diff --git a/Climate/NeuralPDE/2 b/Climate/NeuralPDE/2
new file mode 100644
index 0000000..77045bb
--- /dev/null
+++ b/Climate/NeuralPDE/2
@@ -0,0 +1,137 @@
+cd(@__DIR__)
+using Pkg; Pkg.activate("."); Pkg.instantiate()
+using Revise
+using Zygote, Optim
+using OrdinaryDiffEq, Flux, DiffEqFlux, LinearAlgebra, Plots
+using DiffEqSensitivity
+const EIGEN_EST = Ref(0.0f0)
+const USE_GPU = Ref(false)
+
+USE_GPU[] = false # the network is small enough such that CPU works just great
+
+USE_GPU[] && (using CuArrays)
+
+_gpu(arg) = USE_GPU[] ? gpu(arg) : cpu(arg)
+_cu(arg) = USE_GPU[] ? cu(arg) : identity(arg)
+
+function getops(grid, T=Float32)
+    N, dz = length(grid), step(grid)
+    d = ones(N-2)
+    dl = ones(N-3) # super/lower diagonal
+    zv = zeros(N-2) # zero diagonal used to extend D* for boundary conditions
+
+    # D1 first order discretization of ∂_z
+    D1= diagm(-1 => -dl, 0 => d)
+    D1_B = hcat(zv, D1, zv)
+    D1_B[1,1] = -1
+    D1_B = _cu((1/dz)*D1_B)
+
+    # D2 discretization of ∂_zz
+    D2 = diagm(-1 => dl, 0 => -2*d, 1 => dl)
+    κ = 0.05
+    D2_B = hcat(zv, D2, zv) #add space for the boundary conditions space for "ghost nodes"
+    #we only solve for the interior space steps
+    D2_B[1,1] = D2_B[end, end] = 1
+
+    D2_B = _cu((κ/(dz^2)).*D2_B) #add the constant κ as the equation requires and finish the discretization
+
+    # Boundary conditions matrix QQ
+    Q = Matrix{Int}(I, N-2, N-2)
+    QQ = _cu(vcat(zeros(1,N-2), Q, zeros(1,N-2)))
+
+    D1 = D1_B * QQ
+    D2 = D2_B * QQ
+    EIGEN_EST[] = maximum(abs, eigvals(Matrix(D2)))
+    return (D1=T.(D1), D2=T.(D2))
+end
+
+function getu0(grid, T=Float32)
+    z = grid[2:N-1]
+    f0 = z -> T(exp(-200*(z-0.75)^2))
+    u0 = f0.(z) |> _gpu
+end
+
+function ode_i(u, p, t)
+    Φ = u -> cos.(sin.(u.^3) .+ sin.(cos.(u.^2)))
+    return p.D1*Φ(u) + p.D2*u
+end
+
+function ground_truth(grid, tspan)
+    prob = ODEProblem(ode_i, u0, (tspan[1], tspan[2]+0.1), ops)
+    sol = solve(prob, ROCK4(eigen_est = (integ)->integ.eigen_est = EIGEN_EST[]), abstol = 1e-9, reltol = 1e-9)
+    return sol
+end
+
+N = 32
+grid = range(0, 1, length = N)
+tspan = (0.0f0, 1.5f0)
+u0 = getu0(grid)
+ops = getops(grid)
+soldata = ground_truth(grid, tspan)
+
+ann = FastChain(FastDense(30,8,tanh), FastDense(8,30,tanh)) |> _gpu
+pp = initial_params(ann)
+lyrs = Flux.params(pp)
+function dudt_(u,p,t)
+    Φ = ann 
+    return ops.D1*Φ(u, p) + ops.D2*u
+end
+
+function predict_adjoint(iterat, fullp)
+    Array(concrete_solve(prob,
+                         ROCK4(eigen_est = (integ)->integ.eigen_est = EIGEN_EST[]),
+    u0, fullp, saveat = saveat))
+end
+
+function loss_adjoint(iterat, fullp)
+    pre = predict_adjoint(fullp)
+    sum(abs2, training_data - pre)
+end
+
+function random_data()
+    print("here")
+    ones(N, N)
+end
+
+function cb(opt_state:: Optim.OptimizationState)
+    cur_pred = collect(predict_adjoint(opt_state.metadata["x"]))
+    n = size(training_data, 1)
+    #pl = scatter(1:n,training_data[:,10],label="data", legend =:bottomright,title="Spatial Plot at t=$(saveat[10])")
+    #scatter!(pl,1:n,cur_pred[:,10],label="prediction")
+    #pl2 = scatter(saveat,training_data[N÷2,:],label="data", legend =:bottomright, title="Timeseries Plot at Middle X")
+    #scatter!(pl2,saveat,cur_pred[N÷2,:],label="prediction")
+    #display(plot(pl, pl2, size=(600, 300)))
+    display(opt_state.value)    
+    false
+end
+
+cb(trace::Optim.OptimizationTrace) = cb(last(trace))
+
+
+saveat = range(tspan..., length = 30) #time range
+prob = ODEProblem{false}(dudt_,u0,tspan,pp)
+training_data = _cu(soldata(saveat))
+
+epochs = Iterators.repeated(random_data(), 20)
+concrete_solve(prob, ROCK4(eigen_est = (integ)->integ.eigen_est = EIGEN_EST[]), u0, pp) 
+loss_adjoint(pp)
+
+#function loss_adjoint_gradient!(G, fullp)
+#    G .= Zygote.gradient(loss_adjoint, fullp)[1]
+#end
+res = DiffEqFlux.sciml_train(loss_adjoint, pp, BFGS(initial_stepnorm=0.01), epochs;cb = cb,maxiters = 1000)
+#result =  optimize(loss_adjoint, loss_adjoint_gradient!, pp, BFGS(), Optim.Options(extended_trace=true,callback = cb))
+
+#prob2 = ODEProblem{false}(dudt_,u0,(0f0,10f0),pp)
+#@time full_sol = solve(prob2,
+#                       ROCK2(eigen_est = (integ)->integ.eigen_est = EIGEN_EST[]),
+#                       saveat = saveat, abstol=1e-4, reltol=1e-2)
+#
+#cur_pred = collect((predict_adjoint(result.minimizer)))
+#n = size(training_data, 1)
+#pl = scatter(1:n,training_data[:,10],label="data", legend =:bottomright)
+#scatter!(pl,1:n,cur_pred[:,10],label="prediction",title="Spatial Plot at t=$(saveat[10])")
+#pl2 = scatter(saveat,training_data[N÷2,:],label="data", legend =:bottomright, title="Time Series Plot: Middle X")
+#scatter!(pl2,saveat,cur_pred[N÷2,:],label="prediction")
+#plot(pl, pl2, size=(600, 300))
+#savefig("npde_fit.pdf")
diff --git a/Climate/NeuralPDE/Manifest.toml b/Climate/NeuralPDE/Manifest.toml
index 1c7962c..99e0cc1 100644
--- a/Climate/NeuralPDE/Manifest.toml
+++ b/Climate/NeuralPDE/Manifest.toml
@@ -8,15 +8,15 @@ version = "0.5.0"
 
 [[AbstractTrees]]
 deps = ["Markdown"]
-git-tree-sha1 = "940760b82db1f7090f7d16fe6e4b121cc181db45"
+git-tree-sha1 = "86d092c2599f1f7bb01668bf8eb3412f98d61e47"
 uuid = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
-version = "0.3.1"
+version = "0.3.2"
 
 [[Adapt]]
 deps = ["LinearAlgebra"]
-git-tree-sha1 = "82dab828020b872fa9efd3abec1152b075bc7cbf"
+git-tree-sha1 = "c88cfc7f9c1f9f8633cddf0b56e86302b70f64c5"
 uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
-version = "1.0.0"
+version = "1.0.1"
 
 [[ApproxFun]]
 deps = ["AbstractFFTs", "ApproxFunBase", "ApproxFunFourier", "ApproxFunOrthogonalPolynomials", "ApproxFunSingularities", "Calculus", "DomainSets", "DualNumbers", "FFTW", "FastTransforms", "LinearAlgebra", "RecipesBase", "Reexport"]
@@ -68,9 +68,9 @@ version = "3.5.0+2"
 
 [[ArrayInterface]]
 deps = ["LinearAlgebra", "Requires", "SparseArrays"]
-git-tree-sha1 = "656fd4bcdf204ea96945d9bc1068c0056013438a"
+git-tree-sha1 = "7ab65638f4664498b01aeddf2e82f93780ba5e21"
 uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
-version = "2.3.1"
+version = "2.6.0"
 
 [[ArrayLayouts]]
 deps = ["FillArrays", "LinearAlgebra"]
@@ -123,21 +123,21 @@ version = "1.0.0"
 
 [[CUDAapi]]
 deps = ["Libdl", "Logging"]
-git-tree-sha1 = "56a813440ac98a1aa64672ab460a1512552211a7"
+git-tree-sha1 = "d7ceadd8f821177d05b897c0517e94633db535fe"
 uuid = "3895d2a7-ec45-59b8-82bb-cfc6a382f9b3"
-version = "2.1.0"
+version = "3.1.0"
 
 [[CUDAdrv]]
 deps = ["CEnum", "CUDAapi", "Printf"]
-git-tree-sha1 = "1fce616fa0806c67c133eb1d2f68f0f1a7504665"
+git-tree-sha1 = "01e90fa34e25776bc7c8661183d4519149ebfe59"
 uuid = "c5f51814-7f29-56b8-a69c-e4d8f6be1fde"
-version = "5.0.1"
+version = "6.0.0"
 
