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Merge pull request #146 from ggebbie/ggebbie/invert-model
Julia 1.10 plus initial code for circulation inversion
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| #=%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | ||
| % Under development: the goal is to invert model output | ||
| % and get the transport matrix | ||
| % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% =# | ||
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| import Pkg; Pkg.activate(".") | ||
| using Revise | ||
| using TMI | ||
| using Test | ||
| using GGplot | ||
| using LinearAlgebra | ||
| using SparseArrays | ||
| using Statistics | ||
| #, Distributions, LinearAlgebra, Zygote, ForwardDiff, Optim | ||
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| TMIversion = "modern_90x45x33_GH10_GH12" | ||
| A, Alu, γ, TMIfile, L, B = config_from_nc(TMIversion) | ||
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| pkgdir() = dirname(dirname(pathof(TMI))) | ||
| pkgdir(args...) = joinpath(pkgdir(), args...) | ||
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| pkgdatadir() = joinpath(pkgdir(),"data") | ||
| pkgdatadir(args...) = joinpath(pkgdatadir(), args...) | ||
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| TMIfile = pkgdatadir("TMI_"*TMIversion*".nc") | ||
| θtrue = readfield(TMIfile,"θ",γ) | ||
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| ctrue = vec(θtrue) | ||
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| #An = A./sum(A;dims=1) | ||
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| q = A * ctrue | ||
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| # The first guess for the tracer concentration should be close to the actual tracer concentration | ||
| # take first guess as θtrue+0.01 | ||
| cvec=vec(θtrue).+ 0.1 | ||
| θguess = unvec(θtrue,cvec) | ||
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| #first guess tracer control vector is near zero, and we want this to remain relatively small | ||
| u = Field(-0.01.*ones(size(γ.wet)),γ,θtrue.name,θtrue.longname,θtrue.units) | ||
| uvec = vec(u) | ||
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| #We need an error covariance matrix | ||
| W⁻ = Diagonal(1 ./( ones(sum(γ.wet))).^2)#(1/sum(γ.wet)) | ||
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| #I want to allow a bunch of error in the surface part of the tracer conservation please | ||
| Qerror = ones(size(γ.wet)) | ||
| Qerror[:,:,1].=0 | ||
| Qfield = Field(Qerror,γ,θtrue.name,θtrue.longname,θtrue.units) | ||
| Qvec = vec(Qfield) | ||
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| Q⁻ = Diagonal(1 ./( ones(sum(γ.wet))).^2) | ||
| A0= A .* 0.2 | ||
| non_zero_indices1, non_zero_indices2, non_zero_values = findnz(A0) | ||
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| non_zero_indices = hcat(non_zero_indices1, non_zero_indices2) | ||
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| convec = [uvec; non_zero_values] | ||
| ulength=length(uvec) | ||
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| # get sample J value | ||
| F = costfunction_gridded_model(convec,non_zero_indices,u,A0,ctrue,cvec,q,W⁻,Q⁻,γ) | ||
| fg!(F,G,x) = costfunction_gridded_model!(F,G,x,non_zero_indices,u,A0,ctrue,cvec,q,W⁻,Q⁻,γ) | ||
| fg(x) = costfunction_gridded_model(x,non_zero_indices,u,A0,ctrue,cvec,q,W⁻,Q⁻,γ) | ||
| f(x) = fg(x)[1] | ||
| J₀,gJ₀ = fg(convec) | ||
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| #### gradient check ################### | ||
| # check with forward differences | ||
| ϵ = 1e-3 | ||
| #ii = rand(1:sum(γ.wet[:,:,1])) | ||
| println(size(length(convec))) | ||
| ii = rand(1:length(convec)) | ||
| println("Location for test =",ii) | ||
| δu = copy(convec); δu[ii] += ϵ | ||
| ∇f_finite = (f(δu) - f(convec))/ϵ | ||
| println(∇f_finite) | ||
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| fg!(J₀,gJ₀,(convec+δu)./2) # J̃₀ is not overwritten | ||
| ∇f = gJ₀[ii] | ||
| println(∇f) | ||
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| # error less than 10 percent? | ||
| println("Percent error ",100*abs(∇f - ∇f_finite)/abs(∇f + ∇f_finite)) | ||
| #### end gradient check ################# | ||
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| #print(length(convec)) | ||
| # filter the data with an Optim.jl method | ||
| iterations = 5 | ||
| out = steadyclimatology(convec,fg!,iterations) | ||
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| # reconstruct by hand to double-check. | ||
| ũ = unvec((W⁻ * u),out.minimizer[begin:ulength]) | ||
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| # reconstruct tracer map | ||
| c₀ = θguess | ||
| c̃ = θguess+ũ | ||
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| Δc̃ = c̃ - θtrue | ||
| Δc₀ = θguess - θtrue | ||
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| Anew = A0 + sparse(non_zero_indices[:, 1], non_zero_indices[:, 2], out.minimizer[ulength+1:end]) | ||
| onesvec = ones(size(q)) | ||
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| Adiff1 = sum((A.-A0).^2) | ||
| Adiff2 = sum((A.-Anew).^2) | ||
| oldf = sum((non_zero_values).^2) | ||
| newf = sum((out.minimizer[ulength+1:end]).^2) | ||
| tracer_cons1 = sum((A0*cvec-q).^2) | ||
| tracer_cons2 = sum((Anew*(cvec+out.minimizer[begin:ulength])-q).^2) | ||
| mass_cons1 = sum((A0*onesvec-onesvec).^2) | ||
| mass_cons2 = sum((Anew*onesvec-onesvec).^2) | ||
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| println("A difference before: $Adiff1") | ||
| println("A difference after: $Adiff2") | ||
| println("old tracer cons:$tracer_cons1") | ||
| println("new tracer cons:$tracer_cons2") | ||
| println("old mass cons:$mass_cons1") | ||
| println("new mass cons:$mass_cons2") | ||
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| # plot the difference | ||
| level = 15 # your choice 1-33 | ||
| depth = γ.depth[level] | ||
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| cntrs = 0:0.5:15 | ||
| label = "True θ" | ||
| planviewplot(θtrue, depth, cntrs, titlelabel=label) | ||
| readline() | ||
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| cntrs = 0:0.5:15 | ||
| label = "Optimized θ" | ||
| planviewplot(c̃, depth, cntrs, titlelabel=label) | ||
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