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 = 3
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)3×2048 Matrix{Float32}:
1.0495 0.106115 -0.139734 -0.258606 1.27227 1.09832 -0.0260479 0.537882 1.09659 0.123439 -1.00718 -0.703977 1.84712 0.105464 -0.446833 -1.25863 -0.480365 0.607836 0.119576 -0.0847813 1.049 0.0893785 -0.539319 1.09989 -0.0479418 -1.68779 0.107189 -0.838627 -1.34571 1.60062 -0.146302 0.837187 -0.267169 -1.58602 0.88615 1.19569 0.143375 -0.399061 -0.912459 -1.10007 -1.03905 -1.38835 0.715076 -0.174862 0.485713 -0.599656 -0.242941 0.496977 0.723763 -0.647916 -0.560364 0.899553 -0.614644 -0.0171181 -0.298857 0.687247 -1.01075 -0.567347 0.728556 1.10049 -1.03332 -0.721213 0.655752 1.91446 -0.281179 -1.45636 -1.49397 -1.37412 -0.601753 0.483482 -0.300313 0.0911757 -1.55244 0.188929 0.238306 -0.687606 -0.309212 -0.0610444 0.200808 -0.909504 -0.976449 0.493777 -0.807406 -1.12096 -0.435598 0.814127 0.388279 -1.37115 0.886006 -1.31529 -0.357851 -0.871 0.476094 -0.439822 1.38111 -0.451795 -0.215687 -1.00834 1.08753 0.0350957 -0.787908 1.23784 0.358694 -0.663131 -0.2503 0.36699 0.38239 -1.54299 0.0625861 -1.00445 -0.00922651 1.26707 0.313315 -0.658674 0.647361 -0.777936 0.0143748 0.789717 0.981862 0.153309 0.134593 0.502681 0.310718 -0.8912 1.45548 0.160926 -0.527139 -0.821154 0.248379 0.66918 0.0843901 -0.554377 0.324652 -0.00667898 -0.108107 0.683061 -0.472714 0.195599 -1.4869 0.966376 0.354047 0.383971 -0.25414 1.39715 -0.228039 1.48699 0.204681 -0.792578 -0.178094 -0.0642397 -0.7351 0.961622 0.648202 1.11808 0.329248 1.34224 -0.760385 -0.0552901 -0.825024 1.38073 0.138478 0.521143 0.919334 0.105415 -0.413811 -0.261102 1.39982 1.05168 -0.271251 -0.702037 -0.899515 0.0792869 0.405168 0.856523 0.479213 -0.322658 -0.105473 1.22966 0.642266 -0.333669 0.532345 -0.993288 -1.05401 -0.154259 0.950884 -2.04751 0.565112 0.101566 0.877695 1.51892 1.71924 -0.474739 1.1 0.608867 0.175793 -0.677388 0.495701 1.44447 0.58639 -1.91199 0.512618 -0.653124 -0.163527 0.186806 -0.280992 0.362385 0.0771407 -0.246414 -0.305285 -0.875778 0.0229047 0.118534 -0.716015 0.184988 0.245342 0.134395 0.189395 -0.254358 0.975224 1.12362 0.0438448 -0.923537 -0.911743 -1.13122 -0.202311 1.8756 -1.09467 0.421279 -0.651124 0.836688 -0.509772 -0.943695 0.0769392 -1.72087 1.29402 0.263185 -0.334816 -0.772104 0.107706 -0.428549 0.216274 0.12767 0.435592 -1.24184 0.300245 -0.448869 -0.52464 1.64854 -2.5668 0.970086 0.826527 -0.126967 -0.633725 -1.55346 -0.939384 0.757822 1.02828 1.19227 -0.876463 0.212214 -0.242675 -1.03275 0.803834 0.129364 0.462323 -0.515642 -0.0527387 -0.825352 -2.18675 -0.260594 0.278547 -0.950166 -0.731968 -1.65239 0.0596441 0.704014 -0.295121 0.394391 1.13985 0.820746 -0.0401746 -0.312038 0.927812 0.0748415 -0.467017 -2.08491 0.491174 -1.49381 2.34305 -1.4358 1.42099 -2.46142 -0.959477 -0.605335 -0.0850034 