 [[CUDAnative]]
 deps = ["Adapt", "CEnum", "CUDAapi", "CUDAdrv", "DataStructures", "InteractiveUtils", "LLVM", "Libdl", "Printf", "TimerOutputs"]
-git-tree-sha1 = "ba0725f487fb4a6c63efad7890a659659b6a6754"
+git-tree-sha1 = "f86269ff60ebe082a2806ecbce51f3cadc68afe9"
 uuid = "be33ccc6-a3ff-5ff2-a52e-74243cff1e17"
-version = "2.8.1"
+version = "2.10.2"
 
 [[Calculus]]
 deps = ["LinearAlgebra"]
@@ -145,17 +145,11 @@ git-tree-sha1 = "f641eb0a4f00c343bbc32346e1217b86f3ce9dad"
 uuid = "49dc2e85-a5d0-5ad3-a950-438e2897f1b9"
 version = "0.5.1"
 
-[[CategoricalArrays]]
-deps = ["Compat", "DataAPI", "Future", "JSON", "Missings", "Printf", "Reexport", "Statistics", "Unicode"]
-git-tree-sha1 = "23d7324164c89638c18f6d7f90d972fa9c4fa9fb"
-uuid = "324d7699-5711-5eae-9e2f-1d82baa6b597"
-version = "0.7.7"
-
 [[ChainRulesCore]]
 deps = ["MuladdMacro"]
-git-tree-sha1 = "eb54d7349210f37c142e58d67668951efc1e5cdc"
+git-tree-sha1 = "840cdd255e267a4dfcb14cecd872facb2997a326"
 uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
-version = "0.6.1"
+version = "0.7.1"
 
 [[CodeTracking]]
 deps = ["InteractiveUtils", "UUIDs"]
@@ -171,15 +165,15 @@ version = "0.6.0"
 
 [[ColorTypes]]
 deps = ["FixedPointNumbers", "Random"]
-git-tree-sha1 = "7b62b728a5f3dd6ee3b23910303ccf27e82fad5e"
+git-tree-sha1 = "b9de8dc6106e09c79f3f776c27c62360d30e5eb8"
 uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
-version = "0.8.1"
+version = "0.9.1"
 
 [[Colors]]
 deps = ["ColorTypes", "FixedPointNumbers", "InteractiveUtils", "Printf", "Reexport"]
-git-tree-sha1 = "c9c1845d6bf22e34738bee65c357a69f416ed5d1"
+git-tree-sha1 = "177d8b959d3c103a6d57574c38ee79c81059c31b"
 uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
-version = "0.9.6"
+version = "0.11.2"
 
 [[CommonSubexpressions]]
 deps = ["Test"]
@@ -188,28 +182,34 @@ uuid = "bbf7d656-a473-5ed7-a52c-81e309532950"
 version = "0.2.0"
 
 [[Compat]]
-deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
-git-tree-sha1 = "ed2c4abadf84c53d9e58510b5fc48912c2336fbb"
+deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
+git-tree-sha1 = "0198d18b28c093bef39872a22f1a897218a925f5"
 uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
-version = "2.2.0"
+version = "3.8.0"
 
 [[CompilerSupportLibraries_jll]]
 deps = ["Libdl", "Pkg"]
-git-tree-sha1 = "b57c5d019367c90f234a7bc7e24ff0a84971da5d"
+git-tree-sha1 = "aa832564f930a7fc9290972526908d01a35aefac"
 uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
-version = "0.2.0+1"
+version = "0.3.0+0"
+
+[[ConsoleProgressMonitor]]
+deps = ["Logging", "ProgressMeter"]
+git-tree-sha1 = "3ab7b2136722890b9af903859afcf457fa3059e8"
+uuid = "88cd18e8-d9cc-4ea6-8889-5259c0d15c8b"
+version = "0.1.2"
 
 [[Contour]]
-deps = ["LinearAlgebra", "StaticArrays", "Test"]
-git-tree-sha1 = "b974e164358fea753ef853ce7bad97afec15bb80"
+deps = ["StaticArrays"]
+git-tree-sha1 = "6d56f927b33d3820561b8f89d7de311718683846"
 uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
-version = "0.5.1"
+version = "0.5.2"
 
 [[CuArrays]]
 deps = ["AbstractFFTs", "Adapt", "CEnum", "CUDAapi", "CUDAdrv", "CUDAnative", "DataStructures", "GPUArrays", "Libdl", "LinearAlgebra", "MacroTools", "NNlib", "Printf", "Random", "Requires", "SparseArrays", "TimerOutputs"]
-git-tree-sha1 = "4e536542c5c898b1bf43011b6187f3c97ebcc91e"
+git-tree-sha1 = "7fa1331a0e0cd10e43b94b280027bda45990cb63"
 uuid = "3a865a2d-5b23-5a0f-bc46-62713ec82fae"
-version = "1.7.0"
+version = "1.7.3"
 
 [[DSP]]
 deps = ["FFTW", "IterTools", "LinearAlgebra", "Polynomials", "Random", "Reexport", "SpecialFunctions", "Statistics"]
@@ -222,22 +222,11 @@ git-tree-sha1 = "674b67f344687a88310213ddfa8a2b3c76cc4252"
 uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
 version = "1.1.0"
 
-[[DataFrames]]
-deps = ["CategoricalArrays", "Compat", "DataAPI", "Future", "InvertedIndices", "IteratorInterfaceExtensions", "Missings", "PooledArrays", "Printf", "REPL", "Reexport", "SortingAlgorithms", "Statistics", "TableTraits", "Tables", "Unicode"]
-git-tree-sha1 = "00136fcd39d503e66ab1b2eab800c47deaf7ca04"
-uuid = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
-version = "0.20.0"
-
 [[DataStructures]]
 deps = ["InteractiveUtils", "OrderedCollections"]
-git-tree-sha1 = "b7720de347734f4716d1815b00ce5664ed6bbfd4"
+git-tree-sha1 = "5a431d46abf2ef2a4d5d00bd0ae61f651cf854c8"
 uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
-version = "0.17.9"
-
-[[DataValueInterfaces]]
-git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
-uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464"
-version = "1.0.0"
+version = "0.17.10"
 
 [[Dates]]
 deps = ["Printf"]
@@ -248,28 +237,28 @@ deps = ["Mmap"]
 uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
 
 [[DiffEqBase]]
-deps = ["ArrayInterface", "ChainRulesCore", "Compat", "DataStructures", "Distributed", "DocStringExtensions", "FunctionWrappers", "IterativeSolvers", "IteratorInterfaceExtensions", "LinearAlgebra", "MuladdMacro", "Parameters", "Printf", "RecipesBase", "RecursiveArrayTools", "RecursiveFactorization", "Requires", "Roots", "SparseArrays", "StaticArrays", "Statistics", "SuiteSparse", "TableTraits", "TreeViews", "ZygoteRules"]
-git-tree-sha1 = "3ef848bc1b8b09ce3cc14b53ddd0b4abec0407ae"
+deps = ["ArrayInterface", "ChainRulesCore", "ConsoleProgressMonitor", "DataStructures", "Distributed", "DocStringExtensions", "FunctionWrappers", "IterativeSolvers", "IteratorInterfaceExtensions", "LinearAlgebra", "Logging", "LoggingExtras", "MuladdMacro", "Parameters", "Printf", "ProgressLogging", "RecipesBase", "RecursiveArrayTools", "RecursiveFactorization", "Requires", "Roots", "SparseArrays", "StaticArrays", "Statistics", "SuiteSparse", "TableTraits", "TerminalLoggers", "TreeViews", "ZygoteRules"]
+git-tree-sha1 = "b20a1c5741d279787c7db100e11106ea14ee6dbf"
 uuid = "2b5f629d-d688-5b77-993f-72d75c75574e"
-version = "6.13.1"
+version = "6.25.0"
 
 [[DiffEqCallbacks]]
 deps = ["DataStructures", "DiffEqBase", "ForwardDiff", "LinearAlgebra", "NLsolve", "OrdinaryDiffEq", "RecipesBase", "RecursiveArrayTools", "StaticArrays"]
-git-tree-sha1 = "573b46d716ff12b79e9f6e1c1602b0553b619e84"
+git-tree-sha1 = "3aadf5d6b987aaec2bb7421aba522df744609960"
 uuid = "459566f4-90b8-5000-8ac3-15dfb0a30def"
-version = "2.11.0"
+version = "2.12.1"
 
 [[DiffEqFlux]]
-deps = ["Adapt", "DiffEqBase", "DiffEqSensitivity", "DiffResults", "Flux", "ForwardDiff", "LinearAlgebra", "RecursiveArrayTools", "Requires", "Tracker", "ZygoteRules"]
-git-tree-sha1 = "db1b35fb42fb81325a4aa0fb7d7d599d4352b07c"
+deps = ["Adapt", "DiffEqBase", "DiffEqSensitivity", "DiffResults", "Flux", "ForwardDiff", "Juno", "LinearAlgebra", "Logging", "Optim", "RecursiveArrayTools", "Requires", "ReverseDiff", "StaticArrays", "Tracker", "ZygoteRules"]
+git-tree-sha1 = "145c4578542cf7ba8781d672dae1b6e371810f2d"
 uuid = "aae7a2af-3d4f-5e19-a356-7da93b79d9d0"
-version = "1.1.1"
+version = "1.7.0"
 
