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well-jutul.jl
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## Author: Ziyi Yin, [email protected]
## Date: Sep 17, 2023
## Permeability inversion
## Observed data: well
## Methods: unconstrained optimization with numerical solver
using DrWatson
@quickactivate "FNO-NF"
using Pkg; Pkg.add(url="https://github.com/slimgroup/FNO4CO2/", rev="v1.1.4")
using Pkg; Pkg.instantiate();
nthreads = try
# Slurm
parse(Int, ENV["SLURM_CPUS_ON_NODE"])
catch e
# Desktop
Sys.CPU_THREADS
end
using LinearAlgebra
BLAS.set_num_threads(nthreads)
using JutulDarcyRules
using PyPlot
using JLD2
using Flux
using Random
using LineSearches
using InvertibleNetworks
using FNO4CO2
using Statistics
using JOLI
Random.seed!(2023)
matplotlib.use("agg")
include(srcdir("utils.jl"))
sim_name = "flow-inversion"
exp_name = "jutul"
JLD2.@load datadir("examples", "K.jld2") K
mkpath(datadir())
mkpath(plotsdir())
## grid size
n = (64, 1, 64)
d = (15.0, 10.0, 15.0)
## permeability
K = md * K
ϕ = 0.25 * ones(n)
model = jutulModel(n, d, vec(ϕ), K1to3(K))
## simulation time steppings
tstep = 100 * ones(8)
tot_time = sum(tstep)
## injection & production
inj_loc = (3, 1, 32) .* d
prod_loc = (62, 1, 32) .* d
irate = 5e-3
q = jutulSource(irate, [inj_loc, prod_loc])
## set up modeling operator
S = jutulModeling(model, tstep)
## simulation
logK = log.(K)
mesh = CartesianMesh(model)
T(x) = log.(KtoTrans(mesh, K1to3(exp.(x))))
@time state = S(T(logK), q)
prj(x::AbstractArray{T}; upper=T(log(130*md)), lower=T(log(10*md))) where T = max.(min.(x,T(upper)),T(lower))
# Main loop
niterations = 100
fhistory = zeros(niterations)
obs_loc = zeros(Float32, n[1], n[end], length(tstep))
subsamp = 3
obs_loc[Int.(round.(range(1, stop=n[1], length=subsamp))),:,:] .= 1f0
obs_loc = vec(obs_loc)
obj(logK) = .5 * norm(obs_loc .* (S(T(prj(logK)), q)[1:length(tstep)*prod(n)]-state[1:length(tstep)*prod(n)]))^2f0
# Define raw data directory
mkpath(datadir("gen-train","flow-channel"))
perm_path = joinpath(datadir("gen-train","flow-channel"), "irate=0.005_nsample=2000.jld2")
# Download the dataset into the data directory if it does not exist
if ~isfile(perm_path)
run(`wget https://www.dropbox.com/s/8jb5g4rmamigoqf/'
'irate=0.005_nsample=2000.jld2 -q -O $perm_path`)
end
dict_data = JLD2.jldopen(perm_path, "r")
perm = Float32.(dict_data["Ks"]);
K0 = mean(perm, dims=3)[:,:,1] * md
logK0 = log.(K0)
@time state_init = S(T(logK0), q)
ls = BackTracking(order=3, iterations=10)
for j=1:niterations
@time fval, gs = Flux.withgradient(() -> obj(logK0), Flux.params(logK0))
g = gs[logK0]
p = -g/norm(g, Inf)
println("Inversion iteration no: ",j,"; function value: ",fval)
fhistory[j] = fval
# linesearch
function f_(α)
misfit = obj(prj(logK0 .+ α * p))
@show α, misfit
return misfit
end
step, fval = ls(f_, 5e-1, fval, dot(g, p))
# Update model and bound projection
global logK0 = prj(logK0 .+ step .* p)
fig_name = @strdict j subsamp n d ϕ logK0 tstep irate niterations inj_loc
### plotting
fig=figure(figsize=(20,12));
subplot(1,3,1);
imshow(exp.(logK)'./md, vmin=minimum(exp.(logK))./md, vmax=maximum(exp.(logK)./md)); colorbar(); title("true permeability")
subplot(1,3,2);
imshow(exp.(logK0)'./md, vmin=minimum(exp.(logK))./md, vmax=maximum(exp.(logK)./md)); colorbar(); title("inverted permeability")
subplot(1,3,3);
imshow(abs.(exp.(logK)'./md.-exp.(logK0)'./md), vmin=minimum(exp.(logK)), vmax=maximum(exp.(logK)./md)); colorbar(); title("diff")
suptitle("Flow Inversion at iter $j")
tight_layout()
safesave(joinpath(plotsdir(sim_name, exp_name), savename(fig_name; digits=6)*"_diff.png"), fig);
close(fig)
state_predict = S(T(logK0), q)
## data fitting
fig = figure(figsize=(20,12));
for i = 1:5
subplot(4,5,i);
imshow(reshape(Saturations(state_init.states[3+i]), n[1], n[end])', vmin=0, vmax=0.9); colorbar();
title("initial prediction at snapshot $(3+i)")
subplot(4,5,i+5);
imshow(reshape(Saturations(state.states[3+i]), n[1], n[end])', vmin=0, vmax=0.9); colorbar();
title("true at snapshot $(3+i)")
subplot(4,5,i+10);
imshow(reshape(Saturations(state_predict.states[3+i]), n[1], n[end])', vmin=0, vmax=0.9); colorbar();
title("predict at snapshot $(3+i)")
subplot(4,5,i+15);
imshow(5*abs.(reshape(Saturations(state.states[3+i]), n[1], n[end])'-reshape(Saturations(state_predict.states[3+i]), n[1], n[end])'), vmin=0, vmax=0.9); colorbar();
title("5X diff at snapshot $(3+i)")
end
suptitle("Flow Inversion at iter $j")
tight_layout()
safesave(joinpath(plotsdir(sim_name, exp_name), savename(fig_name; digits=6)*"_co2.png"), fig);
close(fig)
## loss
fig = figure(figsize=(20,12));
plot(fhistory[1:j]);title("loss=$(fhistory[j])");
suptitle("Flow Inversion at iter $j")
tight_layout()
safesave(joinpath(plotsdir(sim_name, exp_name), savename(fig_name; digits=6)*"_loss.png"), fig);
close(fig)
end
save_dict = @strdict sim_name exp_name subsamp niterations logK0 fhistory fnoerror
@tagsave(
joinpath(datadir(sim_name, exp_name), savename(save_dict, "jld2"; digits=6)),
save_dict;
safe=true
)