0.297914 -0.98129 -1.32622 -0.385003 0.712002 0.0241078 -1.15579 -0.789601 0.430343 -0.164843 0.257498 -0.729349 -0.496839 -0.513731 -0.865611 0.153582 0.494233 0.591194 0.307755 0.740445 -1.13279 -2.35548 0.590851 -0.139715 0.174887 1.5602 -0.266254 -0.174849 -0.00882995 -0.945928 -0.166883 -1.38691 0.198527 -0.258119 -1.06585 0.417062 -0.697358 -0.100769 -0.489877 0.417468 -0.658017 0.289382 0.448109 0.000319571 0.577381 0.573647 -0.167278 -0.226079 1.5478 1.20394 -0.0526055 0.902774 0.307843 -0.764671 -1.19467 0.030872 0.379227 -1.82524 -1.23846 0.0247533 0.0162912 -0.955216 -1.25222 1.29938 1.04098 0.136256 -0.788789 -0.407224 0.432994 0.812614 -0.138479 -0.60006 -1.07775 -0.792563 -1.74867 -1.4707 -0.328361 -0.22659 -0.442078 -0.0677071 -0.731971 1.41998 -1.54346 0.233781 -0.0880531 0.901353 -1.34225 -0.756773 -0.182606 1.03178 0.61686 0.46504 0.511055 0.369297 0.269895 -1.72316 -0.48317 0.375355 -1.36458 1.94944 0.0802841 -0.295683 1.10045 -0.757593 0.179411 0.132911 -0.15508 1.08845 -0.718173 0.175231 -0.0775876 -0.241722 -0.450012 1.4227 -0.141731 0.251286 -1.07825 0.62189 -0.258166 -1.14123 -0.404159 1.22476 0.0207772 0.470431 -0.248308 -0.416824 0.414343 0.0840015 -0.603211 0.238226 1.39492 0.115747 0.181939 -0.560786 -1.35939 1.12474 1.09757 -1.55361 0.670014 -0.656913 -1.39567 -0.661713 0.310635 -0.567338 0.503673 0.625909 -0.359892 -0.709058 -0.000800108 -0.582275 -0.172852 -1.27247 0.0403551 -0.589395 0.765009 1.1516 0.976518 -0.98209 -0.383907 0.208448 -0.0136549 -1.06399 0.4341 0.264118 -0.514467 -0.215738 -0.10443 0.0784241 0.95746 2.8207 -0.48 -0.706934 -1.59716 1.14108 -0.623583 -0.436063 0.636638 1.26069 -0.0213365 -0.369782 -0.230046 0.362724 0.607673 -0.138458 -0.110158 -1.58552 0.894746 -0.400626 0.671852 1.0161 -0.00852964 1.41534 -0.766629 0.952216 -0.572322 1.31338 -0.553626 0.194855 0.150382 0.995178 0.103883 0.984669 0.44655 0.608168 0.898504 1.37749 -0.668744 -1.83417 -0.385214 0.462759 1.08069 -1.54612 0.748486 -0.329886 -1.30484 0.654928 1.03804 -0.0365783 0.164072 0.791216 -0.475967 3.54068 -1.09502 1.06142 0.996766 -0.638812 1.64508 0.65617 -0.564786 0.491558 -1.27998 0.350481 -0.853227 0.557129 0.765319 1.36087 -0.417588 -1.63108 0.21474 0.299473 -0.71333 0.109331 -0.77581 -0.0170867 -1.28776 -0.106581 1.37755 0.498093 -1.01843 -0.833847 0.404621 0.119544 0.53179 -0.140301 0.436517 -2.06358 0.528671 -1.13603 0.890381 1.10018 0.581538 0.030833 -0.87075 0.596619 -1.04209 -0.0329625 -0.519951 0.241507 1.31972 0.360348 -0.208578 -0.411007 0.295955 -0.23506 0.788748 -1.37466 0.162367 0.0433288 1.17561 0.120126 1.52292 -0.137969 0.852356 -1.27111 0.280224 0.814285 0.588312 0.560738 -0.880255 1.02483 0.474733 0.714547 0.0219463 0.146429 0.886412 -0.546175 -0.108709 0.40222 0.558194 -0.192887 0.787901 -0.585996 0.482502 0.340554 0.950996 -0.067148 0.780736 1.55814 0.956219 0.259331 