 [[DiffEqSensitivity]]
-deps = ["Adapt", "DataFrames", "DiffEqBase", "DiffEqCallbacks", "Distributions", "FFTW", "FiniteDiff", "ForwardDiff", "GLM", "LinearAlgebra", "Parameters", "QuadGK", "QuasiMonteCarlo", "RecursiveArrayTools", "Statistics", "Tracker", "Zygote", "ZygoteRules"]
-git-tree-sha1 = "2e60be09027dc348480467c8d1cd7c5779dff6cb"
+deps = ["Adapt", "DiffEqBase", "DiffEqCallbacks", "Distributions", "FFTW", "FiniteDiff", "ForwardDiff", "LinearAlgebra", "Parameters", "QuadGK", "QuasiMonteCarlo", "RecursiveArrayTools", "ReverseDiff", "Statistics", "Tracker", "Zygote", "ZygoteRules"]
+git-tree-sha1 = "00a6d02598e6fa54c88d43feed3c0baaf8280278"
 uuid = "41bf760c-e81c-5289-8e54-58b1f1f8abe2"
-version = "6.6.0"
+version = "6.8.0"
 
 [[DiffResults]]
 deps = ["StaticArrays"]
@@ -279,9 +268,9 @@ version = "1.0.2"
 
 [[DiffRules]]
 deps = ["NaNMath", "Random", "SpecialFunctions"]
-git-tree-sha1 = "10dca52cf6d4a62d82528262921daf63b99704a2"
+git-tree-sha1 = "eb0c34204c8410888844ada5359ac8b96292cfd1"
 uuid = "b552c78f-8df3-52c6-915a-8e097449b14b"
-version = "1.0.0"
+version = "1.0.1"
 
 [[Distances]]
 deps = ["LinearAlgebra", "Statistics"]
@@ -295,9 +284,9 @@ uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 
 [[Distributions]]
 deps = ["FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns"]
-git-tree-sha1 = "e063d0b5d27180b98edacd2b1cb90ecfbc171385"
+git-tree-sha1 = "55e1de79bd2c397e048ca47d251f8fa70e530550"
 uuid = "31c24e10-a181-5473-b8eb-7969acd0382f"
-version = "0.21.12"
+version = "0.22.6"
 
 [[DocStringExtensions]]
 deps = ["LibGit2", "Markdown", "Pkg", "Test"]
@@ -337,9 +326,9 @@ version = "1.2.0"
 
 [[FFTW_jll]]
 deps = ["Libdl", "Pkg"]
-git-tree-sha1 = "05674f209a6e3387dd103a945b0113eeb64b1a58"
+git-tree-sha1 = "ddb57f4cf125243b4aa4908c94d73a805f3cbf2c"
 uuid = "f5851436-0d7a-5f13-b9de-f02708fd171a"
-version = "3.3.9+3"
+version = "3.3.9+4"
 
 [[FastGaussQuadrature]]
 deps = ["LinearAlgebra", "SpecialFunctions"]
@@ -361,24 +350,24 @@ version = "0.2.13+0"
 
 [[FileIO]]
 deps = ["Pkg"]
-git-tree-sha1 = "74585bf1f7ed7259e166011e89f49363d7fa89a6"
+git-tree-sha1 = "250ac7dfd54b5ce47372505b392756633d4e9732"
 uuid = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
-version = "1.2.1"
+version = "1.2.3"
 
 [[FileWatching]]
 uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee"
 
 [[FillArrays]]
 deps = ["LinearAlgebra", "Random", "SparseArrays"]
-git-tree-sha1 = "fec413d4fc547992eb62a5c544cedb6d7853c1f5"
+git-tree-sha1 = "85c6b57e2680fa28d5c8adc798967377646fbf66"
 uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
-version = "0.8.4"
+version = "0.8.5"
 
 [[FiniteDiff]]
 deps = ["ArrayInterface", "LinearAlgebra", "Requires", "SparseArrays", "StaticArrays"]
-git-tree-sha1 = "109cca539ac87b1b95538f539ed8eb7e3f35eee5"
+git-tree-sha1 = "f60e5d6944975f7140bde67278e10b6b01fb4f29"
 uuid = "6a86dc24-6348-571c-b903-95158fe2bd41"
-version = "2.1.0"
+version = "2.3.0"
 
 [[FixedPointNumbers]]
 git-tree-sha1 = "d14a6fa5890ea3a7e5dcab6811114f132fec2b4b"
@@ -387,9 +376,9 @@ version = "0.6.1"
 
 [[Flux]]
 deps = ["AbstractTrees", "Adapt", "CodecZlib", "Colors", "CuArrays", "DelimitedFiles", "Juno", "MacroTools", "NNlib", "Pkg", "Printf", "Random", "Reexport", "SHA", "Statistics", "StatsBase", "Test", "ZipFile", "Zygote"]
-git-tree-sha1 = "8134adbb0f10b0d22b22f8b4299d0d20509edc5f"
+git-tree-sha1 = "b5647a92b4d547f835b0eac904331a97c45d773d"
 uuid = "587475ba-b771-5e3f-ad9e-33799f191a9c"
-version = "0.10.1"
+version = "0.10.3"
 
 [[ForwardDiff]]
 deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "NaNMath", "Random", "SpecialFunctions", "StaticArrays"]
@@ -398,20 +387,9 @@ uuid = "f6369f11-7733-5829-9624-2563aa707210"
 version = "0.10.9"
 
 [[FunctionWrappers]]
-deps = ["Compat"]
-git-tree-sha1 = "49bf793ebd37db5adaa7ac1eae96c2c97ec86db5"
+git-tree-sha1 = "e4813d187be8c7b993cb7f85cbf2b7bfbaadc694"
 uuid = "069b7b12-0de2-55c6-9aab-29f3d0a68a2e"
-version = "1.0.0"
-
-[[Future]]
-deps = ["Random"]
-uuid = "9fa8497b-333b-5362-9e8d-4d0656e87820"
-
-[[GLM]]
-deps = ["Distributions", "LinearAlgebra", "Printf", "Random", "Reexport", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns", "StatsModels"]
-git-tree-sha1 = "9768bbf52d4fbb2e2bb3e4e304a787c4cb8aa980"
-uuid = "38e38edf-8417-5370-95a0-9cbb8c7f171a"
-version = "1.3.6"
+version = "1.1.1"
 
 [[GMP_jll]]
 deps = ["Libdl", "Pkg"]
@@ -439,9 +417,9 @@ version = "0.2.2"
 
 [[GeometryTypes]]
 deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "StaticArrays"]
-git-tree-sha1 = "a96baa00f5ac755689c82c29bc3395e161337c69"
+git-tree-sha1 = "78f0ce9d01993b637a8f28d84537d75dc0ce8eef"
 uuid = "4d00f742-c7ba-57c2-abde-4428a4b178cb"
-version = "0.7.7"
+version = "0.7.10"
 
 [[IRTools]]
 deps = ["InteractiveUtils", "MacroTools", "Test"]
@@ -477,22 +455,16 @@ git-tree-sha1 = "4214b48a62eb8f2c292b2ee34a508c256c0cdbc9"
 uuid = "8197267c-284f-5f27-9208-e0e47529a953"
 version = "0.3.2"
 
-[[InvertedIndices]]
-deps = ["Test"]
-git-tree-sha1 = "15732c475062348b0165684ffe28e85ea8396afc"
-uuid = "41ab1584-1d38-5bbf-9106-f11c6c58b48f"
-version = "1.0.0"
-
 [[IterTools]]
 git-tree-sha1 = "05110a2ab1fc5f932622ffea2a003221f4782c18"
 uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
 version = "1.3.0"
 
 [[IterativeSolvers]]
-deps = ["LinearAlgebra", "Printf", "Random", "RecipesBase", "SparseArrays", "Test"]
-git-tree-sha1 = "5687f68018b4f14c0da54d402bb23eecaec17f37"
+deps = ["LinearAlgebra", "Printf", "Random", "RecipesBase", "SparseArrays"]
+git-tree-sha1 = "f272a02b57a1a1d2150a1a6cc4a3441ee806ab96"
 uuid = "42fd0dbc-a981-5370-80f2-aaf504508153"
-version = "0.8.1"
+version = "0.8.3"
 
 [[IteratorInterfaceExtensions]]
 git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
@@ -501,9 +473,9 @@ version = "1.0.0"
 
 [[JLD2]]
 deps = ["CodecZlib", "DataStructures", "FileIO", "Mmap", "Pkg", "Printf", "UUIDs"]
-git-tree-sha1 = "5deae9f0745ef505ed155a0029629cf08502ccab"
+git-tree-sha1 = "d6cfa7c24e27d7eaa2290372739c8298257dae16"
 uuid = "033835bb-8acc-5ee8-8aae-3f567f8a3819"
-version = "0.1.11"
+version = "0.1.12"
 
 [[JSON]]
 deps = ["Dates", "Mmap", "Parsers", "Unicode"]
@@ -513,33 +485,39 @@ version = "0.21.0"
 
