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figures_neoclassical_growth_robustness_2_1.py
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figures_neoclassical_growth_robustness_2_1.py
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import jax.numpy as jnp
import matplotlib.pyplot as plt
import os
from new_neoclassical_growth_matern import neoclassical_growth_matern
# from neoclassical_growth_dae_matern import neoclassical_growth_dae_matern
from new_neoclassical_growth_neural import neoclassical_growth_neural
from mpl_toolkits.axes_grid1.inset_locator import (
zoomed_inset_axes,
mark_inset,
inset_axes,
)
fontsize = 14
ticksize = 14
figsize = (15, 10)
params = {
"font.family": "serif",
"figure.figsize": figsize,
"figure.dpi": 80,
"figure.edgecolor": "k",
"font.size": fontsize,
"axes.labelsize": fontsize,
"axes.titlesize": fontsize,
"xtick.labelsize": ticksize,
"ytick.labelsize": ticksize,
}
plt.rcParams.update(params)
## Plot given solution
def plot_neoclassical_growth(
sol,
output_path,
output_path_rel_error,
k_rel_error_ylim=(1e-6, 2 * 1e-2),
c_rel_error_ylim=(1e-6, 2 * 1e-2),
zoom=True,
zoom_loc=[50, 60],
):
t = sol["t_test"]
T = sol["t_train"].max()
c_hat = sol["c_test"]
k_hat = sol["k_test"]
c_benchmark = sol["c_benchmark"]
k_benchmark = sol["k_benchmark"]
k_rel_error = sol["k_rel_error"]
c_rel_error = sol["c_rel_error"]
# Plotting
plt.figure(figsize=(15, 10))
ax_capital = plt.subplot(1, 2, 1)
plt.plot(t, k_hat, color="k", label=r"$\hat{x}(t)$: Matérn Kernel Approximation")
plt.plot(
t, k_benchmark, linestyle="--", color="k", label=r"$x(t)$: Benchmark Solution"
)
plt.axvline(x=T, color="k", linestyle=":", label="Extrapolation/Interpolation")
plt.ylabel("Capital: $x(t)$")
plt.xlabel("Time")
plt.legend() # Show legend with labels
ax_consumption = plt.subplot(1, 2, 2)
plt.plot(t, c_hat, color="b", label=r"$\hat{y}(t)$: Matérn Kernel Approximation")
plt.plot(
t, c_benchmark, linestyle="--", color="b", label=r"$y(t)$: Benchmark Solution"
)
plt.axvline(x=T, color="k", linestyle=":", label="Extrapolation/Interpolation")
plt.ylabel("Consumption: $y(t)$")
plt.xlabel("Time")
plt.legend() # Show legend with labels
plt.tight_layout() # Adjust layout to prevent overlap
# Zoom in part of the plot
if zoom == True:
time_window = (
zoom_loc # Indices: The window on the x-axis that want to be zoomed in
)
ave_value = 0.5 * (
k_benchmark[time_window[0]] + k_benchmark[time_window[1]]
) # The average on the y-axis that want to be zoomed in
window_width = 0.01 * ave_value
axins = zoomed_inset_axes(
ax_capital,
3,
loc="center",
bbox_to_anchor=(0.5, 0.7, -0.3, -0.3),
bbox_transform=ax_capital.transAxes,
)
axins.plot(
t[time_window[0] - 1 : time_window[1] + 1],
k_hat[time_window[0] - 1 : time_window[1] + 1],
color="k",
)
axins.plot(
t[time_window[0] - 1 : time_window[1] + 1],
k_benchmark[time_window[0] - 1 : time_window[1] + 1],
linestyle="--",
color="k",
)
x1, x2, y1, y2 = (
t[time_window[0]],
t[time_window[1]],
ave_value - window_width,
ave_value + window_width,
)
axins.set_xlim(x1, x2)
axins.set_ylim(y1, y2)
plt.xticks(fontsize=8, visible=False)
plt.tick_params(