0.424021 -0.928822 -1.11161 0.445359 0.754325 -0.108461 -0.9399 -0.144056 -0.206907 0.183528 -0.691409 -0.822225 -0.752477 -1.25673 0.432965 0.413872 -0.767364 0.900314 -0.242344 -0.0821123 -0.0985877 1.18754 0.1951 -0.0273278 1.74219 -0.271605 -0.0470292 -0.418683 -0.185433 0.192539 0.616691 -0.519337 -0.89494 -0.406604 0.205991 0.334709 -0.658042 1.2019 -0.116875 -0.00470144 0.169986 1.74069 0.112133 -0.493109 0.0284911 0.709544 1.23435 1.93968 -1.05921 -0.345028 0.101078 -0.520211 0.0197368 -0.893162 0.275839 -0.172946 0.0749474 0.787153 -0.064195 -0.0923886 0.801427 0.424249 -0.289809 0.651191 0.247163 0.555648 -0.0283967 0.0268726 -0.177039 -0.475606 0.167762 0.556636 -2.11937 0.509559 -0.239122 -0.935765 -1.12643 -0.704589 0.335921 0.362455 0.534903 -1.50922 -0.700387 -0.47429 -0.576057 0.3631 0.510941 -0.243643 -0.376645 0.172232 0.0648055 0.246811 -1.35784 0.841016 -0.467316 0.349716 -1.59806 0.451069 0.552574 1.26953 0.335973 -0.475224 -0.8006 -0.407148 0.566926 -0.330033 0.298085 0.162563 0.614031 -0.204561 0.486073 0.741466 1.71365 -1.12257 -0.765894 -0.628303 -0.259836 -0.811946 0.802558 1.03151 -0.464198 -0.883828 -0.155208 0.786792 1.32675 1.03339 0.0696849 -1.53709 0.811188 -0.0988306 0.992312 1.29034 -0.235215 0.147973 0.737557 -1.33835 1.02259 0.739453 0.683626 -0.338081 0.0401706 -0.282385 0.698365 0.74207 0.987452 0.784331 -0.174056 1.11115 -0.341754 0.893346 -0.550203 0.35719 -0.682124 1.65799 -0.918513 -2.31482 0.345057 -1.43378 -0.980542 -1.18817 -0.0658779 0.70303 1.07183 -0.859187 0.152923 0.624311 0.242426 1.44292 0.347248 0.971626 0.65435 0.165482 -0.740458 1.08123 1.16351 -0.80697 -0.794036 -0.0201182 0.09143 0.51598 -0.592476 0.153494 1.75512 -0.121715 -1.39863 0.430805 -1.02852 0.528002 0.23197 0.972984 0.20207 -0.473977 0.262502 0.350151 0.437585 -1.02349 0.232067 1.15301 0.184764 0.00252206 0.0865871 -1.26057 1.09195 -0.231778 -0.294253 1.61976 0.786753 0.184194 -0.808605 -0.439722 1.79105 -2.13697 -0.905271 1.73567 0.323521 -1.40831 -0.27552 -1.50025 -0.0201872 1.10289 -0.358649 -1.11284 -0.596255 0.494149 -1.72842 -0.853323 0.551184 -1.35743 -0.141134 0.866464 1.99869 -0.952912 0.6311 1.24396 1.14305 -0.50474 -0.988326 0.0601866 0.145664 -1.30098 1.20464 -0.5009 -0.420918 -0.361456 -0.258401 0.169689 0.90823 -1.19698 -0.137903 -1.63852 0.0540762 0.40898 0.529664 -0.595451 -0.883938 0.372429 -0.771745 -1.02166 -0.215806 -0.257109 -0.209861 -0.230168 -0.0879366 0.0172836 0.581896 0.709789 -0.548175 -0.240455 -0.383774 0.486473 -1.6954 0.284297 -0.671743 -0.207131 0.767567 -1.01705 -1.59079 -0.755931 1.0332 -0.495962 -0.211914 -0.566424 0.495449 -0.566496 -1.78921 -1.32098 0.486505 0.0359703 -0.203693 -0.53005 -0.45352 0.326554 -0.373496 -1.12921 0.822914 -0.961713 1.1862 -1.36554 1.34335 1.23194 0.262843 0.00424318 0.408957 -1.08748 2.56244 0.71165 -0.430302 -0.57464 1.24872 1.10283 -1.18263 0.165874 -0.123648 -1.60101 -1.30377 -0.804104 -1.16995 -0.333238 -0.102078 -0.673163 0.737985 0.841149 1.35218 -0.305176 -0.318699 0.0396947 1.44797 -0.0526571 0.648566 0.115192 0.370208 0.612819 -0.44857 -0.0251495 1.04705 -0.690094 -0.00634888 0.408977 -0.411055 -0.156361 0.306933 -1.78772 -0.548954 -0.206587 -0.339406 -1.92191 1.1676 -0.860623 0.575043 -1.25801 0.348201 0.523492 0.639733 -0.619345 -0.848795 0.75892 -0.724954 0.605129 0.980063 0.783137 -1.93033 0.133031 1.69196 -0.741147 -0.211651 -0.477191 0.53343 0.916981 0.356395 0.14072 -1.06422 -0.763755 -0.465298 -0.114934 -0.544025 -0.0636355 0.817149 1.28135 0.659873 0.392761 -0.154343 0.0558545 0.603669 0.357 0.3782 0.756445 0.0667235 -1.40313 -1.17983 -0.043158 -0.542114 0.1519 -0.731865 0.153908 0.70332 1.26881 0.0992614 -0.215281 -0.185382 -0.58519 0.782509 0.409834 1.27394 -0.556949 0.489528 0.586937 -0.940409 -0.44775 0.532671 0.51645 1.14897 -0.462082 0.678631 0.254933 -1.41609 1.29837 1.3406 -0.876897 -0.355529 0.783863 0.134222 -0.255671 -0.909446 -0.868198 -1.45835 0.27801 0.258064 -0.327537 -0.473787 2.1838 -1.27992 -1.12085 0.688166 0.584791 -0.744946 0.433221 -1.54726 1.45966 -0.613315 -0.566315 -0.906204 0.848312 -0.137748 0.287659 -0.487595 0.00293518 -0.428013 0.541641 -0.872473 -0.746234 -0.17834 -0.147031 -1.70594 -0.494723 0.962622 -1.48046 1.53375 -0.34134 -0.929019 -1.12617 -0.763831 -0.507675 -0.412475 0.677359 0.336633 -1.51491 -0.326684 -0.87192 0.547663 1.24562 0.675536 -0.46653 -0.437418 1.25688 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0.396996 0.375053 0.108459 1.3699 1.1072 0.176439 0.0714965 -0.59889 0.812036 0.621268 -0.409059 0.890954 0.420451 -0.310915 0.347983 0.796215 0.930683 0.814839 0.0750708 -0.973093 0.826168 0.308912 0.0898575 0.274562 0.0788726 -0.248604 -0.258081 -1.08689 -0.622784 0.103459 1.08256 -0.284091 -0.00211216 0.06761 0.456907 1.06206 -0.382675 -0.22896 -0.924681 0.630525 -1.52224 -0.0890937 -0.311119 2.17238 -0.834947 0.139234 -1.75312 -0.0475341 -0.828566 -0.41834 -0.24692 0.821287 0.816294 -0.683944 0.948858 0.0832119 0.192703 0.272628 -0.507182 -0.844853 -0.00804485 0.404474 -0.246134 -0.905973 -0.384928 -0.494068 -0.513982 0.147393 0.0443136 1.31803 -0.525014 0.476771 0.476769 -1.17716 0.950264 -0.076494 0.514711 1.20153 0.379562 0.0480522 -1.04056 -0.1413 -0.0748758 -0.329776 1.27498 0.581806 0.422431 -0.919681 0.233393 0.207582 -0.918493 -0.643211 0.441254 0.55324 0.307253 -0.354171 0.246026 1.40412 -0.449337 0.0932287 0.676885 -1.67146 1.05605 0.00577887 -2.48422 -0.868183 0.389363 0.206786 0.748482 -0.881538 -0.646095 0.304471 0.0978683 -1.97599 0.707941 -1.20006 0.703693 -0.258922 -0.491472 1.51466 0.697909 -0.958426 -0.00653058 0.109057 0.289534 -0.264443 -0.610217 -0.332008 0.401846 -1.13867 -0.680143 0.775641 0.218889 0.177971 -0.646653 -0.620813 1.03905 0.244559 