 [[JuliaInterpreter]]
 deps = ["CodeTracking", "InteractiveUtils", "Random", "UUIDs"]
-git-tree-sha1 = "a4f675340a109713f74c47a2b499df06f800c8d0"
+git-tree-sha1 = "2eadbbde5534346cbb837c3a75b377cba477a06d"
 uuid = "aa1ae85d-cabe-5617-a682-6adf51b2e16a"
-version = "0.7.8"
+version = "0.7.13"
 
 [[Juno]]
-deps = ["Base64", "Logging", "Media", "Profile", "Test"]
-git-tree-sha1 = "30d94657a422d09cb97b6f86f04f750fa9c50df8"
+deps = ["Base64", "Logging", "Media", "Profile"]
+git-tree-sha1 = "e1ba2a612645b3e07c773c3a208f215745081fe6"
 uuid = "e5e0dc1b-0480-54bc-9374-aad01c23163d"
-version = "0.7.2"
+version = "0.8.1"
 
 [[LLVM]]
 deps = ["CEnum", "Libdl", "Printf", "Unicode"]
-git-tree-sha1 = "1d08d7e4250f452f6cb20e4574daaebfdbee0ff7"
+git-tree-sha1 = "b6b86801ae2f2682e0a4889315dc76b68db2de71"
 uuid = "929cbde3-209d-540e-8aea-75f648917ca0"
-version = "1.3.3"
+version = "1.3.4"
 
 [[LatinHypercubeSampling]]
 deps = ["Random", "StatsBase", "Test"]
-git-tree-sha1 = "f049eba097c2a93a6ac6d5babb6bd711a8123444"
+git-tree-sha1 = "b6d72344668dba064cc5791681bac7d55d272b6e"
 uuid = "a5e1c1ea-c99a-51d3-a14d-a9a37257b02d"
-version = "1.4.0"
+version = "1.6.3"
 
 [[LazyArrays]]
 deps = ["ArrayLayouts", "FillArrays", "LinearAlgebra", "MacroTools", "StaticArrays"]
-git-tree-sha1 = "6e818d550c2158def13c236c3b825fc14995160c"
+git-tree-sha1 = "b799f90cd9a1d90a54038f8263e701023bce1af8"
 uuid = "5078a376-72f3-5289-bfd5-ec5146d43c02"
-version = "0.15.0"
+version = "0.15.1"
+
+[[LeftChildRightSiblingTrees]]
+deps = ["AbstractTrees"]
+git-tree-sha1 = "71be1eb5ad19cb4f61fa8c73395c0338fd092ae0"
+uuid = "1d6d02ad-be62-4b6b-8a6d-2f90e265016e"
+version = "0.1.2"
 
 [[LibGit2]]
 uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"
@@ -549,9 +527,9 @@ uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
 
 [[LightGraphs]]
 deps = ["ArnoldiMethod", "DataStructures", "Distributed", "Inflate", "LinearAlgebra", "Random", "SharedArrays", "SimpleTraits", "SparseArrays", "Statistics"]
-git-tree-sha1 = "a0d4bcea4b9c056da143a5ded3c2b7f7740c2d41"
+git-tree-sha1 = "f40c4dbcd957cc3afc8cca0ff26c9f8304def00d"
 uuid = "093fc24a-ae57-5d10-9952-331d41423f4d"
-version = "1.3.0"
+version = "1.3.1"
 
 [[LineSearches]]
 deps = ["LinearAlgebra", "NLSolversBase", "NaNMath", "Parameters", "Printf", "Test"]
@@ -566,6 +544,11 @@ uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 [[Logging]]
 uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
 
+[[LoggingExtras]]
+git-tree-sha1 = "c867b50bfc564f0beded1c566f4fc66cfd8b5418"
+uuid = "e6f89c97-d47a-5376-807f-9c37f3926c36"
+version = "0.4.0"
+
 [[LowRankApprox]]
 deps = ["FFTW", "FillArrays", "LinearAlgebra", "Nullables", "Random", "SparseArrays", "Test"]
 git-tree-sha1 = "1963361c4e8a837b9ca7cca3f45372f953e6b0ed"
@@ -574,9 +557,9 @@ version = "0.4.0"
 
 [[LoweredCodeUtils]]
 deps = ["JuliaInterpreter"]
-git-tree-sha1 = "b416a30717e9109fffd4d9869f2f962b5dca3162"
+git-tree-sha1 = "1c41621653250b2824b6e664ac5bd805558aeff9"
 uuid = "6f1432cf-f94c-5a45-995e-cdbf5db27b0b"
-version = "0.4.2"
+version = "0.4.3"
 
 [[MKL_jll]]
 deps = ["IntelOpenMP_jll", "Libdl", "Pkg"]
@@ -592,9 +575,9 @@ version = "4.0.2+2"
 
 [[MacroTools]]
 deps = ["DataStructures", "Markdown", "Random"]
-git-tree-sha1 = "e2fc7a55bb2224e203bbd8b59f72b91323233458"
+git-tree-sha1 = "07ee65e03e28ca88bc9a338a3726ae0c3efaa94b"
 uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
-version = "0.5.3"
+version = "0.5.4"
 
 [[Markdown]]
 deps = ["Base64"]
@@ -633,9 +616,9 @@ version = "0.2.2"
 
 [[NLSolversBase]]
 deps = ["DiffResults", "Distributed", "FiniteDiff", "ForwardDiff"]
-git-tree-sha1 = "b13b1f97ce88a37dd55ce7ae7e75b81002bf2b9d"
+git-tree-sha1 = "7c4e66c47848562003250f28b579c584e55becc0"
 uuid = "d41bc354-129a-5804-8e4c-c37616107c6c"
-version = "7.6.0"
+version = "7.6.1"
 
 [[NLsolve]]
 deps = ["Distances", "LineSearches", "LinearAlgebra", "NLSolversBase", "Printf", "Reexport"]
@@ -645,9 +628,9 @@ version = "4.3.0"
 
 [[NNlib]]
 deps = ["BinaryProvider", "Libdl", "LinearAlgebra", "Requires", "Statistics"]
-git-tree-sha1 = "755c0bab3912ff782167e1b4b774b833f8a0e550"
+git-tree-sha1 = "d9f196d911f55aeaff11b11f681b135980783824"
 uuid = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
-version = "0.6.4"
+version = "0.6.6"
 
 [[NaNMath]]
 git-tree-sha1 = "928b8ca9b2791081dc71a51c55347c27c618760f"
@@ -661,21 +644,21 @@ version = "1.0.0"
 
 [[OpenBLAS_jll]]
 deps = ["Libdl", "Pkg"]
-git-tree-sha1 = "3a6e5767e8ae022871c19162cc3ecd80748bd3dc"
+git-tree-sha1 = "139adbff69e8149e68824994b68f06a61a5a2797"
 uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
-version = "0.3.7+4"
+version = "0.3.7+8"
 
 [[OpenSpecFun_jll]]
-deps = ["Libdl", "Pkg"]
-git-tree-sha1 = "65f672edebf3f4e613ddf37db9dcbd7a407e5e90"
+deps = ["CompilerSupportLibraries_jll", "Libdl", "Pkg"]
+git-tree-sha1 = "d51c416559217d974a1113522d5919235ae67a87"
 uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
-version = "0.5.3+1"
+version = "0.5.3+3"
 
 [[Optim]]
-deps = ["FillArrays", "LineSearches", "LinearAlgebra", "NLSolversBase", "NaNMath", "Parameters", "PositiveFactorizations", "Printf", "Random", "SparseArrays", "StatsBase"]
-git-tree-sha1 = "b1e90642d0addb7d9651d409ad465ac5c764c11f"
+deps = ["Compat", "FillArrays", "LineSearches", "LinearAlgebra", "NLSolversBase", "NaNMath", "Parameters", "PositiveFactorizations", "Printf", "SparseArrays", "StatsBase"]
+git-tree-sha1 = "1c44e1ac9c39892ff74de99ec9f7428f03660851"
 uuid = "429524aa-4258-5aef-a3af-852621145aeb"
-version = "0.20.0"
+version = "0.20.4"
 
 [[OrderedCollections]]
 deps = ["Random", "Serialization", "Test"]
@@ -684,16 +667,16 @@ uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
 version = "1.1.0"
 
 [[OrdinaryDiffEq]]
-deps = ["ArrayInterface", "DataStructures", "DiffEqBase", "ExponentialUtilities", "FiniteDiff", "ForwardDiff", "GenericSVD", "LinearAlgebra", "Logging", "MacroTools", "MuladdMacro", "Parameters", "RecursiveArrayTools", "Reexport", "SparseArrays", "SparseDiffTools", "StaticArrays"]
-git-tree-sha1 = "eee8bb40d5265b97b1e6c685d46afbdcc559f789"
+deps = ["ArrayInterface", "DataStructures", "DiffEqBase", "ExponentialUtilities", "FiniteDiff", "ForwardDiff", "GenericSVD", "LinearAlgebra", "Logging", "MacroTools", "MuladdMacro", "NLsolve", "RecursiveArrayTools", "Reexport", "SparseArrays", "SparseDiffTools", "StaticArrays", "UnPack"]
+git-tree-sha1 = "586c962ad54d355f195ef4e2e370d420362820d2"
 uuid = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
-version = "5.28.1"
+version = "5.31.0"
 
 [[PDMats]]
 deps = ["Arpack", "LinearAlgebra", "SparseArrays", "SuiteSparse", "Test"]
-git-tree-sha1 = "5f303510529486bb02ac4d70da8295da38302194"
+git-tree-sha1 = "2fc6f50ddd959e462f0a2dbc802ddf2a539c6e35"
 uuid = "90014a1f-27ba-587c-ab20-58faa44d9150"
-version = "0.9.11"
+version = "0.9.12"
 
