. It's important that these shadows are set to all zero values before trying to use AD - this can be a little tricky for complicated structs like `ocean_model` and `ice_model`, but if we make sure to set fields mentioned earlier like boundary conditions to 0 then we'll be good. Since the diffusivity $\kappa$ and time steps $n_\text{max}$ are both scalars, they don't require shadows to be generated. + +Once all the required shadow variables are set, we can call Enzyme's `autodiff` function in reverse mode by setting the first argument to `Enzyme.reverse`. This will use reverse-mode AD to construct the gradients of $J$ with respect to each of the inputs of ice_ocean_model, storing the gradient data in their shadow variables which are passed along with the actual inputs through `Duplicated` pairings. + +Since we're inverting for $T_i$, we're only interested in the shadow $dT_i$. We apply it in our gradient descent to obtain a better guess for $T_i$, then repeat for `max_steps` iterations. At each step we'll look at the relative error between it and the true initial temperature $T_0$ to see how good our guess actually is. + +*NOTE*: it might take a while for the following code block to run. Since Julia uses just-in-time compilation, complicated functions such as Enzyme's `autodiff` can be slow to compile. But after you finish differentiating the first iteration of gradient descent, subsequent iterations should be output very quickly. +" + +# ╔═╡ 35cdbc37-bff5-4f6c-a691-3feb984fe148 + +# Update our guess of the initial tracer distribution, cᵢ: +for i = 1:max_steps + # Create shadows and set all their values to 0: + docean_model = Enzyme.make_zero(ocean_model) + dice_model = Enzyme.make_zero(ice_model) + dTᵢ = Enzyme.make_zero(Tᵢ) + dTₙ = Enzyme.make_zero(Tₙ) + dhᵢ = Enzyme.make_zero(h₀) + dhₙ = Enzyme.make_zero(hₙ) + set_diffusivity!(docean_model, 0) + + dice_model.heat_boundary_conditions = (top = PrescribedTemperature{Int64}(0), bottom = IceWaterThermalEquilibrium{ConstantField{Int64, 3}}(ConstantField(0))) + dice_model.top_surface_temperature = ConstantField(0) + + # Since we are only interested in duplicated variable Tᵢ for this run, + # we do not use dJ here: + + dJ = autodiff(Enzyme.Reverse, + ice_ocean_model, + Duplicated(ocean_model, docean_model), + Duplicated(ice_model, dice_model), + Const(κ), + Const(n_max), + Duplicated(Tᵢ, dTᵢ), + Duplicated(Tₙ, dTₙ), + Duplicated(h₀, dhᵢ), + Duplicated(hₙ, dhₙ)) + + + @show i + @show norm(dTᵢ) + global Tᵢ .= Tᵢ .- (dTᵢ .* learning_rate) + @show (norm(Tᵢ - T₀) / norm(T₀)) + +end + + +# ╔═╡ 399fde4f-d981-45e6-9258-04befb36d9fc +heatmap(xpoints, ypoints, Tᵢ[1:Nx,1:Ny,Nz], colormap=:bluesreds, colorrange = temp_color_range) + +# ╔═╡ 934fb784-be1b-4b9d-ae5e-57ad07a38cfd +heatmap(xpoints, zpoints, Tᵢ[1:Nx,Int(Ny/2),1:Nz], colormap=:bluesreds, colorrange = temp_color_range) + +# ╔═╡ 222416ae-1aa0-4f48-9e8d-3aabc34e21dd +heatmap(xpoints, ypoints, ocean_model.tracers.T.data[1:Nx,1:Ny,Nz], colormap=:bluesreds, colorrange = (-5, 5)) + +# ╔═╡ ca0ca8a0-1692-4cc0-8726-26de146051b7 +md"### Results + +Our first guess of constant -1 was *very* far off from the true initial temperature distribution, with a relative error of over 600%. After optimizing with gradient descent, our new guess has a much lower relative error of about 36%, but this is still a significant difference from the real value. Why? + +First, inferring parameters for something as complicated as an ocean/ice model is difficult. Usually a model such as this is ill-conditioned in some way" + +# ╔═╡ Cell order: +# ╟─92d7f11a-6a68-4d2e-9a5f-ee0798528c43 +# ╟─32388534-3ac7-497d-a933-086100ff0c20 +# ╠═9afd85ee-b9de-4629-b9a8-3ce6ea0f10db +# ╟─3adeeda5-7db4-4d38-a0c4-2adee41c14e8 +# ╠═071a8881-0be3-4052-9c28-bc76057b6b5a +# ╟─9637e4af-6176-490d-9c96-c2d3b2a7b32d +# ╠═31ea7ca7-9e45-4722-9282-a636823f9a4e +# ╠═a30d3476-fe00-4e2c-a786-8673a64bc8cf +# ╟─1819e8b4-2902-4d43-95ea-e2748513ba6b +# ╠═1853ac7c-b18a-43df-86a9-1f5195b19fda +# ╟─dd2b04b7-d35d-42ad-8887-206da0576688 +# ╠═a3efa97e-467b-43a2-87db-8c3bdc251d25 +# ╠═63f3f573-d12f-4c22-aeec-275c33750ab9 +# ╟─f8194371-97d4-45f4-8441-309bc535302c +# ╠═fc39f605-9635-402d-b60a-1c8c15a82c89 +# ╟─62b3adee-63b0-4f05-b304-d1d8b0d40ef9 +# ╠═7cc53014-2395-4357-bbbb-d2d7eff59e20 +# ╠═0b04432b-0e5d-4d99-9808-0a1ad7765f72 +# ╠═045b79be-be33-4f17-b142-5f5b82c9e1f1 +# ╟─023737b6-401f-4ebf-8295-a2d783400a40 +# ╟─042ee0ec-58b2-470d-84f5-302c87a88281 +# ╟─aa51161a-f1b6-4389-a9f8-b5c3ac1bc63e +# ╟─d6e9261a-5455-4bdf-86cd-dc52d70411fa +# ╟─39555d5c-b20e-4058-a0d0-846723560fbb +# ╟─843067f7-034f-4483-bcec-0b99af8b0862 +# ╟─76727025-342d-4cec-b632-e66e2b655ff1 +# ╠═66bef546-fe87-4d73-b6b5-9a305bff3765 +# ╟─b5d3f15a-aafe-43c0-8c09-ca8e6c6cbc13 +# ╠═e0b647ee-827f-4bce-9b0c-244b7e55af75 +# ╠═44400683-d766-4fe1-b53b-03f5d2f60776 +# ╟─b7abbc43-4af1-4d20-9d01-14b28dc63cc0 +# ╠═35cdbc37-bff5-4f6c-a691-3feb984fe148 +# ╠═399fde4f-d981-45e6-9258-04befb36d9fc +# ╠═934fb784-be1b-4b9d-ae5e-57ad07a38cfd +# ╠═222416ae-1aa0-4f48-9e8d-3aabc34e21dd +# ╠═ca0ca8a0-1692-4cc0-8726-26de146051b7 diff --git a/ClimaIceOcean_tutorial/ice_ocean_notebook_tutorial.plutostate b/ClimaIceOcean_tutorial/ice_ocean_notebook_tutorial.plutostate new file mode 100644 index 0000000000000000000000000000000000000000..dd6259a4c15e6025f38356780617bd9061104322 GIT binary patch literal 143168 zcmeFaYmg+@btVRgv?z@nUVC@L+6Zr~lfVQu5T~m1T~$565QBLD1I}QE(~XDNq?`G; z*mG=vXNH 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    \ No newline at end of file diff --git a/DJUICE_tutorials/Tutorial_DJUICE_1_basic.jl b/DJUICE_tutorials/Tutorial_DJUICE_1_basic.jl new file mode 100644 index 0000000..45e1058 --- /dev/null +++ b/DJUICE_tutorials/Tutorial_DJUICE_1_basic.jl @@ -0,0 +1,2504 @@ +### A Pluto.jl notebook ### +# v0.19.42 + +using Markdown +using InteractiveUtils + +# ╔═╡ 47d2e93e-096d-4983-99ab-f138fd0057d8 +using DJUICE + +# ╔═╡ bd86b569-aabc-43da-9802-ac531d28a591 +md""" +# Basics of DJUICE: A square ice shelf + +This tutorial demonstrates how to compute the velocity field of a steady-state square ice shelf using the Differentiable Julia ICE (DJUICE) model. We follow the approach outlined in the Ice-Sheet and Sea-Level System Model (ISSM) tutorial, adapted from its original C++ implementation to Julia. The original ISSM tutorial can be found [here](https://issm.jpl.nasa.gov/documentation/tutorials/squareiceshelf/). +""" + +# ╔═╡ deb25c09-55a6-4b95-a2ca-b90845d3806b +md""" +## Install the package + +To follow this tutorial, you need to install the [`DJUICE`](https://github.com/DJ4Earth/DJUICE.jl) package. DJUICE is available on Julia package registry, and you can install it directly from the repository. + +### Option 1: Let Pluto.jl to handle the package + +You can simply use `using DJUICE` and let `Pluto.jl` to handle the package. For the first time, this may take a few minutes. + + +### Option 2: Using the Julia Package Manager +1. Open your Julia REPL. +2. Enter the package manager mode by pressing `]`. +3. Run the following command to add DJUICE from the main branch of the repository: +```julia +]add DJUICE#main +``` + +### Option 3: Using `Pkg` +Use `Pkg` to instantiate the environment and install the dependencies in `Project.toml` from the mini-tutorial. +""" + +# ╔═╡ 95641af7-1cbf-4a43-84ea-be40ca4a0acc +md""" +After installing, import the package: +""" + +# ╔═╡ 2c3fc78b-595b-40d0-a16d-6058e76d5bb1 +md""" +## Initialize the model + + +All the data belonging to a model (geometry, node coordinates, results, etc.) is held in the single object `Model`. This will create a new model named `md` whose `struct` is `DJUICE.Model`. The information contained in the model `md` is grouped by `struct`, that contain fields related to a particular aspect of the model (e.g. mesh, ice geometry, material properties, friction, stressbalance solution, results of the runs, etc.). When one creates a new model, all these fields are initialized, and ready to be used as a `DJUICE` model. + + +To create a new model, use the following command. This command initializes the `md` object, setting