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geothermal_2D_gpu_kp_ad_inv.jl
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geothermal_2D_gpu_kp_ad_inv.jl
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using Printf, LinearAlgebra
using CairoMakie
using CUDA
using Enzyme
macro d_xa(A) esc(:($A[ix+1, iz] - $A[ix, iz])) end
macro d_za(A) esc(:($A[ix, iz+1] - $A[ix, iz])) end
macro avx(A) esc(:(0.5 * ($A[ix, iz] + $A[ix+1, iz]))) end
macro avz(A) esc(:(0.5 * ($A[ix, iz] + $A[ix, iz+1]))) end
@views avx(A) = 0.5 .* (A[1:end-1, :] .+ A[2:end, :])
@views avz(A) = 0.5 .* (A[:, 1:end-1] .+ A[:, 2:end])
@views maxloc(A) = max.(A[2:end-1, 2:end-1], max.(max.(A[1:end-2, 2:end-1], A[3:end, 2:end-1]),
max.(A[2:end-1, 1:end-2], A[2:end-1, 3:end])))
function smooth_d!(A2, A)
ix = (blockIdx().x - 1) * blockDim().x + threadIdx().x
iz = (blockIdx().y - 1) * blockDim().y + threadIdx().y
if (ix>1 && ix<size(A, 1) && iz>1 && iz<size(A, 2))
@inbounds A2[ix, iz] = A[ix, iz] + 0.2 * (A[ix+1, iz] - 2A[ix, iz] + A[ix-1, iz] + A[ix, iz+1] - 2A[ix, iz] + A[ix, iz-1])
end
return
end
function smooth!(A2, A, nthread, nblock; nsm=1)
for _ ∈ 1:nsm
CUDA.@sync @cuda threads=nthread blocks=nblock smooth_d!(A2, A)
A, A2 = A2, A
end
return
end
# forward
function residual_fluxes!()
#= ??? =#
return
end
function residual_pressure!()
#= ??? =#
return
end
function update_fluxes!()
#= ??? =#
return
end
function update_pressure!()
#= ??? =#
return
end
@inline ∇(fun,args...) = (Enzyme.autodiff_deferred(Enzyme.Reverse, fun, args...); return)
const DupNN = DuplicatedNoNeed
@views function forward_solve!(logK, fields, scalars, iter_params; visu=nothing)
(;Pf, qx, qz, Qf, RPf, Rqx, Rqz, K) = fields
(;nx, nz, dx, dz, nthread, nblock) = scalars
(;cfl, re, vdτ, lz, ϵtol, maxiter, ncheck, K_max) = iter_params
isnothing(visu) || ((;qx_c, qz_c, qM, fig, plt, st) = visu)
K .= exp.(logK)
# approximate diagonal (Jacobi) preconditioner
K_max .= K; K_max[2:end-1, 2:end-1] .= maxloc(K); K_max[:, [1, end]] .= K_max[:, [2, end-1]]
# iterative loop
iters_evo = Float64[]; errs_evo = Float64[]
err = 2ϵtol; iter = 1
while err >= ϵtol && iter <= maxiter
#= ??? =#
#= ??? =#
#= ??? =#
#= ??? =#
if iter % ncheck == 0
err = maximum(abs.(RPf))
push!(iters_evo, iter/nx); push!(errs_evo, err)
@printf(" #iter/nx=%.1f, max(err)=%1.3e\n", iter/nx, err)
if !isnothing(visu)
qx_c .= Array(avx(qx)); qz_c .= Array(avz(qz)); qM .= sqrt.(qx_c.^2 .+ qz_c.^2)
qx_c ./= qM; qz_c ./= qM
plt.fld.Pf[3] = Array(Pf)
plt.fld.K[3] = Array(log10.(K))
plt.fld.qM[3] = qM
plt.fld.ar[3] = qx_c[1:st:end, 1:st:end]
plt.fld.ar[4] = qz_c[1:st:end, 1:st:end]
plt.err[1] = Point2.(iters_evo, errs_evo)
display(fig)
end
end
iter += 1
end
return
end
@views function adjoint_solve!(logK, fwd_params, adj_params, loss_params)
# unpack forward
(;Pf, qx, qz, Qf, RPf, Rqx, Rqz, K) = fwd_params.fields
(;nx, nz, dx, dz, nthread, nblock) = fwd_params.scalars
# unpack adjoint
(;P̄f, q̄x, q̄z, R̄Pf, R̄qx, R̄qz, Ψ_qx, Ψ_qz, Ψ_Pf) = adj_params.fields
(;∂J_∂Pf) = loss_params.fields
(;cfl, re_a, vdτ, lz, ϵtol, maxiter, ncheck, K_max) = adj_params.iter_params
# iterative loop
iters_evo = Float64[]; errs_evo = Float64[]
err = 2ϵtol; iter = 1
while err >= ϵtol && iter <= maxiter
R̄qx .= Ψ_qx
R̄qz .= Ψ_qz
P̄f .= #= ??? =#
q̄x .= 0.0
q̄z .= 0.0
#= ??? =#
#= ??? =#
#= ??? =#
R̄Pf .= #= ??? =#
#= ??? =#
#= ??? =#
if iter % ncheck == 0
err = maximum(abs.(P̄f))
push!(iters_evo, iter/nx); push!(errs_evo, err)
@printf(" #iter/nx=%.1f, max(err)=%1.6e\n", iter/nx, err)
end
iter += 1
end
return
end
@views function loss(logK, fwd_params, loss_params; kwargs...)