0.644522 1.1729 1.16205 1.19766 1.04604 -0.0703259 0.471699 -0.380495 -0.244316 -1.1099 -0.805241 -0.640027 -0.722665 -0.673397 -1.15623 1.25184 0.614961 0.0215217 0.930767 -0.0532292 0.536108 0.311602 0.940964 0.576477 0.323785 -0.171799 0.551242 0.371717 -0.639535 0.661326 1.1904 0.273974 -0.323711 -0.498299 -0.0429984 1.43088 -0.519709 0.772045 0.246028 1.06994 -0.0653521 -1.26967 -1.52134 0.364387 0.170904 0.339559 -0.548783 1.20083 0.805049 1.39637 -0.551024 -0.307573 -1.43061 -0.678284 -0.484649 0.210896 -0.0240797 -0.928913 -0.809088 0.2901 -1.3361 0.515649 -0.692858 -0.333793 1.26531 0.221003 -0.465016 -0.937505 -1.31387 1.72938 0.594804 -0.528664 0.0594149 -0.236277 -0.370423 -0.360793 -0.606025 -0.467747 -1.31361 0.340271 0.231779 0.468308 0.0383909 -0.159927 0.643059 0.113078 -0.770846 1.53051 -0.357352 -0.23191 1.38393 0.881073 -0.449215 1.29993 -0.730824 -0.761519 0.00125249 -0.349927 0.901147 -0.512245 0.94012 -0.341806 0.113508 -1.97458 -0.0655225 0.232833 1.1072 -0.551155 0.821524 1.2827 0.661753 0.936445 -1.10896 -0.0383568 0.558944 0.702657 -0.780054 0.170321 -1.00455 0.385714 -0.247155 1.71881 -0.575881 -0.0344357 1.03377 -0.511353 0.869787 -0.369658 -0.341921 -0.77338 -0.668669 0.772206 0.871128 -1.84781 -0.846244 0.295791 0.893015 -0.483609 -0.866613 1.37513 0.0809963 0.0778632 -0.45685 0.960727 -0.584964 0.522798 -1.57052 -0.0252869 -1.37122 -1.19643 0.943335 0.725091 0.910739 -0.886625 -1.02903 0.742703 0.556859 0.138057 -0.373164 -0.675567 1.48737 -1.01952 -0.548968 0.776262 1.21824 0.632254 0.179413 -0.347155 -0.176578 -1.21112 0.598314 -0.136389 0.473231 0.727165 -0.108082 -0.660796 -0.176695 -0.274817 0.587499 0.821606 1.1385 0.594107 -1.33478 -1.8478 1.0624 -0.0738901 0.697909 0.689973 0.864306 -1.99233 1.66536 -1.00922 -0.912392 -0.307011 -0.33911 -0.88598 -1.52183 -1.72979 0.493942 -0.214375 -0.644677 1.35713 2.01114 -0.0123051 0.888878 0.355753 0.361832 1.15631 -1.27251 0.877084 -0.368958 0.666742 -0.173092 0.208703 0.204853 0.119311 0.365301 0.00585019 1.16078 -0.540596 1.19912 1.1091 -0.865799 0.694091 0.133853 0.0352889 -1.03462 0.360353 -0.317775 -0.941909 -0.0332092 0.171371 -1.31617 0.455025 -0.154829 0.206033 -1.28043 -0.111383 1.09696 -0.781916 1.19858 0.369014 -0.332761 0.234402 -0.102415 0.42709 -0.89513 0.0737619 1.15514 0.943269 0.775886 0.771018 0.444406 0.646068 2.044 0.879728 1.45405 -0.25701 0.243084 0.0164813 0.979162 -0.600863 0.821574 0.672201 -1.4877 0.541125 1.61104 -0.134184 -0.172351 0.211135 -1.72837 1.79319 0.605424 -0.446187 -1.09292 -2.05274 0.35455 -0.0823156 -0.532393 -0.100379 -0.125895 0.0732678 -1.66335 0.452748 0.717352 0.883947 -1.30128 -0.320132 -0.139185 -0.702111 0.329159 -0.0349112 0.376414 -1.45247 -1.30618 -0.571621 1.82444 1.62335 0.424706 -0.713359 0.0172964 -0.4845 -0.31439 0.0212558 -0.18229 1.2328 0.203906 0.212237 0.203731 0.217105 