up the model structure with all necessary fields. + +""" + +# ╔═╡ e19d512d-0a02-4e30-a06c-4ffd2576dd4b +begin + model() +end + +# ╔═╡ 246e4613-f7c5-4fc0-bee0-33fb521d189d +md"""## Generate Mesh + +Use `md=triangle(md,domainname,resolution)` to generate an unstructured triangular mesh based on the domain outline defined in the file `domainname`, with a characteristic length `resolution` for the mesh. + +We start with a square domain of $[0, 10^6]\times[0,10^6]$ with $5\times10^3~$ mesh resolution, all the units are in meters. Indeed, in `DJUICE` we use [SI](https://en.wikipedia.org/wiki/International_System_of_Units) unit system. + +Then, we set the whole domain to be ice-covered, as an ice shelf. +""" + +# ╔═╡ 1bf7fb45-de6e-4227-917c-7d8bd2738479 +begin + md = triangle(model(), issmdir()*"/test/Exp/Square.exp",50000.) + # set ice mask + md = setmask(md,"all","") + plotmodel(md, "mesh") +end + +# ╔═╡ 416c8beb-b4b7-4a15-8584-a86fd8461aac +md"""## Set the geometry + +We define the ice geometry on the given domain. +### Ice thickness +Let's set the `thickness` of the ice shelf to be +$$H(x,y)=h_{\max} + \frac{h_{\min}-h_{\max}}{L_y}y+0.1\frac{h_{\min}-h_{\max}}{L_x}x$$ +where $h_\min=300$ and $h_\max=1000$""" + +# ╔═╡ a6c3eb4a-fd60-4671-9bf7-a95df2b5ec5f +begin + hmin=300. + hmax=1000. + ymin=minimum(md.mesh.y) + ymax=maximum(md.mesh.y) + xmin=minimum(md.mesh.x) + xmax=maximum(md.mesh.x) + + md.geometry.thickness = hmax .+ (hmin-hmax)*(md.mesh.y .- ymin)./(ymax-ymin) .+ + 0.1*(hmin-hmax)*(md.mesh.x .- xmin)./(xmax-xmin) + # plot the ice thickness + plotmodel(md, md.geometry.thickness) +end + +# ╔═╡ dd19725d-d256-46a2-894c-13202a1b775d +md"""### Ice base +Because the ice shelf is floating, we can determine the `base` of the ice by the flotation criteria +$$b=-\frac{\rho_i}{\rho_w}*H,$$ where $\rho_i$ and $\rho_w$ are the density of ice and water. The physical constants are given by default in `md.materials` when initialize the model. """ + +# ╔═╡ a65e6922-2873-410e-8cb1-9f7a7a9763b2 +begin + md.geometry.base = -md.materials.rho_ice/md.materials.rho_water*md.geometry.thickness + plotmodel(md, md.geometry.base) +end + +# ╔═╡ 1d8e62dc-8cbf-4252-a00c-ba28372d8556 +md"""### Ice surface + +The `surface` of the ice is then calculated as $s=b+H$. """ + +# ╔═╡ 635a67ca-dae3-46ea-b509-bc8d04745040 +begin + md.geometry.surface = md.geometry.base+md.geometry.thickness + plotmodel(md, md.geometry.surface) +end + +# ╔═╡ 22dc7566-ac5d-4f1c-bee5-cab4e52a4573 +md"""### Bedrock +In this tutorial, we are going to work on an ice shelf. To gurantee the ice is completely floating, we set the sea `bed` (bedrock) elevation to be 10 meters deeper than the `base` of the ice:""" + +# ╔═╡ 6120e046-c134-4f53-a92f-f25afe55ae86 +begin + md.geometry.bed = md.geometry.base .-10 + plotmodel(md, md.geometry.bed) +end + +# ╔═╡ 72fa1779-c2b6-4194-acc4-23ce24147bc6 +md"""## Set intitial conditions + +We set the initial velocity to zeros. """ + +# ╔═╡ cd0668fe-b4f2-45ee-a5b8-6db01210cda6 +begin + md.initialization.vx = zeros(md.mesh.numberofvertices) + md.initialization.vy = zeros(md.mesh.numberofvertices) +end; + +# ╔═╡ 5ded5721-77f7-41e3-a6d8-b51f2f738bf7 +md""" +## Set physical parameters + +Ice in large scale is a non-Neutownian, viscos fluid. Its governing dynamics are described by the Shelfy Stream Approximation (SSA), expressed as a system of PDEs: + +$$\nabla\cdot\boldsymbol{\sigma}+{\boldsymbol{\tau}}_b=\rho_i g H \nabla s$$ +where $\boldsymbol{\tau}_b=(\tau_{bx}, \tau_{by})^T$ represents the basal shear stress, $\rho_i$ is the ice density, $g$ is the gravitational acceleration. $\boldsymbol{\sigma}$ is the stress tensor of the SSA model defined as + +$$\boldsymbol{\sigma} = \mu H + \begin{bmatrix} + \displaystyle 4\frac{\partial u}{\partial x}+2\frac{\partial v}{\partial y} + & + \displaystyle \frac{\partial u}{\partial y}+\frac{\partial v}{\partial x} \\ + \\ + \displaystyle \frac{\partial u}{\partial y}+\frac{\partial v}{\partial x} + & + \displaystyle 2\frac{\partial u}{\partial x}+4\frac{\partial v}{\partial y} + \end{bmatrix}.