(;Pf_obs) = loss_params.fields
(;ixobs, izobs) = loss_params.scalars
@info "Forward solve"
#= ??? =#
Pf = fwd_params.fields.Pf
return 0.5*sum((Pf[ixobs, izobs] .- Pf_obs).^2)
end
function ∇loss!(logK̄, logK, fwd_params, adj_params, loss_params; reg=nothing, kwargs...)
# unpack
(;R̄qx, R̄qz, Ψ_qx, Ψ_qz) = adj_params.fields
(;Pf, qx, qz, Rqx, Rqz, K) = fwd_params.fields
(;dx, dz, nthread, nblock) = fwd_params.scalars
(;Pf_obs, ∂J_∂Pf) = loss_params.fields
(;ixobs, izobs) = loss_params.scalars
@info "Forward solve"
#= ??? =#
# set tangent
∂J_∂Pf[ixobs, izobs] .= #= ??? =#
@info "Adjoint solve"
#= ??? =#
# evaluate gradient dJ_dK
R̄qx .= .-Ψ_qx
R̄qz .= .-Ψ_qz
logK̄ .= 0.0
#= ??? =#
# Tikhonov regularisation (smoothing)
if !isnothing(reg)
(;nsm, Tmp) = reg
Tmp .= logK̄; smooth!(logK̄, Tmp, nthread, nblock; nsm)
end
logK̄ .*= K # convert to dJ_dlogK by chain rule
return
end
@views function main()
CUDA.device!(0) # select your GPU
# physics
lx, lz = 2.0, 1.0 # domain extend
k0_μ = 1.0 # background permeability / fluid viscosity
kb_μ = 1e-6 # barrier permeability / fluid viscosity
Q_in = 1.0 # injection flux
b_w = 0.02lx # barrier width
b_b = 0.3lz # barrier bottom location
b_t = 0.8lz # barrier top location
# observations
xobs_rng = LinRange(-lx / 6, lx / 6, 8)
zobs_rng = LinRange(0.25lz, 0.85lz , 8)
# numerics
nz = 255
nx = ceil(Int, (nz + 1) * lx / lz) - 1
nthread = (16, 16)
nblock = cld.((nx, nz), nthread)
cfl = 1 / 2.1
ϵtol = 1e-6
maxiter = 30nx
ncheck = 2nx
re = 0.8π # fwd re
st = ceil(Int, nx / 30)
# GD params
ngd = 50
Δγ = 0.2
# preprocessing
re_a = 2re # adjoint re
dx, dz = lx / nx, lz / nz
xc, zc = LinRange(-lx / 2 + dx / 2, lx / 2 - dx / 2, nx), LinRange(dz / 2, lz - dz / 2, nz)
vdτ = cfl * min(dx, dz)
ixobs = floor.(Int, (xobs_rng .- xc[1]) ./ dx) .+ 1
izobs = floor.(Int, (zobs_rng .- zc[1]) ./ dz) .+ 1
# init
Pf = CUDA.zeros(Float64, nx, nz)
RPf = CUDA.zeros(Float64, nx, nz)
qx = CUDA.zeros(Float64, nx + 1, nz)
Rqx = CUDA.zeros(Float64, nx + 1, nz)
qz = CUDA.zeros(Float64, nx, nz + 1)
Rqz = CUDA.zeros(Float64, nx, nz + 1)
Qf = CUDA.zeros(Float64, nx, nz)
K = k0_μ .* CUDA.ones(Float64, nx, nz)
logK = CUDA.zeros(Float64, nx, nz)
Tmp = CUDA.zeros(Float64, nx, nz)
# init adjoint storage
Ψ_qx = CUDA.zeros(Float64, nx + 1, nz)
q̄x = CUDA.zeros(Float64, nx + 1, nz)
R̄qx = CUDA.zeros(Float64, nx + 1, nz)
Ψ_qz = CUDA.zeros(Float64, nx, nz + 1)
q̄z = CUDA.zeros(Float64, nx, nz + 1)
R̄qz = CUDA.zeros(Float64, nx, nz + 1)
Ψ_Pf = CUDA.zeros(Float64, nx, nz)
P̄f = CUDA.zeros(Float64, nx, nz)
R̄Pf = CUDA.zeros(Float64, nx, nz)
∂J_∂Pf = CUDA.zeros(Float64, nx, nz)
dJ_dlogK = CUDA.zeros(Float64, nx, nz)
# set low permeability barrier location
K[ceil(Int, (lx/2-b_w)/dx):ceil(Int, (lx/2+b_w)/dx), ceil(Int, b_b/dz):ceil(Int, b_t/dz)] .= kb_μ
logK .= log.(K)
K_max = copy(K)