 [[Parameters]]
 deps = ["OrderedCollections"]
@@ -703,9 +686,9 @@ version = "0.12.0"
 
 [[Parsers]]
 deps = ["Dates", "Test"]
-git-tree-sha1 = "0139ba59ce9bc680e2925aec5b7db79065d60556"
+git-tree-sha1 = "0c16b3179190d3046c073440d94172cfc3bb0553"
 uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
-version = "0.3.10"
+version = "0.3.12"
 
 [[Pkg]]
 deps = ["Dates", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "UUIDs"]
@@ -719,9 +702,9 @@ version = "1.0.1"
 
 [[PlotUtils]]
 deps = ["Colors", "Dates", "Printf", "Random", "Reexport"]
-git-tree-sha1 = "22bd7d0a1f4665d66317d6c89a57f6bba9f2560d"
+git-tree-sha1 = "132e468bf7d67ee6c997c160b982a7ab2e7c3e37"
 uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
-version = "0.6.2"
+version = "0.6.4"
 
 [[Plots]]
 deps = ["Base64", "Contour", "Dates", "FFMPEG", "FixedPointNumbers", "GR", "GeometryTypes", "JSON", "LinearAlgebra", "Measures", "NaNMath", "Pkg", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "Reexport", "Requires", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs"]
@@ -731,15 +714,9 @@ version = "0.28.4"
 
 [[Polynomials]]
 deps = ["LinearAlgebra", "RecipesBase"]
-git-tree-sha1 = "ae71c2329790af97b7682b11241b3609e4d48626"
+git-tree-sha1 = "1185511cac8ab9d0b658b663eae34fe9a95d4332"
 uuid = "f27b6e38-b328-58d1-80ce-0feddd5e7a45"
-version = "0.6.0"
-
-[[PooledArrays]]
-deps = ["DataAPI"]
-git-tree-sha1 = "b1333d4eced1826e15adbdf01a4ecaccca9d353c"
-uuid = "2dfb63ee-cc39-5dd5-95bd-886bf059d720"
-version = "0.5.3"
+version = "0.6.1"
 
 [[PositiveFactorizations]]
 deps = ["LinearAlgebra", "Test"]
@@ -755,6 +732,18 @@ uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 deps = ["Printf"]
 uuid = "9abbd945-dff8-562f-b5e8-e1ebf5ef1b79"
 
+[[ProgressLogging]]
+deps = ["Logging", "SHA", "UUIDs"]
+git-tree-sha1 = "e47914361d124d8760f5e356403daeb7f3b81633"
+uuid = "33c8b6b6-d38a-422a-b730-caa89a2f386c"
+version = "0.1.2"
+
+[[ProgressMeter]]
+deps = ["Distributed", "Printf"]
+git-tree-sha1 = "ea1f4fa0ff5e8b771bf130d87af5b7ef400760bd"
+uuid = "92933f4c-e287-5a05-a399-4b506db050ca"
+version = "1.2.0"
+
 [[QuadGK]]
 deps = ["DataStructures", "LinearAlgebra"]
 git-tree-sha1 = "dc84e810393cfc6294248c9032a9cdacc14a3db4"
@@ -763,9 +752,9 @@ version = "2.3.1"
 
 [[QuasiMonteCarlo]]
 deps = ["Distributions", "LatinHypercubeSampling", "Sobol"]
-git-tree-sha1 = "e01670ab0faee2fc060e080909cfbba774ab2ee2"
+git-tree-sha1 = "283d3f2f74d38c5b7fc124bc1c476c9a3b8e2e89"
 uuid = "8a4e6c94-4038-4cdc-81c3-7e6ffdb2a71b"
-version = "0.1.0"
+version = "0.1.1"
 
 [[REPL]]
 deps = ["InteractiveUtils", "Markdown", "Sockets"]
@@ -782,9 +771,9 @@ version = "0.7.0"
 
 [[RecursiveArrayTools]]
 deps = ["ArrayInterface", "RecipesBase", "Requires", "StaticArrays", "Statistics", "ZygoteRules"]
-git-tree-sha1 = "275cb9be63cbb8a1e9d5737dac45ecff5840ad48"
+git-tree-sha1 = "bd13db2a3561fb3a3635220c5ee21e3356d7631e"
 uuid = "731186ca-8d62-57ce-b412-fbd966d074cd"
-version = "2.0.4"
+version = "2.1.0"
 
 [[RecursiveFactorization]]
 deps = ["LinearAlgebra"]
@@ -800,27 +789,39 @@ version = "0.2.0"
 
 [[Requires]]
 deps = ["UUIDs"]
-git-tree-sha1 = "999513b7dea8ac17359ed50ae8ea089e4464e35e"
+git-tree-sha1 = "d37400976e98018ee840e0ca4f9d20baa231dc6b"
 uuid = "ae029012-a4dd-5104-9daa-d747884805df"
-version = "1.0.0"
+version = "1.0.1"
+
+[[ReverseDiff]]
+deps = ["DiffResults", "DiffRules", "ForwardDiff", "FunctionWrappers", "LinearAlgebra", "NaNMath", "Random", "SpecialFunctions", "StaticArrays", "Statistics"]
+git-tree-sha1 = "5f7dafd314ff2ada3076797b1edfb71e52151cb9"
+uuid = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
+version = "1.1.0"
 
 [[Revise]]
 deps = ["CodeTracking", "Distributed", "FileWatching", "JuliaInterpreter", "LibGit2", "LoweredCodeUtils", "OrderedCollections", "Pkg", "REPL", "UUIDs", "Unicode"]
-git-tree-sha1 = "2ecbd19f31a934b035bfc38036d5f7ac575d0878"
+git-tree-sha1 = "3c04c929f8720c2fabb12534cd102a2356a7705c"
 uuid = "295af30f-e4ad-537b-8983-00126c2a3abe"
-version = "2.5.0"
+version = "2.5.4"
 
 [[Rmath]]
-deps = ["BinaryProvider", "Libdl", "Random", "Statistics"]
-git-tree-sha1 = "2bbddcb984a1d08612d0c4abb5b4774883f6fa98"
+deps = ["Random", "Rmath_jll"]
+git-tree-sha1 = "86c5647b565873641538d8f812c04e4c9dbeb370"
 uuid = "79098fc4-a85e-5d69-aa6a-4863f24498fa"
-version = "0.6.0"
+version = "0.6.1"
+
+[[Rmath_jll]]
+deps = ["Libdl", "Pkg"]
+git-tree-sha1 = "1660f8fefbf5ab9c67560513131d4e933012fc4b"
+uuid = "f50d1b31-88e8-58de-be2c-1cc44531875f"
+version = "0.2.2+0"
 
 [[Roots]]
 deps = ["Printf"]
-git-tree-sha1 = "dcc013908465ca1019b34b4bf547b6a187d195f9"
+git-tree-sha1 = "869a9990ec6347862d59040d00416ecd0683b965"
 uuid = "f2b01f46-fcfa-551c-844a-d8ac1e96c665"
-version = "0.8.4"
+version = "1.0.0"
 
 [[SHA]]
 uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
@@ -832,11 +833,6 @@ uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
 deps = ["Distributed", "Mmap", "Random", "Serialization"]
 uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
 
-[[ShiftedArrays]]
-git-tree-sha1 = "22395afdcf37d6709a5a0766cc4a5ca52cb85ea0"
-uuid = "1277b4bf-5013-50f5-be3d-901d8477a67a"
-version = "1.0.0"
-
 [[Showoff]]
 deps = ["Dates"]
 git-tree-sha1 = "e032c9df551fb23c9f98ae1064de074111b7bc39"
@@ -870,9 +866,9 @@ uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
 [[SparseDiffTools]]
 deps = ["Adapt", "ArrayInterface", "Compat", "DataStructures", "FiniteDiff", "ForwardDiff", "InteractiveUtils", "LightGraphs", "LinearAlgebra", "Requires", "SparseArrays", "VertexSafeGraphs"]
-git-tree-sha1 = "f65937edd6d1e9ba48da16315c14c12568867dd6"
+git-tree-sha1 = "6429f706e7da24a8c1c5e0416c3f0ce9974ab991"
 uuid = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
-version = "1.3.3"
+version = "1.4.0"
 
 [[SpatialIndexing]]
 deps = ["Printf", "Random", "Test"]
@@ -882,9 +878,9 @@ version = "0.1.2"
 
 [[SpecialFunctions]]
 deps = ["OpenSpecFun_jll"]
-git-tree-sha1 = "268052ee908b2c086cc0011f528694f02f3e2408"
+git-tree-sha1 = "e19b98acb182567bcb7b75bb5d9eedf3a3b5ec6c"
 uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
-version = "0.9.0"
+version = "0.10.0"
 
 [[StaticArrays]]
 deps = ["LinearAlgebra", "Random", "Statistics"]
@@ -898,21 +894,15 @@ uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
 [[StatsBase]]
 deps = ["DataAPI", "DataStructures", "LinearAlgebra", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics"]
-git-tree-sha1 = "c53e809e63fe5cf5de13632090bc3520649c9950"
+git-tree-sha1 = "19bfcb46245f69ff4013b3df3b977a289852c3a1"
 uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
-version = "0.32.0"
+version = "0.32.2"
 