$$ + +The ice viscosity, $\mu$, is determined by Glen's flow-law, which in two dimensions reads: + +$$\mu =\frac{B}{2}\left( \left(\frac{\partial u}{\partial x}\right)^2 + \left(\frac{\partial v}{\partial y}\right)^2 + \frac{1}{4}\left(\frac{\partial u}{\partial y} +\frac{\partial v}{\partial x}\right)^2 + \frac{\partial u}{\partial x}\frac{\partial v}{\partial y}\right)^{\frac{1-n}{2n}},$$ + +where $n = 3$ is the flow-law exponent, and $B$ is the pre-factor dependent on ice temperature, among other factors. + + +The above PDEs is what `DJUICE` is going to solve. We will only need to set the pre-factor $B$ and exponent $n$ in this tutorial. + +""" + +# ╔═╡ 80ba77a2-2829-4f3e-8b45-3047dc7bab51 +begin + md.materials.rheology_B=1.815730284801701e+08*ones(md.mesh.numberofvertices) + md.materials.rheology_n=3*ones(md.mesh.numberofelements); +end; + +# ╔═╡ 131ed044-517b-4754-adf8-053482437689 +md""" +The basal shear stress is related to the ice velocity by a friciton law, here we use the Budd friction law + +$$\tau_b=C^2N^\frac{q}{p}|u_b|^{\frac{1}{q}-1}u_b$$ + +where the effective pressure $N$ is calculated by `dJUICE` at the base of the ice. + +To start, we set the basal friction coefficient $C=20~\text{m}^{-1/2} \text{s}^{1/2}$, and the exponents $p=1$ and $q=1$. + +""" + +# ╔═╡ 2ebc291e-222f-4383-a608-f8558de177b1 +begin + md.friction.coefficient=20*ones(md.mesh.numberofvertices) + md.friction.p=ones(md.mesh.numberofvertices) + md.friction.q=ones(md.mesh.numberofvertices) +end; + +# ╔═╡ c389a807-abe5-43be-9d0d-0a42e9613b97 +md""" +## Boundary conditions + +Let's set the left, bottom, right boundaries to be Dirichlet boundary, and the top boundary to be a calving front boundary. In `dJUICE`, the calving front boundary is automatically determined by the 0-levelset contour of `md.mask.ice_levelset`, which are the nodes inside the polygon defined in `./test/Exp/SquareFront.exp`. + +The Dirichlet boundaries are the rest of the boundaries of the domain, by setting the values in `md.stressbalance.spcvx` and `md.stressbalance.spcvy`. +""" + +# ╔═╡ 4cb62901-cf99-4e60-b778-658f7027b7c8 +begin + #Boundary conditions + nodefront=ContourToNodes(md.mesh.x,md.mesh.y,issmdir()*"/test/Exp/SquareFront.exp",2.0) .& md.mesh.vertexonboundary + md.stressbalance.spcvx = NaN*ones(md.mesh.numberofvertices) + md.stressbalance.spcvy = NaN*ones(md.mesh.numberofvertices) + pos = findall(md.mesh.vertexonboundary .& .~nodefront) + md.mask.ice_levelset[findall(nodefront)] .= 0 + + segmentsfront=md.mask.ice_levelset[md.mesh.segments[:,1:2]]==0 + segments = findall(vec(sum(Int64.(md.mask.ice_levelset[md.mesh.segments[:,1:2]].==0), dims=2)) .!=2) + pos=md.mesh.segments[segments,1:2] + md.stressbalance.spcvx[pos] .= 0.0 + md.stressbalance.spcvy[pos] .= 0.0 +end; + +# ╔═╡ ede33305-2bdc-4ce5-8fbf-215cff47229d +md""" +## Numerical tolerance + +- `restol` is the mechanical equilibrium residual convergence criterion +- `reltol` is the velocity relative convergence criterion +- `abstol` is the velocity absolute convergence criterion + +If the tolerance is set to `NaN`, that means it is not applied. +""" + +# ╔═╡ c3110ce6-3839-4067-be0f-77453c4050c9 +begin + md.stressbalance.restol=0.05 + md.stressbalance.reltol=0.05 + md.stressbalance.abstol=NaN +end; + +# ╔═╡ d67f0dd5-fce4-41fb-a0a7-b31e583f108a +md""" +## Solve + +Now let's solve the nonlinar PDEs +""" + +# ╔═╡ 0fc54de5-c0ac-4622-b681-745c90f2dec1 +solve(md,:Stressbalance) + +# ╔═╡ 4c3bd8b8-8b60-481f-9330-15955486ae6f +md""" +## plot solutions + +The solutions are in `md.results["StressbalanceSolution"]`. We can plot the velocity magnitude by the following command. +""" + +# ╔═╡ f864c816-1f4c-424e-839a-393e476a0557 +plotmodel(md, md.results["StressbalanceSolution"]["Vel"]) + +# ╔═╡ 00000000-0000-0000-0000-000000000001 +PLUTO_PROJECT_TOML_CONTENTS = """ +[deps] +DJUICE = "1cb5fe60-6b70-416b-9050-039c23a62a10" + +[compat] +DJUICE = "~0.1.0" +""" + +# ╔═╡ 00000000-0000-0000-0000-000000000002 +PLUTO_MANIFEST_TOML_CONTENTS = """ +# This file is machine-generated - editing it directly is not advised + +julia_version = "1.10.3" +manifest_format = "2.0" +project_hash = "d37c41cc5f5048d5df3aa7e96f105148d41e5313" + +[[deps.ADTypes]] +git-tree-sha1 = "daf26bbdec60d9ca1c0003b70f389d821ddb4224" +uuid = "47edcb42-4c32-4615-8424-f2b9edc5f35b" +version = "1.2.1" +weakdeps = ["ChainRulesCore", "EnzymeCore"] + + [deps.ADTypes.extensions] + ADTypesChainRulesCoreExt = "ChainRulesCore" + ADTypesEnzymeCoreExt = "EnzymeCore" + +[[deps.AbstractFFTs]] +deps = ["LinearAlgebra"] +git-tree-sha1 = 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+

    \ No newline at end of file diff --git a/DJUICE_tutorials/Tutorial_DJUICE_2_PIG.jl b/DJUICE_tutorials/Tutorial_DJUICE_2_PIG.jl new file mode 100644 index 0000000..ab0d8ea --- /dev/null +++ b/DJUICE_tutorials/Tutorial_DJUICE_2_PIG.jl @@ -0,0 +1,2386 @@ +### A Pluto.jl notebook ### +# v0.19.42 + +using Markdown +using InteractiveUtils + +# ╔═╡ 97fcae33-7c94-4768-8f9f-270fe9572620 +using DJUICE + +# ╔═╡ 7ee597f0-fb53-4865-beee-3104b31c8ef3 +begin + using MAT + + file = matopen(joinpath(@__DIR__, ".", "Data","PIG_Control_drag_dJUICE.mat")) + mat = read(file, "md") + close(file) + md = model(mat) +end; + +# ╔═╡ 2ac93dbd-f7d2-47f0-a68e-8ec9ff9438a1 +begin + using Enzyme + Enzyme.API.typeWarning!(false) + Enzyme.Compiler.RunAttributor[] = false + + using Logging + + md1 = model(mat) + + md1.inversion.iscontrol = 1 + md1.inversion.vx_obs = zeros(md1.mesh.numberofvertices) + md1.inversion.vy_obs = zeros(md1.mesh.numberofvertices) + md1.inversion.independent = md1.friction.coefficient + md1.inversion.independent_string = "FrictionCoefficient" + + with_logger(SimpleLogger(stdout, Logging.Error)) do + solve(md1, :grad) + end +end; + +# ╔═╡ 9ee2316a-0245-11ef-319d-63d9da8d5061 +md""" +# Application of DJUICE: Pine Island Glacier + +In this tutorial, we will work on a real-world case: modeling the [Pine Island Glacier](https://en.wikipedia.org/wiki/Pine_Island_Glacier) in Antarctica. +""" + +# ╔═╡ 8d952814-f4d6-49a1-a961-22e5a34c1aa8 +md""" +## Install the package + +As with the [previous tutorial](https://github.com/DJ4Earth/MPE24/blob/main/DJUICE_tutorials/Tutorial_DJUICE_1_basic.jl), you need to install the package [`DJUICE`](https://github.com/DJ4Earth/DJUICE.jl) if it is not already installed. + +Using the following commands: + +```julia +]add DJUICE#main +``` + +or use `Pkg` to import `Project.toml` from the mini-tutorial + +""" + +# ╔═╡ a6f8b844-b9a2-4692-a747-c183deeade65 +md""" +## Set up the model + +To simplify the model setup process, we will load the model from an [ISSM tutorial of Pine Island Glacier](https://issm.jpl.nasa.gov/documentation/tutorials/pig/). + +Before solving the model, we should take some time to inspect the model by plotting the ice thickness, bed elevation, basal friction coefficients, and other relevant parameters. This helps ensure that the model has been loaded correctly. + + + +**Note**: You might get warnings during this process because the ISSM model contains more fields than the DJUICE model currently supports. You can safely ignore these warnings for now. +""" + +# ╔═╡ 89e889f3-63f8-4f2a-bea3-4d8b736c5aa1 +md""" +### Example Code to Load and Inspect the Model +""" + +# ╔═╡ 771cc220-f9fc-4da3-9cca-f98d93465dff +plotmodel(md, md.friction.coefficient) + +# ╔═╡ 0b7ecb9b-08f6-4e54-8f7c-5d71faa32c59 +plotmodel(md, sqrt.(md.initialization.vx.^2+md.initialization.vy.