1.28609 0.258018 1.76796 0.702754 -0.574488 -1.77472 0.364903 -0.0886961 0.392433 -1.94674 0.884525 -2.2442 -0.787209 -0.109971 1.0566 -0.428514 -0.148076 0.00414756 -0.335507 -0.888484 -0.620897 -0.719228 -0.825525 0.520709 0.574251 0.107683 0.93546 -0.969667 0.731607 0.390385 -0.0239439 -0.133149 0.415462 -0.502895 0.364045 -1.02543 -1.24404 0.937718 0.940159 -0.00219319 0.68723 -0.775112 -1.61866 0.281697 0.797 -0.78858 -1.34527 1.77783 0.843737 0.607323 -0.60592 0.319276 0.523878 1.00203 0.483463 -0.0825665 0.37374 -0.477279 -0.758456 0.462266 0.468484 0.752333 1.89483 -0.378355 -1.03169 0.829312 0.0387006 -0.344427 0.702417 0.720734 1.34439 -0.363162 0.252801 0.393786 -0.303096 -0.433526 0.740959 0.824092 -1.27872 0.0152407 1.0196 0.126695 0.671202 0.140622 -1.35903 -0.914929 0.0397754 0.118266 -0.462091 -0.523362 0.600732 1.0829 -1.83589 -0.797815 -0.046798 0.103265 0.100791 -1.2053 -0.381995 0.239862 0.206837 -0.660852 -0.174238 0.539379 1.94458 0.717659 -1.17834 -1.46109 -0.859035 -0.938716 0.320193 0.395201 -0.219824 -0.327605 1.35351 -0.68991 -1.35299 -0.492513 1.39556 -0.315673 -0.54047 -0.667855 0.234125 -0.812051 0.366362 0.676606 0.269158 3.12748 -0.673722 0.019928 -0.108261 1.37064 -0.839369 -0.941878 -1.1801 -0.550072 -0.681143 0.86039 0.493069 -1.86108 1.57865 0.171859 -0.894223 1.24622 -0.454912 -1.04689 -1.05232 -0.0915122 -0.764881 -0.824266 0.985168 -1.15253 1.32931 0.1896 -0.650013 0.0756801 1.59961 -0.513814 -0.0605022 -1.17164 0.20625 0.946569 0.749507 0.378129 -0.40297 -0.00169963 0.647128 0.716214 0.143602 -0.437542 0.875524 -0.18718 -1.22075 0.395792 0.272191 0.660316 -0.623854 -0.262403 -0.0405872 0.79263 0.458682 -0.630988 -0.524122 -0.598128 0.781008 -0.247746 1.43491 0.354493 1.47071 1.50928 1.02493 1.37521 0.509921 0.328763 -0.95744 -0.687037 -0.640119 1.23151 -0.412385Visualize 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))3×1 Matrix{Float64}:
-4.098284211995207e-17
2.5478751053409354e-18
-3.881443777498106e-17Look at prior covariance.
display_interactive(cov(prior_state; dims=2))3×3 Matrix{Float64}:
1.0 0.00344515 0.0286265
0.00344515 1.0 0.0365354
0.0286265 0.0365354 1.0Look at latent mean.
display_interactive(mean(Z; dims=2))3×1 Matrix{Float32}:
-0.0136672165
-0.0085750185
0.037852332Look at latent covariance.
display_interactive(cov(Z; dims=2))3×3 Matrix{Float32}:
0.980779 0.0180562 -0.0464153
0.0180562 1.1015 0.0305349
-0.0464153 0.0305349 0.980134Look at posterior mean.
display_interactive(mean(posterior; dims=2))3×1 Matrix{Float32}:
0.00048608182
0.05078329
0.012495356Look at posterior covariance.
display_interactive(cov(posterior; dims=2))3×3 Matrix{Float32}:
0.680222 0.00651033 0.0124976
0.00651033 0.712018 0.00995877
0.0124976 0.00995877 0.716246Visualize 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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