Reproducing example
The packages for this example are documented in the Project.toml.
Accessing example
This can also be accessed as a plain script.
Description
This example shows a simple use case for NormalizingFlowFilters.
First, we import the necessary packages.
using Pkg: Pkg
Pkg.activate(@__DIR__)
Pkg.instantiate()
using CairoMakie
using NormalizingFlowFilters
using Random: randn, seed!
using Statistics: mean, std, cov
using Test
using Pkg: Pkg
@static if VERSION >= v"1.10"
using PairPlots: PairPlots, pairplot
end
function display_interactive(fig)
if isinteractive()
display(fig)
else
fig
end
end
smalltest = get(ENV, "NormalizingFlowFilters_smalltest", "false")
if !(smalltest in ("true", "false"))
error("Invalid environment variable value NormalizingFlowFilters_smalltest: $smalltest")
end
smalltest = smalltest == "true"falseThen define the filter.
N = smalltest ? 2^4 : 2^11
Nx = 2
seed!(0x84fb4b2c)
glow_config = ConditionalGlowOptions(; chan_x=Nx, chan_y=Nx)
network = NetworkConditionalGlow(2, glow_config)
optimizer_config = OptimizerOptions(; lr=1e-3)
optimizer = create_optimizer(optimizer_config)
device = cpu
training_config = TrainingOptions(;
n_epochs=smalltest ? 10 : 45,
num_post_samples=1,
noise_lev_y=1e-3,
noise_lev_x=1e-3,
batch_size=smalltest ? 2^2 : 2^9,
validation_perc=2^(-1),
)
filter = NormalizingFlowFilter(network, optimizer; device, training_config)NormalizingFlowFilters.NormalizingFlowFilter(InvertibleNetworks.NetworkConditionalGlow, InvertibleNetworks.NetworkConditionalGlow, Flux.Optimise.Optimiser(Any[Flux.Optimise.ClipNorm{Float32}(3.0f0), Flux.Optimise.Adam(0.001, (0.9, 0.999), 1.0e-8, IdDict{Any, Any}())]), Flux.cpu, NormalizingFlowFilters.TrainingOptions(45, 512, 0.001, 0.001, 1, 0.5, 2))We generate an ensemble.
# N ensemble members from a unit normal.
prior_state = randn(Float64, Nx, N)
prior_state .-= mean(prior_state; dims=2)
prior_state ./= std(prior_state; dims=2)
function to_table(a; prefix=:x)
return (; (Symbol(prefix, i) => row for (i, row) in enumerate(eachrow(a)))...)
end
combine_tables(a, b) = (; a..., b...)
table_prior_state = to_table(prior_state)
@static if VERSION >= v"1.10"
kde_bandwidth =
training_config.noise_lev_x /
PairPlots.KernelDensity.default_bandwidth(prior_state[1, :])
table_prior_state_mean = to_table(mean(prior_state; dims=2)[:, 1])
fig = pairplot(
table_prior_state => (
PairPlots.Hist(; colormap=:Blues),
PairPlots.MarginDensity(;
bandwidth=kde_bandwidth, color=RGBf((49, 130, 189) ./ 255...)
),
PairPlots.TrendLine(; color=:red),
PairPlots.Correlation(),
PairPlots.Scatter(),
),
PairPlots.Truth(
table_prior_state_mean; label="Mean Values", color=(:black, 0.5), linewidth=4
),
)
supertitle = Label(fig[0, :], "prior state"; fontsize=30)
resize_to_layout!(fig)
display_interactive(fig)
end
Apply observation operator.
# Identity observation operator with some noise.
prior_obs = 0.5 .* deepcopy(prior_state) .+ 0.5 .* randn(Float64, size(prior_state))
table_prior_obs = to_table(prior_obs; prefix=:y)
@static if VERSION >= v"1.10"
table_prior_obs_mean = to_table(mean(prior_obs; dims=2)[:, 1]; prefix=:y)
fig = pairplot(
table_prior_obs => (
PairPlots.Hist(; colormap=:Blues),
PairPlots.MarginDensity(;
bandwidth=kde_bandwidth, color=RGBf((49, 130, 189) ./ 255...)
),
PairPlots.TrendLine(; color=:red),
PairPlots.Correlation(),
PairPlots.Scatter(),
),
PairPlots.Truth(
table_prior_obs_mean; label="Mean Values", color=(:black, 0.5), linewidth=4
),
)
supertitle = Label(fig[0, :], "prior observation"; fontsize=30)
resize_to_layout!(fig)
display_interactive(fig)
end
Look at how observations correlate to data.