^2)) + +# ╔═╡ 31624153-1463-4b7e-81f9-d33924b86e5a +md""" +## Solve the forward model + +With all the geometries, boundary conditions, and ice masks properly set up in the model, we can solve the forward problem to get the simulated ice velocity. + + +Call the `solve` function to perform the stress balance computation: +""" + +# ╔═╡ d4f79bc0-d944-4e3a-b2b9-592b1d40c0e4 +begin + md.inversion.iscontrol = false + solve(md, :Stressbalance) +end; + +# ╔═╡ cb691c03-16e1-43ec-bd97-7d7f6dd8ce6d +md""" +Plot the resulting ice velocity field to visualize the results of the forward model: +""" + +# ╔═╡ bf718cfd-140a-4a5a-8f91-22d7841b543f +plotmodel(md, md.results["StressbalanceSolution"]["Vel"]) + +# ╔═╡ 1c0f009c-816b-4f3f-bd92-14c41e9651e9 +md""" +## Sensitivity analysis + +By using `Enzyme`, we can perform sensitivity analysis on the DJUICE model. This allows us to understand how changes in input parameters affect the model outputs. + +In this example, we use a pre-defined *cost function* `SurfaceAbsVelMisfitx` from `DJUICE/src/core/costfunctions.jl`, which compute the absolute velocity misfit between modeled and observed velocity. + +The cost function $J$ in DJUICE is defined as: + +$$J = \frac{1}{2}\int_{\Omega}(u-u_{obs})^2+(v-v_{obs})^2\,\text{d}\Omega$$ + +For this tutorial, we set $u_{obs}$ and $v_{obs}$ to 0, simplifying the cost function to: + +$$J = \frac{1}{2}\int_{\Omega}(u^2+v^2)\,\text{d}\Omega$$ + +Here, $J$ measures the velocity magnitudes of the ice flow. The gradient $\frac{\partial{J}}{\partial{C}}$ we compute is the sensitivity of the velocity to the basal friction coefficents $C$. +""" + +# ╔═╡ a4871152-4810-486d-adef-02163f0a74b8 +md""" +After differentiating `DJUICE` by `Enzyme`, we can visualize the gradient and the friction coefficients: +""" + +# ╔═╡ 4544078c-6ef5-48cb-bb03-81b7c1439fa4 +plotmodel(md1, md1.results["StressbalanceSolution"]["Gradient"]) + +# ╔═╡ be7e4edc-5f33-4414-87f0-253e40928e82 +plotmodel(md1, md1.friction.coefficient) + +# ╔═╡ 28ea699a-58e9-4b68-8ef7-5ec20c5db489 +md""" +## Extra task +Ideally, we can use `Enzyme` to differentiate the cost function $J$ with respect to any variable in `DJUICE`. One example is to change the `independent` and `independent_string` to the ice `rheology_B`. + +```julia +md.inversion.independent = md.materials.rheology_B +md.inversion.independent_string = "MaterialsRheologyB" +``` + +Use the instructions and example code above as a guide to write your own code. Compute the sensitivity and analyze the results. Furthermore, consider experimenting with different cost functions and independent variables to explore various aspects of the DJUICE model. +""" + +# ╔═╡ 00000000-0000-0000-0000-000000000001 +PLUTO_PROJECT_TOML_CONTENTS = """ +[deps] +DJUICE = "1cb5fe60-6b70-416b-9050-039c23a62a10" +Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9" +Logging = "56ddb016-857b-54e1-b83d-db4d58db5568" +MAT = "23992714-dd62-5051-b70f-ba57cb901cac" + +[compat] +DJUICE = "~0.1.1" +Enzyme = "~0.12.6" +MAT = "~0.10.7" +""" + +# ╔═╡ 00000000-0000-0000-0000-000000000002 +PLUTO_MANIFEST_TOML_CONTENTS = """ +# This file is machine-generated - editing it directly is not advised + +julia_version = "1.10.3" +manifest_format = "2.0" +project_hash = "8088cb83089a444660f78ab18569c58c32fd77f9" + +[[deps.ADTypes]] +git-tree-sha1 = "daf26bbdec60d9ca1c0003b70f389d821ddb4224" +uuid = "47edcb42-4c32-4615-8424-f2b9edc5f35b" +version = "1.2.1" +weakdeps = ["ChainRulesCore", "EnzymeCore"] + + [deps.ADTypes.extensions] + 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[deps.Zygote.weakdeps] + Colors = "5ae59095-9a9b-59fe-a467-6f913c188581" + Distances = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7" + Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c" + +[[deps.ZygoteRules]] +deps = ["ChainRulesCore", "MacroTools"] +git-tree-sha1 = "27798139afc0a2afa7b1824c206d5e87ea587a00" +uuid = "700de1a5-db45-46bc-99cf-38207098b444" +version = "0.2.5" + +[[deps.isoband_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "51b5eeb3f98367157a7a12a1fb0aa5328946c03c" +uuid = "9a68df92-36a6-505f-a73e-abb412b6bfb4" +version = "0.2.3+0" + +[[deps.libaec_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "46bf7be2917b59b761247be3f317ddf75e50e997" +uuid = "477f73a3-ac25-53e9-8cc3-50b2fa2566f0" +version = "1.1.2+0" + +[[deps.libaom_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "1827acba325fdcdf1d2647fc8d5301dd9ba43a9d" +uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b" +version = "3.9.0+0" + +[[deps.libass_jll]] +deps = 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+
