File size: 4,179 Bytes
c711202 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 | """
Visualization for Burgers source identification.
"""
using TuePlots
function _icml_theme(; single_column=false, nrows=1, ncols=1, ratio=0.85)
Theme(
TuePlots.SETTINGS[:ICML];
font=true, fontsize=true, figsize=true,
single_column=single_column,
nrows=nrows, ncols=ncols,
subplot_height_to_width_ratio=ratio,
)
end
function plot_source_comparison(result, s_true, xs, ys;
filename::Union{Nothing,String}=nothing)
set_theme!(_icml_theme(single_column=false, nrows=1, ncols=4, ratio=1.0))
fig = Figure()
s_err = abs.(s_true .- result.s_mean)
vmin = min(minimum(s_true), minimum(result.s_mean))
vmax = max(maximum(s_true), maximum(result.s_mean))
ax1 = Axis(fig[1,1]; aspect=DataAspect(), title="True source", xlabel=L"x", ylabel=L"y")
hm1 = heatmap!(ax1, xs, ys, s_true; colorrange=(vmin, vmax), colormap=:viridis)
ax2 = Axis(fig[1,2]; aspect=DataAspect(), title="Posterior mean", xlabel=L"x", yticklabelsvisible=false)
heatmap!(ax2, xs, ys, result.s_mean; colorrange=(vmin, vmax), colormap=:viridis)
Colorbar(fig[1,3], hm1; width=8)
ax3 = Axis(fig[1,4]; aspect=DataAspect(), title="|Error|", xlabel=L"x", yticklabelsvisible=false)
hm3 = heatmap!(ax3, xs, ys, s_err; colormap=:inferno)
Colorbar(fig[1,5], hm3; width=8)
ax4 = Axis(fig[1,6]; aspect=DataAspect(), title="Posterior std", xlabel=L"x", yticklabelsvisible=false)
hm4 = heatmap!(ax4, xs, ys, result.s_std; colormap=:inferno)
Colorbar(fig[1,7], hm4; width=8)
if !isnothing(filename)
mkpath(dirname(filename))
save(filename, fig, pt_per_unit=1)
end
set_theme!()
return fig
end
function plot_solution_snapshots(result, u_truth, xs, ys, ts;
snapshot_times=nothing, filename::Union{Nothing,String}=nothing,
obs_data=nothing)
n_t_total = size(u_truth, 3)
if isnothing(snapshot_times)
snapshot_times = round.(Int, range(1, n_t_total, length=4))
end
n_snap = length(snapshot_times)
set_theme!(_icml_theme(single_column=false, nrows=3, ncols=n_snap, ratio=1.0))
fig = Figure()
for (col, t) in enumerate(snapshot_times)
vmin = min(minimum(u_truth[:,:,t]), minimum(result.u_mean[:,:,t]))
vmax = max(maximum(u_truth[:,:,t]), maximum(result.u_mean[:,:,t]))
ax1 = Axis(fig[1, col]; aspect=DataAspect(),
title=L"t=%$(round(ts[t], digits=2))",
ylabel=col==1 ? "Truth" : "", yticklabelsvisible=col==1)
hm = heatmap!(ax1, xs, ys, u_truth[:,:,t]; colorrange=(vmin, vmax), colormap=:viridis)
ax2 = Axis(fig[2, col]; aspect=DataAspect(),
ylabel=col==1 ? "GP-FVM" : "", yticklabelsvisible=col==1)
heatmap!(ax2, xs, ys, result.u_mean[:,:,t]; colorrange=(vmin, vmax), colormap=:viridis)
if col == n_snap
Colorbar(fig[1:2, n_snap+1], hm; width=8)
end
ax3 = Axis(fig[3, col]; aspect=DataAspect(),
ylabel=col==1 ? "Std" : "", yticklabelsvisible=col==1)
hm_std = heatmap!(ax3, xs, ys, result.u_std[:,:,t]; colormap=:inferno)
# Show observation locations at timesteps where we observe
if !isnothing(obs_data) && t in obs_data.obs_timesteps
scatter!(ax3, obs_data.obs_x, obs_data.obs_y;
color=:white, markersize=3, strokewidth=0.4, strokecolor=:black)
end
if col == n_snap
Colorbar(fig[3, n_snap+1], hm_std; width=8)
end
end
if !isnothing(filename)
mkpath(dirname(filename))
save(filename, fig, pt_per_unit=1)
end
set_theme!()
return fig
end
function plot_convergence(iteration_log; filename::Union{Nothing,String}=nothing)
fig = Figure(size=(500, 350), fontsize=12)
ax = Axis(fig[1, 1]; xlabel="Gauss-Newton iteration", ylabel="Newton decrement",
yscale=log10, title="Convergence of nonlinear solve")
scatterlines!(ax, 1:length(iteration_log), iteration_log;
color=:royalblue, linewidth=2, markersize=6)
if !isnothing(filename)
mkpath(dirname(filename))
save(filename, fig, px_per_unit=3)
end
return fig
end
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