@static if VERSION >= v"1.10"
combo_table = combine_tables(table_prior_state, table_prior_obs)
combo_table_mean = combine_tables(table_prior_state_mean, table_prior_obs_mean)
fig = pairplot(
combo_table => (
PairPlots.Hist(; colormap=:Blues),
PairPlots.MarginDensity(;
bandwidth=kde_bandwidth, color=RGBf((49, 130, 189) ./ 255...)
),
PairPlots.TrendLine(; color=:red),
PairPlots.Correlation(),
PairPlots.Scatter(),
),
PairPlots.Truth(
combo_table_mean; label="Mean Values", color=(:black, 0.5), linewidth=4
),
)
supertitle = Label(fig[0, :], "prior state-observation"; fontsize=30)
resize_to_layout!(fig)
display_interactive(fig)
end
Then we assimilate an observation. Here, we just pick an arbitrary one.
y_obs = zeros(Nx)
log_data = Dict{Symbol,Any}()
posterior = assimilate_data(filter, prior_state, prior_obs, y_obs, log_data)2×2048 Matrix{Float32}:
0.305756 0.81438 -0.228569 0.687502 1.41026 -0.176399 -0.189961 0.813874 0.495936 -0.200409 -0.475669 0.326596 0.624351 -0.264964 -1.31165 -0.462063 1.36516 -1.31596 0.643871 -1.07994 1.13909 -0.55851 1.52112 0.17886 1.01565 0.0300711 1.44019 0.190365 0.783838 1.1157 -0.29932 -0.726548 -0.192394 -0.235631 -0.373807 -0.584762 -0.451893 1.10132 5.84225f-5 0.673692 0.922575 1.19091 -0.36713 1.5131 -1.22852 1.68201 -0.333888 -1.02625 0.16567 -0.128024 -1.12273 0.0252432 1.52731 -0.48407 -1.23421 -0.377696 0.86131 0.436163 -0.714593 -0.132894 -0.308279 0.643637 -1.92185 -0.377593 1.33296 0.655443 -0.523988 -0.72274 0.400464 1.34253 0.0444438 1.21344 0.331165 0.181708 -0.75676 1.52271 -0.905681 2.16266 -0.48158 -0.100409 0.0140773 -0.61112 0.46894 -0.111019 -0.152456 1.70219 0.591855 -0.83641 -0.00246445 -1.40459 0.261119 2.18252 0.966882 2.41383 0.73663 1.35049 0.297246 1.01538 0.302012 0.0838997 -0.500185 0.420571 1.0935 -0.21447 0.893986 -0.242322 -0.146571 1.34787 0.27609 1.57241 -0.0415592 -0.374339 -0.754939 0.425975 -1.31538 -2.32515 0.086923 -0.0330882 -1.33466 -1.16461 -0.517237 0.446693 -0.0861981 0.996119 0.00651673 0.0321351 0.393452 -0.200236 -0.223634 -0.687061 -0.363882 0.0775958 -0.399819 -0.544241 1.43218 0.837052 0.836049 -0.328981 0.147878 0.0941816 -1.73536 0.129704 0.330495 0.727945 0.050864 -0.799246 0.421922 1.15138 1.20123 0.130028 -0.437956 -0.766167 0.121296 0.711231 0.843421 0.241876 0.341554 1.47522 0.866613 0.633163 -0.0897784 0.722346 -0.0449629 0.0353304 0.511094 0.336942 -1.95981 0.811991 -0.422665 0.19057 0.521094 0.62929 -0.121167 0.598005 -0.0770325 0.406657 1.09362 -1.90834 -0.179637 0.447652 0.451365 0.0202193 0.914044 -0.960064 0.753744 0.129748 -1.13679 0.83345 1.01285 -0.4296 -0.258761 0.264563 0.569063 -1.5849 -0.842116 -0.472893 0.774292 0.0140174 0.529812 -0.181071 -0.191234 -1.00108 0.287688 -0.127993 0.84651 -1.36686 0.573319 0.0604721 1.35911 0.632585 0.444985 -0.837424 1.17464 0.917815 0.579404 0.0455122 -0.060993 0.354378 -0.0813707 -0.619719 -1.36147 1.07423 0.474138 0.628317 -0.417253 0.325433 1.04953 -0.440695 -1.01172 0.182729 0.000380392 0.285116 -0.968763 0.529023 0.598228 0.659445 -0.548707 -1.17785 0.32412 0.252442 -0.460311 -1.20743 -1.40766 0.301706 0.0672443 0.513732 -0.982641 0.0323392 0.178333 -1.24616 -0.0496581 -0.318407 0.110459 0.278226 -0.620283 0.323582 1.05424 -1.42535 1.79196 0.0686176 0.0585125 0.896881 -0.149659 -2.37126 0.457429 -0.263795 0.222257 1.12944 -0.616784 -0.248518 -0.986025 1.08082 -0.27806 0.49375 -0.0575066 -1.25196 -0.417965 0.606981 0.310885 1.66303 0.659891 0.299742 1.08787 -0.221367 -0.388738 0.504577 0.150651 0.202265 -0.910569 1.59432 0.427194 -0.509407 -0.185768 1.12864 0.293189 -0.0431767 -0.0848889 -0.178703 -0.149267 -0.757771 0.555848 -0.0367536 -0.150068 -0.023709 -0.466486 1.0926 -1.32451 0.357532 0.475867 0.576065 0.764961 0.0702864 -1.15348 0.263106 -1.4901 -0.509966 0.685445 0.721422 -0.344091 0.640662 0.103716 0.891842 -0.341408 -0.137626 0.662077 -0.0447314 0.262835 0.00780233 0.0759005 0.160091 -1.12535 1.43011 1.28672 -0.51658 0.452004 -0.478034 0.122526 -0.362735 -0.121681 0.38809 -0.267861 0.18884 0.255583 -0.651816 -0.502358 -0.227563 -0.33355 -0.023786 1.33085 0.387826 0.0308594 0.344971 0.334517 -0.764341 0.0785726 0.145167 -0.0469804 -0.387367 -0.0224346 0.0369952 0.492248 0.24714 -1.03713 0.50231 -0.347493 -0.437513 0.39979 0.635796 -0.486245 0.0626491 0.114331 -1.10628 0.859526 0.230818 0.00841113 0.043951 -0.376266 0.448423 0.625755 -1.38608 0.837563 -0.388442 -0.892108 0.231444 0.750805 -1.70556 -0.308823 1.26059 1.03802 0.736658 0.386673 -0.658636 -0.047524 -0.172615 0.802144 0.139499 -0.305257 1.02971 0.443154 0.914014 -1.96061 -1.00998 0.284577 0.0186114 -1.28777 1.23639 1.41593 0.473737 0.590157 0.19964 -0.445898 -0.240353 -0.131446 0.274608 0.0428442 0.306281 0.158647 0.0223959 0.548274 -1.29074 -0.699801 0.964527 -1.28053 -0.635925 -0.413501 0.234396 -0.16219 0.765735 -1.32816 0.0476377 0.0975824 1.02508 -0.219662 -0.00392528 0.27539 0.157524 -0.642921 -0.0474651 -0.0436273 1.24678 0.0369633 0.0703889 0.509285 1.33047 -0.416854 -0.581074 -0.667715 0.849641 -0.140964 -0.687051 -0.53615 0.258373 0.353941 -1.24652 0.70787 -0.207322 -0.231406 0.970866 0.925253 0.059502 1.24476 -1.73267 -0.525059 0.266299 -0.914795 0.252094 -1.10676 -0.135608 -0.0615793 0.738995 -0.798386 0.511616 0.11696 -0.706014 -0.846526 0.168411 0.932491 1.21288 0.812658 0.0836939 -0.151622 -0.435874 -0.917128 -0.1263 0.117793 0.891284 -0.400716 -0.545886 0.473039 -0.913307 0.526913 0.974529 -2.02215 -0.318369 -1.52324 0.817319 1.47294 -0.418046 0.181346 -0.129758 0.428815 -0.687487 -0.885242 0.334579 0.246335 0.46529 0.878716 -1.91105 0.662577 0.617704 -0.347923 -0.757667 -0.158156 0.202393 -1.26563 0.283292 -0.619888 0.267058 -0.661029 0.723395 0.627797 0.243227 1.13686 0.171572 -1.24413 0.447116 0.04918 0.0410332 1.86617 0.0439934 -0.754883 0.0620228 0.595833 0.813978 -0.147042 -0.13117 0.613698 -0.143424 0.199323 -0.165411 0.575437 -1.26806 -0.832519 -0.987614 0.252092 0.412251 -0.0184925 -1.16097 1.99726 -0.052852 -0.040157 0.0351239 -0.00598954 -0.148337 0.0441643 -0.908471 0.0122886 0.52137 -2.00332 -0.619391 -0.861901 -0.0224958 0.87331 -0.159375 -0.34034 -0.532417 0.112446 0.477353 -2.25409 1.25666 0.379108 -0.125389 -0.631944 0.270125 -0.256167 0.653289 0.356966 -0.197045 -0.777374 -0.995124 -0.00912362 0.694018 -0.760114 0.189595 1.26924 0.584941 0.449386 0.677093 -2.3665 1.86475 -0.385289 -0.108151 0.0168363 -0.744723 0.888132 1.582 -2.61952 0.520128 -0.0935746 -0.568656 0.318314 -1.06262 0.333359 -0.363475 0.175364 0.829678 1.14421 0.666971 1.87018 -0.868308 0.809309 0.154507 0.485911 0.0339769 0.246146 -0.258644 -0.250297 -0.293936 -0.585659 -0.0657302 0.119165 -0.114829 0.201454 1.04333 0.0322779 -0.289939 -0.152479 0.0307748 -0.317092 -0.425044 -0.0115695 -1.46456 1.49496 0.348569 0.776491 -1.32601 -0.222 -1.39363 0.918377 1.23114 0.957475 0.0722557 -1.33785 0.287336 -0.59356 -0.525695 1.14831 0.690518 0.195379 -0.527668 -0.878299 0.0470061 0.0152406 -0.519271 -0.654194 -1.07395 1.35808 0.75713 -0.0237459 -1.81714 -1.86543 -1.62155 0.335594 -0.178133 1.33853 0.195714 0.0984758 0.59532 -0.269054 1.81534 -0.419398 0.150269 0.323013 -0.611374 0.204077 -0.475004 -0.15171 0.791568 0.533753 -0.694538 -2.09119 -0.60999 -0.703271 0.869136 0.818394 -0.188329 -1.09022 2.79186 0.862082 1.82611 1.5627 0.0963026 0.096033 0.87129 -0.232176 -0.578523 0.247988 -0.0576272 -0.592033 0.0782034 -0.193315 -0.810109 0.675307 -0.727731 0.456776 -1.23922 0.899687 0.134889 -0.410708 -0.337701 -0.452612 0.782191 -0.979776 -0.255969 -0.772785 1.20254 -0.883888 -0.105561 0.750866 -0.446355 -1.48583 0.598129 -0.156634 1.02268 0.549491 0.30814 1.93103 -1.48991 -1.04567 -0.501877 -1.25481 0.382805 0.848814 0.456595 0.956862 0.710066 -1.26903 -1.71036 1.23316 0.205281 -0.0493139 0.281924 -0.254002 0.671991 -0.343126 0.578893 -0.718033 0.73675 0.352436 0.367075 0.720319 -0.750159 0.182916 -0.799819 -1.01951 -0.258816 0.396695 -0.846321 -0.433853 -0.910715 -0.571477 -1.38664 0.75904 -0.0231163 -0.2911 0.469885 -0.829086 0.077533 -0.383392 -0.0639955 -0.521758 0.727483 -1.14057 -1.24296 0.970237 -0.171212 1.56371 -0.239503 0.676989 -1.12819 0.853132 1.0553 1.37191 -0.412326 0.20399 -1.49856 0.507168 -0.31644 0.332412 0.0388088 -0.257741 -1.54456 0.628568 0.691686 0.239297 -1.89041 -0.205929 0.469799 -1.39909 -0.123011 0.865279 -1.06387 1.93842 -0.381289 0.21553 -0.849261 0.773198 0.237105 -0.205558 -1.29955 -0.644015 -0.290264 -0.0939752 0.440793 -0.100937 0.495285 0.195254 0.0323155 -0.728005 0.0694509 0.715212 0.278788 0.216602 -0.296856 -0.795288 -1.16804 1.79167 1.58687 0.816082 -0.0153456 -0.465086 -1.35031 -0.798678 1.02842 -0.580904 -0.270042 0.203283 1.10186 0.288476 1.41988 -0.704356 -0.346359 -0.416119 -0.0668005 0.53554 -0.55174 0.212535 0.645009 0.0878021 