    \ No newline at end of file diff --git a/Introduction.jl b/Introduction.jl new file mode 100644 index 0000000..7be3829 --- /dev/null +++ b/Introduction.jl @@ -0,0 +1,1993 @@ +### A Pluto.jl notebook ### +# v0.19.41 + +using Markdown +using InteractiveUtils + +# ╔═╡ c4c4ca62-2d63-4876-9027-9ca7f0d6cb37 +using PlutoUI + +# ╔═╡ f6dcabfb-9f97-4be7-a729-eacd9402d4bf +begin + using WGLMakie + WGLMakie.activate!() +end + +# ╔═╡ 05267988-ff9d-4e60-9a10-55864390fd22 +using Enzyme + +# ╔═╡ 07df2151-525e-4fdd-a66a-db211bf02932 +using Optim + +# ╔═╡ 9b96d09c-9c41-42ab-b2cf-a70669647bc8 +md""" +## What's Julia? 🟢 🟣 🔴 + +Julia is a modern, dynamic, general-purpose, compiled programming language. +It's interactive ("like Python"), can be used in a REPL or notebooks, like Jupyter (it's the "Ju") or Pluto (this one🎈). +Julia has a runtime which includes a just-in-time (JIT) compiler and a garbage collector (GC), for automatic memory management. + +Julia is mainly used for technical computing, and addresses a gap in the programming language landscape for numerical computing. + + +Main paradigm of Julia is multiple dispatch, what functions do depend on type and number of _all_ arguments. +""" + +# ╔═╡ 9b770ce2-2285-42e5-9f5e-dcdbcf387768 +md""" +## Why Julia? 😍 + +From "[My Target Audience](https://scientificcoder.com/my-target-audience)" by Matthijs Cox: + +$(Resource("https://cdn.hashnode.com/res/hashnode/image/upload/v1681735971356/91b6e886-7ce1-41a3-9d9f-29b7b096e7f2.png")) +$(Resource("https://cdn.hashnode.com/res/hashnode/image/upload/v1681735992315/62fdd58f-4630-4120-8eb4-5238740543e8.png")) + +* Explorable & Understandable +* Composability thanks to multiple dispatch (ask me more about this at the end!) +* User-defined types are as fast and compact as built-ins +* Code that is close to the mathematics +* No need to switch languages for performance... +* ...but you can still call C-like shared libraries with simple Foreign Function Interface (FFI) if you want to +* MIT licensed: free and open source +""" + +# ╔═╡ 3902e31a-b2bf-4c7c-b44b-d5a5340ca574 +md""" +## What is the 2 language problem? + +You start out proto-typing in one language (high-level, dynamic), but performance forces you to switch to a different one (low-level, static). + +- For convinience use a scripting language (Python, R, Matlab, ...) +- but do all the hard stuff in a systems language (C, C++, Fortran) + +Pragmatic for many applications, but has drawbacks + +- aren't the hard parts exactly where you need an easier language +- creates a social barrier -- a wall between users and developers +- "sandwich problem" -- layering of system & user code is expensive +- prohibits full stack optimisations +""" + +# ╔═╡ 22fb5605-04fd-4f0a-b41a-6c9d65cd9425 +md""" +### Rosenbrock function 🗻 + +Everyone's favourite example function for optimisation problems. + +```math +f(x, y) = (1 - x) ^ 2 + 100 (y - x ^ 2) ^ 2 +``` + +```julia +rosenbrock(x, y) = (1 - x) ^ 2 + 100 * (y - x ^ 2) ^ 2 +``` +""" + +# ╔═╡ 9536e1ca-7d5f-47bb-8ecc-55f38e7df1a2 +rosenbrock(x, y) = (1 - x) ^ 2 + 100 * (y - x ^ 2) ^ 2; + +# ╔═╡ 92b71ff8-0dc5-481c-9d05-19d3db73cbcc +begin + xs = -6:0.04:6 + ys = -2:0.04:5 + zs = [log10(rosenbrock(x, y)) for x in xs, y in ys] +end; + +# ╔═╡ 81bd99c3-3e38-4fff-83af-37faa014429f +surface(xs, ys, zs, axis=(type=Axis3,)) + +# ╔═╡ efd6eb23-be46-437e-9c87-a6f770dc3613 +contourf(xs, ys, zs) + +# ╔═╡ 12d80cd2-542b-4844-8957-9337640a84c2 +md""" +## Automatic differentiation 📈 + +In mathematics, contrary to integration, computing the derivative of an expression is a mechanical process. +Wouldn't it be nice to automatically compute the exact derivative of mathematical functions in your code? + +Automatic differentiation (autodiff in short) is a set of techniques to automatically compute the derivative of a function in a computer program. + +[Enzyme](https://enzyme.mit.edu/) is a source code transformation autodiff engine operating at the LLVM level: it analysis the LLVM IR of the source code and takes the derivative of all the instructions, based