 [[StatsFuns]]
 deps = ["Rmath", "SpecialFunctions"]
-git-tree-sha1 = "79982835d2ff3970685cb704500909c94189bde9"
+git-tree-sha1 = "f290ddd5fdedeadd10e961eb3f4d3340f09d030a"
 uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
-version = "0.9.3"
-
-[[StatsModels]]
-deps = ["DataAPI", "DataStructures", "LinearAlgebra", "ShiftedArrays", "SparseArrays", "StatsBase", "Tables"]
-git-tree-sha1 = "f4a967704cae9426654cf4649561f263a6dc8419"
-uuid = "3eaba693-59b7-5ba5-a881-562e759f1c8d"
-version = "0.6.7"
+version = "0.9.4"
 
 [[SuiteSparse]]
 deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
@@ -924,11 +914,11 @@ git-tree-sha1 = "b1ad568ba658d8cbb3b892ed5380a6f3e781a81e"
 uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
 version = "1.0.0"
 
-[[Tables]]
-deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
-git-tree-sha1 = "aaed7b3b00248ff6a794375ad6adf30f30ca5591"
-uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
-version = "0.2.11"
+[[TerminalLoggers]]
+deps = ["LeftChildRightSiblingTrees", "Logging", "Markdown", "Printf", "ProgressLogging", "UUIDs"]
+git-tree-sha1 = "8c05be75dfe73d90e5dfb6293e0c852013f7282d"
+uuid = "5d786b92-1e48-4d6f-9151-6b4477ca9bed"
+version = "0.1.1"
 
 [[Test]]
 deps = ["Distributed", "InteractiveUtils", "Logging", "Random"]
@@ -942,9 +932,9 @@ version = "0.5.3"
 
 [[ToeplitzMatrices]]
 deps = ["AbstractFFTs", "FFTW", "LinearAlgebra", "StatsBase"]
-git-tree-sha1 = "5351f20c159d02fa1372076d0731a38066efd137"
+git-tree-sha1 = "8bc327ddbce87cb5976e27ab4adb9ffce5345a05"
 uuid = "c751599d-da0a-543b-9d20-d0a503d91d24"
-version = "0.6.0"
+version = "0.6.1"
 
 [[Tracker]]
 deps = ["Adapt", "DiffRules", "ForwardDiff", "LinearAlgebra", "MacroTools", "NNlib", "NaNMath", "Printf", "Random", "Requires", "SpecialFunctions", "Statistics", "Test"]
@@ -968,6 +958,11 @@ version = "0.3.0"
 deps = ["Random", "SHA"]
 uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 
+[[UnPack]]
+git-tree-sha1 = "e0cb9715adda456f7657e45377fd3063bf87179a"
+uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
+version = "0.1.0"
+
 [[Unicode]]
 uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
 
@@ -985,15 +980,15 @@ version = "0.9.1"
 
 [[Zlib_jll]]
 deps = ["Libdl", "Pkg"]
-git-tree-sha1 = "5618a43055eb09377edca21d19d0e99bce24a9c3"
+git-tree-sha1 = "fd36a6739e256527287c5444960d0266712cd49e"
 uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
-version = "1.2.11+7"
+version = "1.2.11+8"
 
 [[Zygote]]
-deps = ["DiffRules", "FFTW", "FillArrays", "ForwardDiff", "IRTools", "InteractiveUtils", "LinearAlgebra", "MacroTools", "NNlib", "NaNMath", "Random", "Requires", "SpecialFunctions", "Statistics", "ZygoteRules"]
-git-tree-sha1 = "ca4dfa4de0a0e2c1da6c8c67d3b9af99645b57fc"
+deps = ["ArrayLayouts", "DiffRules", "FFTW", "FillArrays", "ForwardDiff", "IRTools", "InteractiveUtils", "LinearAlgebra", "MacroTools", "NNlib", "NaNMath", "Random", "Requires", "SpecialFunctions", "Statistics", "ZygoteRules"]
+git-tree-sha1 = "4a3c8decdf1d498cd13fe29827350d727a3b3854"
 uuid = "e88e6eb3-aa80-5325-afca-941959d7151f"
-version = "0.4.6"
+version = "0.4.10"
 
 [[ZygoteRules]]
 deps = ["MacroTools"]
diff --git a/Climate/NeuralPDE/Project.toml b/Climate/NeuralPDE/Project.toml
index 37c6125..7623417 100644
--- a/Climate/NeuralPDE/Project.toml
+++ b/Climate/NeuralPDE/Project.toml
@@ -1,10 +1,10 @@
 [deps]
 ApproxFun = "28f2ccd6-bb30-5033-b560-165f7b14dc2f"
 BlackBoxOptim = "a134a8b2-14d6-55f6-9291-3336d3ab0209"
-CuArrays = "3a865a2d-5b23-5a0f-bc46-62713ec82fae"
 DiffEqFlux = "aae7a2af-3d4f-5e19-a356-7da93b79d9d0"
 DiffEqSensitivity = "41bf760c-e81c-5289-8e54-58b1f1f8abe2"
 Flux = "587475ba-b771-5e3f-ad9e-33799f191a9c"
+IterTools = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
 JLD2 = "033835bb-8acc-5ee8-8aae-3f567f8a3819"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Optim = "429524aa-4258-5aef-a3af-852621145aeb"
diff --git a/Climate/NeuralPDE/data_copy.jl b/Climate/NeuralPDE/data_copy.jl
new file mode 100644
index 0000000..73b5779
--- /dev/null
+++ b/Climate/NeuralPDE/data_copy.jl
@@ -0,0 +1,109 @@
+cd(@__DIR__)
+using Pkg; Pkg.activate("."); Pkg.instantiate()
+
+using Revise
+using Optim, Zygote
+using OrdinaryDiffEq, Flux, DiffEqFlux, LinearAlgebra, Plots
+using DiffEqSensitivity, JLD2
+const EIGEN_EST = Ref(0.0f0)
+const USE_GPU = Ref(false)
+USE_GPU[] = false # the network is small enough such that CPU works just great
+#USE_GPU[] = true
+
+USE_GPU[] && (using CuArrays)
+
+_gpu(arg) = USE_GPU[] ? gpu(arg) : cpu(arg)
+_cu(arg) = USE_GPU[] ? cu(arg) : identity(arg)
+
+function getops(grid, T=Float32)
+    N, dz = length(grid), step(grid)
+    d = ones(N-2)
+    dl = ones(N-3) # super/lower diagonal
+    zv = zeros(N-2) # zero diagonal used to extend D* for boundary conditions
+
+    # D1 first order discretization of ∂_z
+    D1 = diagm(-1 => -dl, 0 => d)
+    D1[1, :] .= 0
+    D1[end, :] .= 0
+
+    # D2 discretization of ∂_zz
+    D2 = diagm(-1 => dl, 0 => -2*d, 1 => dl)
+    κ = 0.05
+    D2[1, 1] = D2[end, end] = -1
+    D2 = (κ/(dz^2)).*D2 #add the constant κ as the equation requires and finish the discretization
+    display(D2), display(D1)
+
+    EIGEN_EST[] = maximum(abs, eigvals(D2))
+    D1 = _cu(D1)
+    D2 = _cu(D2)
+    return (D1=T.(D1), D2=T.(D2))
+end
+
+file = jldopen("../DataGeneration/rayleigh_taylor_instability_3d_horizontal_averages.jld2")
+
+Is = keys(file["timeseries/t"])
+
+N = file["grid/Nz"]
+Lz = file["grid/Lz"]
+Nt = length(Is)
+
+t = Float32.(zeros(Nt))
+soldata = Float32.(zeros(Nt, N))
+
+for (i, I) in enumerate(Is)
+    t[i] = file["timeseries/t/$I"]
+    soldata[i, :] .= file["timeseries/b/$I"]
+end
+
+grid = range(0, 1, length = N)
+tspan = (t[1], t[end])
+u0 = _cu(soldata[1,2:end-1])
+ops = getops(grid)
+
+ann = FastChain(FastDense(N-2,N-2,tanh), FastDense(N-2,N-2,tanh), FastDense(N-2,N-2,tanh),
+            FastDense(N-2,N-2,tanh), FastDense(N-2,N-2,tanh)) |> _gpu
+pp = initial_params(ann)
+lyrs = Flux.params(pp)
+
+function dudt_(u,p,t)
+    Φ = ann
+    return ops.D1*Φ(u, p) + ops.D2*u
+end
+
+function predict_adjoint(fullp)
+    Array(concrete_solve(prob, 
+			  ROCK4(eigen_est = (integ)->integ.eigen_est = EIGEN_EST[]),
+			  u0, fullp, saveat = saveat))
+end
+
+function loss_adjoint(fullp)
+    pre = predict_adjoint(fullp)
+    sum(abs2, training_data - pre)
+end
+
+function cb(opt_state:: Optim.OptimizationState)
+    display(opt_state.value)
+    false
+end
+
+cb(trace::Optim.OptimizationTrace) = cb(last(trace))
+
+prob = ODEProblem{false}(dudt_,u0,tspan,pp)
+nn = 1
+print("here")
+saveat = t
+soldata = soldata'
+soldata = soldata[2:end-1, :]
+training_data = _cu(soldata)
+epochs = Iterators.repeated((), 20)
+concrete_solve(prob, ROCK4(eigen_est = (integ)->integ.eigen_est = EIGEN_EST[]), u0, pp)
+learning_rate = ADAM(0.01)
+res = DiffEqFlux.sciml_train(loss_adjoint, pp, BFGS(initial_stepnorm=0.01), cb=cb)
+
+#Flux.train!(loss_adjoint, lyrs, epochs, learning_rate, cb=cb)
+#=
+learning_rate = ADAM(0.001)
+epochs = Iterators.repeated((), 300)
+Flux.train!(loss_adjoint, lyrs, epochs, learning_rate, cb=cb)
+@time loss_adjoint()
+=#
diff --git a/Climate/NeuralPDE/example.jl b/Climate/NeuralPDE/example.jl
new file mode 100644
index 0000000..c4d2305
--- /dev/null
+++ b/Climate/NeuralPDE/example.jl
@@ -0,0 +1,50 @@
+using DiffEqFlux, Flux, Optim, OrdinaryDiffEq, IterTools
+
+u0 = Float32(1.1)
+tspan = (0.0f0,25.0f0)
+
+ann = FastChain(FastDense(2,16,tanh), FastDense(16,16,tanh), FastDense(16,1))
+p1 = initial_params(ann)
+p2 = Float32[0.5,-0.5]
+p3 = [p1;p2]
+θ = Float32[u0;p3]
+
+function dudt_(du,u,p,t)
+    x, y = u
+    du[1] = ann(u,p[1:length(p1)])[1]
+    du[2] = p[end-1]*y + p[end]*x
+end
+prob = ODEProblem(dudt_,u0,tspan,p3)
+concrete_solve(prob,Tsit5(),[0f0,u0],p3,abstol=1e-8,reltol=1e-6)
+
+function predict_adjoint(θ)
+  Array(concrete_solve(prob,Tsit5(),[0f0,θ[1]],θ[2:end],saveat=0.0:1:25.0))
+end
+function loss_adjoint(θ, X, Y)
+	print("X", X)
+	print("Y", Y)
+	sum(abs2,predict_adjoint(θ)[2,:].-1)
+end
+#l = loss_adjoint(θ, "x0", "y0")
+
+cb = function (θ,l)
+  println(l)
+  #display(plot(solve(remake(prob,p=Flux.data(p3),u0=Flux.data(u0)),Tsit5(),saveat=0.1),ylim=(0,6)))
+  return false
+end
+
+# Display the ODE with the current parameter values.
+#cb(θ,l)
+
+function mini_batch(X, Y)
+	i = rand(1:size(X)[1])
+	return (x[i,:], Y[i,:])
+end
+
+
+x = [1 2; 3 4; 5 6; 7 8]
+y = [1 ; 0 ; 1; 0]
+data = [mini_batch(x,y) for i in 1:20]
+#train_loader = Flux.Data.Data
+#loss1 = loss_adjoint(θ)
+res = DiffEqFlux.sciml_train(loss_adjoint, θ, BFGS(initial_stepnorm=0.01), data, cb = cb)
diff --git a/Climate/NeuralPDE/julia-vim b/Climate/NeuralPDE/julia-vim
new file mode 160000
index 0000000..1db5eed
--- /dev/null
+++ b/Climate/NeuralPDE/julia-vim
@@ -0,0 +1 @@
+Subproject commit 1db5eed71d7f5fe4b95b0dadfb3f798983485554
diff --git a/Climate/NeuralPDE/npde.jl b/Climate/NeuralPDE/npde.jl
index 1193b31..01e2bd8 100644
--- a/Climate/NeuralPDE/npde.jl
+++ b/Climate/NeuralPDE/npde.jl
@@ -4,16 +4,24 @@ using Revise
 using Zygote, Optim
 using OrdinaryDiffEq, Flux, DiffEqFlux, LinearAlgebra, Plots
 using DiffEqSensitivity
+using IterTools
+using Random
+#using CuArrays
+#Random.seed!(0)
+print(rand(1:100))
+
 const EIGEN_EST = Ref(0.0f0)
+
 const USE_GPU = Ref(false)
 