0.00252312 1.30821 0.178694 -0.763702 -0.17912 -1.49669 1.28009 -0.932152 -0.0817221 -0.464164 1.59756 -0.603266 -0.199946 -1.07242 -1.58083 0.809466 -1.98604 0.815815 1.40189 -1.45128 -1.46863 0.980593 0.0813055 -0.791754 -0.303011 -0.718376 0.604617 -0.444813 -0.390149 -1.14162 -0.740099 0.171271 6.38641f-5 -0.542155 -0.126741 0.29251 -0.83861 0.6872 1.91034 -0.736051 0.997129 1.23204 0.12189 -0.677931 -0.154049 0.120278 0.535886 -0.0351898 0.861397 -0.38695 -0.467818 0.283446 -0.188764 0.822097 0.30731 -0.842555 0.342057 -1.7973 0.241758 -2.11971 0.962895 -0.678934 0.029544 -0.335604 -0.0834471 -1.50517 0.295171 -0.695597 1.04385 0.205114 -1.52963 0.433635 -0.195495 -0.148179 0.995461 0.856131 -0.617196 -0.877749 0.19656 -0.303994 1.39664 -1.03398 -1.26089 0.170991 0.762957 0.624662 -1.60118 -0.086409 -0.136437 1.20223 -0.112088 -0.0175233 -0.838218 -0.109593 0.674892 -0.448936 -0.743989 0.559834 0.751166 -0.0881912 0.328193 1.14709 0.231342 -0.42915 0.397929 -1.0593 0.704812 -0.099343 0.497617 0.0776916 -0.373304 0.120674 0.0651401 0.701271 -1.07547 0.125968 -0.55993 0.331474 -0.910961 0.518788 -1.70579 -0.156133 0.33999 -0.19755 0.56932 -0.7773 0.991282 -1.53978 0.370663 0.340405 -2.12659 -0.484506 -0.185028 0.454469 0.590177 0.465187 0.33795 0.438711 0.407942 -1.88251 0.932993 0.897486 -0.152046 -0.113137 0.799379 0.605148 -0.0947559 0.530893 -1.09865 0.781451 -1.07434 1.37138 0.942694 -0.643778 0.00443348 0.363016 0.999665 0.310877 -0.214181 -0.606253 -0.0646343 -0.969671 -1.25378 0.735171 0.458937 0.651991 0.0360511 -0.549356 -0.765192 0.301257 -0.138369 0.342301 -0.643628 -0.311645 1.1094 1.40886 0.0694226 -0.716894 -1.15363 -1.01558 0.837252 -0.584078 0.103342 -0.135896 -1.14734 -1.07109 0.211245 0.250338 0.664024 0.714962 -0.216354 -2.40176 0.412798 -2.09834f-6 -0.478326 -0.00458238 -0.0963439 0.897577 0.325083 1.32279 0.366374 1.19935 0.865741 0.186594 1.26905 0.980017 0.920455 -0.83261 0.155171 1.9029 -0.180473 0.658651 0.0105739 -0.587927 1.58065 -1.88275 0.686682 -0.545743 -1.00701 0.616592 -0.767471 -0.704019 1.2983 0.214656 -0.0449489 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1.88768 0.132003 0.101459 0.945535 1.40706 1.0621 1.02243 -0.073851 -0.59681 -0.722054 -0.520462 1.35612 0.65568 -0.717069 -0.218095 -0.359068 1.44359 0.497135 -1.22533Visualize conditionally normalized state.
X = prior_state
Y = prior_obs
X = reshape(X, (1, 1, size(X, 1), size(X, 2)))
Y = reshape(Y, (1, 1, size(Y, 1), size(Y, 2)))
Z = normalize_samples(
filter.network_device,
X,
Y,
size(X);
device=filter.device,
num_samples=N,
batch_size=filter.training_config.batch_size,
)
Z = Z[1, 1, :, :]
table_Z = to_table(Z; prefix=:z)
@static if VERSION >= v"1.10"
table_Z_mean = to_table(mean(Z; dims=2)[:, 1]; prefix=:z)
fig = pairplot(
table_Z => (
PairPlots.Hist(; colormap=:Blues),
PairPlots.MarginDensity(;
bandwidth=kde_bandwidth, color=RGBf((49, 130, 189) ./ 255...)