on the built-in differentiation rules. +The fact that it works at the LLVM level means that it's _mostly_ front-end-language-agnostic and can be used to take derivative of source code combining multiple languages or using parallelisation frameworks (["Scalable automatic differentiation of multiple parallel paradigms through compiler augmentation"](https://dl.acm.org/doi/abs/10.5555/3571885.3571964) won Best Student Paper award at SuperComputing 2022). +""" + +# ╔═╡ 7553f962-90fc-4ec2-892f-f73b300e0850 +md""" +Finding the valley is trivial, but converging to the global minimum is hard. + +The Rosenbrock function is a polynomial function, easy to compute its gradient: + +```math +\nabla{}f(x, y) = +\begin{bmatrix} + 400x^3 - 400xy + 2x - 2\\ + 200 (y -x^2) +\end{bmatrix} +``` + +We can ask Enzyme to compute the partial derivative on the second argument: +""" + +# ╔═╡ 6f87e98a-3767-4c5e-a24f-f9cb0698346b +∂f_∂x(f, x, y) = first(autodiff(Enzyme.Reverse, f, Active(x), Const(y))); + +# ╔═╡ 8bde3cd7-32c5-4d21-ba13-34d63bc143b5 +∂f_∂y(f, x, y) = first(autodiff(Enzyme.Reverse, f, Const(x), Active(y))); + +# ╔═╡ 415df7a4-a127-4cb6-a7fc-132a83883474 +∂f(f, x, y) = first(autodiff(Enzyme.Reverse, f, Active(x), Active(y))); + +# ╔═╡ 174d5b15-743c-4a0b-a49c-020315e2f601 +∂f_∂y(rosenbrock, 0.0, 1.0) + +# ╔═╡ b85ec6d8-735f-49ab-b9d5-dccf76754335 +∂f_∂x(rosenbrock, 1.0, 0.0) + +# ╔═╡ 9d9c6b7f-a73b-4e39-812f-00d30ab3c201 +∂f(rosenbrock, 0.0, 1.0) + +# ╔═╡ fafcf585-4f4e-4f2d-89a1-8f410a683754 +contourf(xs, ys, ((x,y)->∂f_∂x(rosenbrock, x, y)[1]).(xs, ys')) + +# ╔═╡ 99f8f148-5c6c-436e-a2e7-a69ad3c1bdbe +contourf(xs, ys, ((x,y)->∂f_∂y(rosenbrock, x, y)[2]).(xs, ys')) + +# ╔═╡ 8f9294c6-172e-41d9-83b8-93991a7a989a +Enzyme.Compiler.enzyme_code_llvm(stdout, + rosenbrock, Active, Tuple{Const{Float64}, Active{Float64}}, + debuginfo=:none) + +# ╔═╡ 950b361d-c603-49bd-8e0f-ab49971db1a0 +let + f(x) = rosenbrock(x...) + sol = optimize(f, [0.0, 0.0]) + @show Optim.minimizer(sol) + sol +end + +# ╔═╡ ecc9581f-4efc-408c-832a-ac33b2392d55 +let + f(x) = rosenbrock(x[1], x[2]) + function g!(storage, x) + fill!(storage, 0) + autodiff(Enzyme.Reverse, f, Duplicated(x, storage)) + nothing + end + sol = optimize(f, g!, [0.0, 0.0]) + @show Optim.minimizer(sol) + sol +end + +# ╔═╡ 00000000-0000-0000-0000-000000000001 +PLUTO_PROJECT_TOML_CONTENTS = """ +[deps] +Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9" +Optim = "429524aa-4258-5aef-a3af-852621145aeb" +PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8" +WGLMakie = "276b4fcb-3e11-5398-bf8b-a0c2d153d008" + +[compat] +Enzyme = "~0.12.0" +Optim = "~1.9.4" +PlutoUI = "~0.7.58" +WGLMakie = "~0.9.9" +""" + +# ╔═╡ 00000000-0000-0000-0000-000000000002 +PLUTO_MANIFEST_TOML_CONTENTS = """ +# This file is machine-generated - editing it directly is not advised + +julia_version = "1.10.2" +manifest_format = "2.0" +project_hash = "eea180b1ba9e6e0c79e12ec122c7d9676a1013e0" + 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╟─22fb5605-04fd-4f0a-b41a-6c9d65cd9425 +# ╟─9536e1ca-7d5f-47bb-8ecc-55f38e7df1a2 +# ╠═92b71ff8-0dc5-481c-9d05-19d3db73cbcc +# ╠═81bd99c3-3e38-4fff-83af-37faa014429f +# ╠═efd6eb23-be46-437e-9c87-a6f770dc3613 +# ╟─12d80cd2-542b-4844-8957-9337640a84c2 +# ╟─7553f962-90fc-4ec2-892f-f73b300e0850 +# ╠═05267988-ff9d-4e60-9a10-55864390fd22 +# ╠═6f87e98a-3767-4c5e-a24f-f9cb0698346b +# ╠═8bde3cd7-32c5-4d21-ba13-34d63bc143b5 +# ╠═415df7a4-a127-4cb6-a7fc-132a83883474 +# ╠═174d5b15-743c-4a0b-a49c-020315e2f601 +# ╠═b85ec6d8-735f-49ab-b9d5-dccf76754335 +# ╠═9d9c6b7f-a73b-4e39-812f-00d30ab3c201 +# ╠═fafcf585-4f4e-4f2d-89a1-8f410a683754 +# ╠═99f8f148-5c6c-436e-a2e7-a69ad3c1bdbe +# ╠═8f9294c6-172e-41d9-83b8-93991a7a989a +# ╠═07df2151-525e-4fdd-a66a-db211bf02932 +# ╠═950b361d-c603-49bd-8e0f-ab49971db1a0 +# ╠═ecc9581f-4efc-408c-832a-ac33b2392d55 +# ╟─00000000-0000-0000-0000-000000000001 +# ╟─00000000-0000-0000-0000-000000000002 diff --git a/Introduction.plutostate b/Introduction.plutostate new file mode 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