-USE_GPU[] = false # the network is small enough such that CPU works just great
+USE_GPU[] = false# the network is small enough such that CPU works just great
 
 USE_GPU[] && (using CuArrays)
 
 _gpu(arg) = USE_GPU[] ? gpu(arg) : cpu(arg)
 _cu(arg) = USE_GPU[] ? cu(arg) : identity(arg)
 
+
 function getops(grid, T=Float32)
     N, dz = length(grid), step(grid)
     d = ones(N-2)
@@ -45,6 +53,7 @@ function getops(grid, T=Float32)
     return (D1=T.(D1), D2=T.(D2))
 end
 
+
 function getu0(grid, T=Float32)
     z = grid[2:N-1]
     f0 = z -> T(exp(-200*(z-0.75)^2))
@@ -57,7 +66,7 @@ function ode_i(u, p, t)
 end
 
 function ground_truth(grid, tspan)
-    prob = ODEProblem(ode_i, u0, (tspan[1], tspan[2]+0.1), ops)
+    prob = ODEProblem(ode_i, u0, (tspan[1], tspan[2]), ops)
     sol = solve(prob, ROCK4(eigen_est = (integ)->integ.eigen_est = EIGEN_EST[]), abstol = 1e-9, reltol = 1e-9)
     return sol
 end
@@ -65,68 +74,66 @@ end
 N = 32
 grid = range(0, 1, length = N)
 tspan = (0.0f0, 1.5f0)
-u0 = getu0(grid)
+u0 = getu0(grid) 
 ops = getops(grid)
 soldata = ground_truth(grid, tspan)
 
-ann = Chain(Dense(30,8,tanh), Dense(8,30,tanh)) |> _gpu
-pp, re = Flux.destructure(ann)
+
+ann = FastChain(FastDense(30,8,tanh), FastDense(8,30,tanh)) |> _gpu
+pp = initial_params(ann)
 lyrs = Flux.params(pp)
+
+
+
 function dudt_(u,p,t)
-    Φ = re(p)
-    return ops.D1*Φ(u) + ops.D2*u
+    return ops.D1*ann(u,p) + ops.D2*u
 end
 
-function predict_adjoint(fullp)
+function predict_adjoint(fullp, i)
     Array(concrete_solve(prob,
                          ROCK4(eigen_est = (integ)->integ.eigen_est = EIGEN_EST[]),
-    u0, fullp, saveat = saveat))
+    u0, fullp, saveat = saveat[i[1]:i[1]+i[2]]))
 end
 
-function loss_adjoint(fullp)
-    pre = predict_adjoint(fullp)
-    sum(abs2, training_data - pre)
+function loss_adjoint(fullp, x, y)
+    pre = predict_adjoint(fullp,(x,y))
+    sum(abs2, training_data[:,x:x+y] - pre)
 end
 
 
-
-function cb(opt_state:: Optim.OptimizationState)
-    cur_pred = collect(predict_adjoint(opt_state.metadata["x"]))
-    n = size(training_data, 1)
-    pl = scatter(1:n,training_data[:,10],label="data", legend =:bottomright,title="Spatial Plot at t=$(saveat[10])")
-    scatter!(pl,1:n,cur_pred[:,10],label="prediction")
-    pl2 = scatter(saveat,training_data[N÷2,:],label="data", legend =:bottomright, title="Timeseries Plot at Middle X")
-    scatter!(pl2,saveat,cur_pred[N÷2,:],label="prediction")
-    display(plot(pl, pl2, size=(600, 300)))
-    display(opt_state.value)    
-    false
+function mini_batch(training_data, k)
+	return ((rand(1:size(training_data)[2] -k), k) for i in 1:10000)
 end
 
-cb(trace::Optim.OptimizationTrace) = cb(last(trace))
+
+cb = function(fullp, l)
+    display(l)
+    return false
+end
 
 
-saveat = range(tspan..., length = 30) #time range
+saveat = range(tspan..., length = 40) 
 prob = ODEProblem{false}(dudt_,u0,tspan,pp)
 training_data = _cu(soldata(saveat))
-concrete_solve(prob, ROCK4(eigen_est = (integ)->integ.eigen_est = EIGEN_EST[]), u0, pp) 
-loss_adjoint(pp)
 