# set wells location
x_iw, x_ew, z_w = ceil.(Int, (lx / 5 / dx, 4lx / 5 / dx, 0.45lz / dz))
Qf[x_iw:x_iw, z_w:z_w] .= Q_in / dx / dz # injection
Qf[x_ew:x_ew, z_w:z_w] .= -Q_in / dx / dz # extraction
# init visu
iters_evo = Float64[]; errs_evo = Float64[]
qM, qx_c, qz_c = zeros(nx, nz), zeros(nx, nz), zeros(nx, nz)
fig = Figure(resolution=(2500, 1200), fontsize=32)
ax = ( Pf = Axis(fig[1, 1][1, 1]; aspect=DataAspect(), title="Pf"),
K = Axis(fig[1, 2][1, 1]; aspect=DataAspect(), title="log10(K)"),
qM = Axis(fig[2, 1][1, 1]; aspect=DataAspect(), title="|q|"),
err = Axis(fig[2, 2]; yscale=log10, title="Convergence", xlabel="# iter/nx", ylabel="error"), )
plt = (fld = ( Pf = heatmap!(ax.Pf, xc, zc, Array(Pf); colormap=:turbo, colorrange=(-1,1)),
K = heatmap!(ax.K , xc, zc, Array(log10.(K)); colormap=:turbo, colorrange=(-6,0)),
xobs = scatter!(ax.K , vec(Point2.(xobs_rng, zobs_rng')); color=:white),
qM = heatmap!(ax.qM, xc, zc, qM; colormap=:turbo, colorrange=(0,30)),
ar = arrows!(ax.Pf, xc[1:st:end], zc[1:st:end], qx_c[1:st:end, 1:st:end], qz_c[1:st:end, 1:st:end]; lengthscale=0.05, arrowsize=15), ),
err = scatterlines!(ax.err, Point2.(iters_evo, errs_evo), linewidth=4), )
Colorbar(fig[1, 1][1, 2], plt.fld.Pf)
Colorbar(fig[1, 2][1, 2], plt.fld.K)
Colorbar(fig[2, 1][1, 2], plt.fld.qM)
# action
fwd_params = (
fields = (;Pf, qx, qz, Qf, RPf, Rqx, Rqz, K),
scalars = (;nx, nz, dx, dz, nthread, nblock),
iter_params = (;cfl, re, vdτ, lz, ϵtol, maxiter, ncheck, K_max),
)
fwd_visu = (;qx_c, qz_c, qM, fig, plt, st)
@info "Synthetic solve"
#= ??? =#
# store true data
Pf_obs = copy(Pf[ixobs, izobs])
adj_params = (
fields = (;P̄f, q̄x, q̄z, R̄Pf, R̄qx, R̄qz, Ψ_qx, Ψ_qz, Ψ_Pf),
iter_params = (;cfl, re_a, vdτ, lz, ϵtol, maxiter, ncheck, K_max),
)
loss_params = (
fields = (;Pf_obs, ∂J_∂Pf),
scalars = (;ixobs, izobs),
)
reg = (;nsm=20, Tmp)
# loss functions
J(_logK) = loss(_logK, fwd_params, loss_params)
∇J!(_logK̄, _logK) = ∇loss!(_logK̄, _logK, fwd_params, adj_params, loss_params; reg)
@info "Inversion for K"
# initial guess
K .= k0_μ
logK .= log.(K)
@info "Gradient descent - inversion for K"
cost_evo = Float64[]
for igd in 1:ngd
printstyled("> GD iter $igd \n"; bold=true, color=:green)
# evaluate gradient of the cost function
#= ??? =#
# update logK
γ = Δγ / maximum(abs.(dJ_dlogK))
@. logK -= #= ??? =#
@printf " min(K) = %1.2e \n" minimum(K)
# loss
push!(cost_evo, J(logK))
@printf " --> Loss J = %1.2e (γ = %1.2e)\n" last(cost_evo)/first(cost_evo) γ
# visu
qx_c .= Array(avx(qx)); qz_c .= Array(avz(qz)); qM .= sqrt.(qx_c.^2 .+ qz_c.^2)
qx_c ./= qM; qz_c ./= qM
plt.fld.Pf[3] = Array(Pf)
plt.fld.K[3] = Array(log10.(K))
plt.fld.qM[3] = qM
plt.fld.ar[3] = qx_c[1:st:end, 1:st:end]
plt.fld.ar[4] = qz_c[1:st:end, 1:st:end]
plt.err[1] = Point2.(1:igd, cost_evo ./ 0.999cost_evo[1])
display(fig)
end
return
end
main()