),
PairPlots.TrendLine(; color=:red),
PairPlots.Correlation(),
PairPlots.Scatter(),
),
PairPlots.Truth(
table_Z_mean; label="Mean Values", color=(:black, 0.5), linewidth=4
),
)
supertitle = Label(fig[0, :], "latent state"; fontsize=30)
resize_to_layout!(fig)
display_interactive(fig)
end
Look at prior mean.
display_interactive(mean(prior_state; dims=2))2×1 Matrix{Float64}:
6.429318882839041e-17
2.168404344971009e-18Look at prior covariance.
display_interactive(cov(prior_state; dims=2))2×2 Matrix{Float64}:
1.0 -0.00306359
-0.00306359 1.0Look at latent mean.
display_interactive(mean(Z; dims=2))2×1 Matrix{Float32}:
-0.0141018275
-0.009051329Look at latent covariance.
display_interactive(cov(Z; dims=2))2×2 Matrix{Float32}:
0.9829 -0.0229044
-0.0229044 1.04116Look at posterior mean.
display_interactive(mean(posterior; dims=2))2×1 Matrix{Float32}:
0.002552625
0.03136942Look at posterior covariance.
display_interactive(cov(posterior; dims=2))2×2 Matrix{Float32}:
0.621413 -0.0111148
-0.0111148 0.513831Visualize posterior.
table_posterior = to_table(posterior)
@static if VERSION >= v"1.10"
table_posterior_mean = to_table(mean(posterior; dims=2)[:, 1])
fig = pairplot(
table_posterior => (
PairPlots.Hist(; colormap=:Blues),
PairPlots.MarginDensity(;
bandwidth=kde_bandwidth, color=RGBf((49, 130, 189) ./ 255...)
),
PairPlots.TrendLine(; color=:red),
PairPlots.Correlation(),
PairPlots.Scatter(),
),
PairPlots.Truth(
table_posterior_mean; label="Mean Values", color=(:black, 0.5), linewidth=4
),
)
supertitle = Label(fig[0, :], "posterior state"; fontsize=30)
resize_to_layout!(fig)
display_interactive(fig)
end
The posterior should have mean 0 and some TBD variance.
X = reshape(prior_state, (1, 1, size(prior_state, 1), size(prior_state, 2)))
Y = reshape(prior_obs, (1, 1, size(prior_obs, 1), size(prior_obs, 2)))
y_obs_r = reshape(y_obs, (1, 1, size(y_obs, 1), size(y_obs, 2)))
fresh_samples = draw_posterior_samples(
filter.network_device,
y_obs_r,
size(X);
device=filter.device,
num_samples=32,
batch_size=filter.training_config.batch_size,
log_data=nothing,
)[
1, 1, :, :,
]
@test true;Plot some training metrics.
common_kwargs = (; linewidth=3)
fig = Figure()
ax = Axis(fig[1, 1])
misfit_train = log_data[:network_training][:training][:loss]
misfit_test = log_data[:network_training][:testing][:loss]
# The training metrics are recorded for each batch, but test metrics are computed each
# epoch.
num_batches = length(misfit_train)
num_epochs = length(misfit_test)
batches_per_epochs = div(num_batches, num_epochs)
test_epochs = 1:num_epochs
train_epochs = (1:num_batches) ./ batches_per_epochs
lines_train = lines!(ax, train_epochs, misfit_train; label="train", common_kwargs...)
lines_test = lines!(ax, test_epochs, misfit_test; label="test", common_kwargs...)
ax.xlabel = "epoch number"
ax.ylabel = "loss: 2-norm"
fig[1, end + 1] = Legend(fig, ax; labelsize=14, unique=true)
N_train = round(Int, N * training_config.validation_perc)
N_valid = N - N_train
ax.title = "Training: $N_train, Validation: $N_valid, Batch size: $(training_config.batch_size)"
ax = Axis(fig[2, 1])
x = log_data[:network_training][:training][:logdet]
lines!(ax, train_epochs, x; color=lines_train.color, common_kwargs...)
x = log_data[:network_training][:testing][:logdet]
lines!(ax, test_epochs, x; color=lines_test.color, common_kwargs...)
ax.xlabel = "epoch number"
ax.ylabel = "loss: log determinant"
supertitle = Label(fig[0, :], "Training log"; fontsize=30)
resize_to_layout!(fig)
display_interactive(fig)
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