-function loss_adjoint_gradient!(G, fullp)
-    G .= Zygote.gradient(loss_adjoint, fullp)[1]
-end
-
-result =  optimize(loss_adjoint, loss_adjoint_gradient!, pp, BFGS(), Optim.Options(extended_trace=true,callback = cb))
-
-prob2 = ODEProblem{false}(dudt_,u0,(0f0,10f0),pp)
-@time full_sol = solve(prob2,
-                       ROCK2(eigen_est = (integ)->integ.eigen_est = EIGEN_EST[]),
-                       saveat = saveat, abstol=1e-4, reltol=1e-2)
-
-cur_pred = collect((predict_adjoint(result.minimizer)))
-n = size(training_data, 1)
-pl = scatter(1:n,training_data[:,10],label="data", legend =:bottomright)
-scatter!(pl,1:n,cur_pred[:,10],label="prediction",title="Spatial Plot at t=$(saveat[10])")
-pl2 = scatter(saveat,training_data[N÷2,:],label="data", legend =:bottomright, title="Time Series Plot: Middle X")
-scatter!(pl2,saveat,cur_pred[N÷2,:],label="prediction")
-plot(pl, pl2, size=(600, 300))
-savefig("npde_fit.pdf")
+concrete_solve(prob, ROCK4(eigen_est = (integ)->integ.eigen_est = EIGEN_EST[]), u0, pp) 
+#loss_adjoint(pp)
+
+
+k = 15
+data = ((rand(1:size(training_data)[2] -k), k) for i in 1:10000)
+res = DiffEqFlux.sciml_train(loss_adjoint, pp, BFGS(initial_stepnorm=0.01), data,cb = cb)
+
+#prob2 = ODEProblem{false}(dudt_,u0,(0f0,10f0),pp)
+#@time full_sol = solve(prob2,
+#                       ROCK2(eigen_est = (integ)->integ.eigen_est = EIGEN_EST[]),
+#                       saveat = saveat, abstol=1e-4, reltol=1e-2)
+#
+#cur_pred = collect((predict_adjoint(result.minimizer)))
+#n = size(training_data, 1)
+#pl = scatter(1:n,training_data[:,10],label="data", legend =:bottomright)
+#scatter!(pl,1:n,cur_pred[:,10],label="prediction",title="Spatial Plot at t=$(saveat[10])")
+#pl2 = scatter(saveat,training_data[N÷2,:],label="data", legend =:bottomright, title="Time Series Plot: Middle X")
+#scatter!(pl2,saveat,cur_pred[N÷2,:],label="prediction")
+#plot(pl, pl2, size=(600, 300))
+#savefig("npde_fit.pdf")
diff --git a/Climate/NeuralPDE/npde_data.jl b/Climate/NeuralPDE/npde_data.jl
index 9a6d6f2..16feaf4 100644
--- a/Climate/NeuralPDE/npde_data.jl
+++ b/Climate/NeuralPDE/npde_data.jl
@@ -4,10 +4,11 @@ using Pkg; Pkg.activate("."); Pkg.instantiate()
 using Revise
 using OrdinaryDiffEq, Flux, DiffEqFlux, LinearAlgebra, Plots
 using DiffEqSensitivity, JLD2
+using Zygote, Optim
 const EIGEN_EST = Ref(0.0f0)
 const USE_GPU = Ref(false)
 #USE_GPU[] = false # the network is small enough such that CPU works just great
-USE_GPU[] = true
+USE_GPU[] = false
 
 USE_GPU[] && (using CuArrays)
 
@@ -39,77 +40,73 @@ function getops(grid, T=Float32)
 end
 
 file = jldopen("../DataGeneration/rayleigh_taylor_instability_3d_horizontal_averages.jld2")
-
 Is = keys(file["timeseries/t"])
 
-N = file["grid/Nz"]
+N = floor(Int, file["grid/Nz"]/2)
 Lz = file["grid/Lz"]
-Nt = length(Is)
+Nt = floor(Int, length(Is))
 
 t = Float32.(zeros(Nt))
 soldata = Float32.(zeros(Nt, N))
-
 for (i, I) in enumerate(Is)
-    t[i] = file["timeseries/t/$I"]
-    soldata[i, :] .= file["timeseries/b/$I"]
+        t[i] = file["timeseries/t/$I"]
+        soldata[i, :] .= file["timeseries/b/$I"][1:2:end]
 end
-
 grid = range(0, 1, length = N)
 tspan = (t[1], t[end])
-u0 = _cu(soldata[1,2:end-1])
+u0 = _cu(soldata[1, 2:end-1])
 ops = getops(grid)
-
-ann = Chain(Dense(N-2,N-2,tanh), Dense(N-2,N-2,tanh), Dense(N-2,N-2,tanh),
-            Dense(N-2,N-2,tanh), Dense(N-2,N-2,tanh)) |> _gpu
-pp = param(Flux.data(DiffEqFlux.destructure(ann)))
+ann = FastChain(FastDense(N-2,N-2,tanh), FastDense(N-2,N-2,tanh), FastDense(N-2,N-2,tanh),
+           FastDense(N-2,N-2,tanh), FastDense(N-2,N-2,tanh))
+pp = initial_params(ann)
 lyrs = Flux.params(pp)
 
-function dudt(u::TrackedArray,p,t)
-    Φ = DiffEqFlux.restructure(ann, p)
-    return ops.D1*Φ(u) + ops.D2*u
+
+
+
+function dudt_(u,p,t)
+    Φ = ann
+    return ops.D1*Φ(u,p) + ops.D2*u
 end
-function dudt(u::AbstractArray,p,t)
-    Φ = DiffEqFlux.restructure(ann, p)
-    return ops.D1*Tracker.data(Φ(u)) + ops.D2*u
+
+function predict_adjoint(fullp, i)    
+	Array(concrete_solve(prob,
+			     ROCK4(eigen_est = (integ)->integ.eigen_est = EIGEN_EST[]),
+			     u0, fullp, saveat = saveat[i[1]:i[1]+i[2]]))
 end
 
-predict_adjoint() = diffeq_adjoint(pp,
-                              prob,
-                              ROCK4(eigen_est = (integ)->integ.eigen_est = EIGEN_EST[]),
-                              u0=u0, saveat = saveat,
-                              reltol=1e-5, abstol=1e-6,
-                              # no back solve
-                              sensealg=SensitivityAlg(quad=false, backsolve=false))
-
-function loss_adjoint()
-    pre = predict_adjoint()
-    sum(abs2, training_data - pre)
+function loss_adjoint(fullp, x, y)
+    pre = predict_adjoint(fullp, (x,y))
+    sum(abs2, training_data[:, x:x+y] - pre)
 end
 
-cb = function ()
-    arr = Array(training_data)
-    cur_pred = collect(Flux.data(predict_adjoint()))
-    n = size(arr, 1)
-    pl = scatter(1:n,arr[:,10],label="data", legend =:bottomright, title = "10th time over space")
-    scatter!(pl,1:n,cur_pred[:,10],label="prediction")
-    pl2 = scatter(saveat,arr[end÷2,:],label="data", legend =:bottomright, title = "middle point over time")
-    scatter!(pl2,saveat,cur_pred[end÷2,:],label="prediction")
-    #display(plot(pl, pl2, size=(600, 300)))
-    display(loss_adjoint())
+function cb(p, l)
+	display(l)
+	false
 end
 
-prob = ODEProblem{false}(dudt,u0,tspan,pp)
+
+prob = ODEProblem{false}(dudt_,u0,tspan,pp)
+#concrete_solve(prob, ROCK4(eigen_est = (integ)->integ.eigen_est = EIGEN_EST[]), u0, pp)
+
 nn = 1
 saveat = t
 soldata = soldata'
 soldata = soldata[2:end-1, :]
 training_data = _cu(soldata)
-epochs = Iterators.repeated((), 20)
-learning_rate = ADAM(0.01)
-Flux.train!(loss_adjoint, lyrs, epochs, learning_rate, cb=cb)
+
+k = 15
+data = ((rand(1:size(training_data)[2] -k), k) for i in 1:10000) 
+
+res = DiffEqFlux.sciml_train(loss_adjoint, pp, BFGS(initial_stepnorm=0.01), data, cb=cb)
+
+
+#=
 #=
 learning_rate = ADAM(0.001)
 epochs = Iterators.repeated((), 300)
 Flux.train!(loss_adjoint, lyrs, epochs, learning_rate, cb=cb)
 @time loss_adjoint()
 =#
+=#
+
diff --git a/Climate/NeuralPDE/npde_fit.pdf b/Climate/NeuralPDE/npde_fit.pdf
index f69dcc2..3dd5502 100644
Binary files a/Climate/NeuralPDE/npde_fit.pdf and b/Climate/NeuralPDE/npde_fit.pdf differ
diff --git a/Climate/NeuralPDE/temp.jl b/Climate/NeuralPDE/temp.jl
new file mode 100644
index 0000000..106d5ce
--- /dev/null
+++ b/Climate/NeuralPDE/temp.jl
@@ -0,0 +1,36 @@
+using DiffEqFlux, Flux, Optim, OrdinaryDiffEq
+
+u0 = Float32(1.1)
+tspan = (0.0f0,25.0f0)
+
+ann = FastChain(FastDense(2,16,tanh), FastDense(16,16,tanh), FastDense(16,1))
+p1 = initial_params(ann)
+p2 = Float32[0.5,-0.5]
+p3 = [p1;p2]
+θ = Float32[u0;p3]
+
+function dudt_(du,u,p,t)
+    x, y = u
+    du[1] = ann(u,p[1:length(p1)])[1]
+    du[2] = p[end-1]*y + p[end]*x
+end
+prob = ODEProblem(dudt_,u0,tspan,p3)
+concrete_solve(prob,Tsit5(),[0f0,u0],p3,abstol=1e-8,reltol=1e-6)
+
+function predict_adjoint(θ)
+  Array(concrete_solve(prob,Tsit5(),[0f0,θ[1]],θ[2:end],saveat=0.0:1:25.0))
+end
+loss_adjoint(θ) = sum(abs2,predict_adjoint(θ)[2,:].-1)
+l = loss_adjoint(θ)
+
+cb = function (θ,l)
+  println(l)
+  #display(plot(solve(remake(prob,p=Flux.data(p3),u0=Flux.data(u0)),Tsit5(),saveat=0.1),ylim=(0,6)))
+  return false
+end
+
+# Display the ODE with the current parameter values.
+cb(θ,l)
+
+loss1 = loss_adjoint(θ)
+res = DiffEqFlux.sciml_train(loss_adjoint, θ, BFGS(initial_stepnorm=0.01), cb = cb)