axis="x", which="both", bottom=False, top=False, labelbottom=False
)
plt.yticks(fontsize=8)
mark_inset(
ax_capital, axins, loc1=1, loc2=3, linewidth="0.7", ls="--", ec="0.5"
)
time_window = (
zoom_loc # Indices: The window on the x-axis that want to be zoomed in
)
ave_value = 0.5 * (
c_benchmark[time_window[0]] + c_benchmark[time_window[1]]
) # The average on the y-axis that want to be zoomed in
window_width = 0.01 * ave_value
axins = zoomed_inset_axes(
ax_consumption,
3,
loc="center",
bbox_to_anchor=(0.5, 0.7, -0.3, -0.3),
bbox_transform=ax_consumption.transAxes,
)
axins.plot(
t[time_window[0] - 1 : time_window[1] + 1],
c_hat[time_window[0] - 1 : time_window[1] + 1],
color="b",
)
axins.plot(
t[time_window[0] - 1 : time_window[1] + 1],
c_benchmark[time_window[0] - 1 : time_window[1] + 1],
linestyle="--",
color="b",
)
x1, x2, y1, y2 = (
t[time_window[0]],
t[time_window[1]],
ave_value - window_width,
ave_value + window_width,
)
axins.set_xlim(x1, x2)
axins.set_ylim(y1, y2)
plt.xticks(fontsize=8, visible=False)
plt.tick_params(
axis="x", which="both", bottom=False, top=False, labelbottom=False
)
plt.yticks(fontsize=8)
mark_inset(
ax_consumption, axins, loc1=1, loc2=3, linewidth="0.7", ls="--", ec="0.5"
)
plt.savefig(output_path, format="pdf")
plt.figure(figsize=(15, 10))
ax_rel_k = plt.subplot(1, 2, 1)
plt.plot(
t,
k_rel_error,
color="k",
label=r"$\varepsilon_x(t)$: Rel. Errors for $x(t)$, Matérn Kernel Approx.",
)
plt.axvline(x=T, color="k", linestyle=":", label="Extrapolation/Interpolation")
plt.yscale("log") # Set y-scale to logarithmic
plt.ylim(k_rel_error_ylim[0], k_rel_error_ylim[1])
plt.xlabel("Time")
plt.legend() # Show legend with labels
ax_rel_c = plt.subplot(1, 2, 2)
plt.plot(
t,
c_rel_error,
color="b",
label=r"$\varepsilon_y(t)$: Rel. Errors for $y(t)$, Matérn Kernel Approx.",
)
plt.axvline(x=T, color="k", linestyle=":", label="Extrapolation/Interpolation")
plt.yscale("log") # Set y-scale to logarithmic
plt.ylim(c_rel_error_ylim[0], c_rel_error_ylim[1])
plt.xlabel("Time")
plt.legend() # Show legend with labels
plt.tight_layout() # Adjust layout to prevent overlap
plt.savefig(output_path_rel_error, format="pdf")
# Plots with various parameters
sol = neoclassical_growth_matern(
train_points_list=[0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 10.0, 15.0, 20.0, 25.0, 30.0, 35.0, 36.0, 37.0, 38.0, 39.0, 40.0], lambda_p = 1e-4
)
plot_neoclassical_growth(
sol,
"figures/neoclassical_growth_model_2_by_1_sparse.pdf",
"figures/neoclassical_growth_model_2_by_1_sparse_rel_error.pdf",
c_rel_error_ylim=(1e-7, 2 * 1e-2),
zoom=True,
zoom_loc=[10, 20],
)
sol = neoclassical_growth_matern(train_T=10.0, train_points=11, test_T=15.0)
plot_neoclassical_growth(
sol,
"figures/neoclassical_growth_model_2_by_1_far_steady_state.pdf",
"figures/neoclassical_growth_model_2_by_1_far_steady_state_rel_error.pdf",
k_rel_error_ylim=(1e-5, 1e-1),
c_rel_error_ylim=(1e-5, 1e-1),
zoom=False,
)
sol = neoclassical_growth_matern(nu=1.5)
plot_neoclassical_growth(
sol,
"figures/neoclassical_growth_model_2_by_1_nu_1_5.pdf",
"figures/neoclassical_growth_model_2_by_1_nu_1_5_rel_error.pdf",
k_rel_error_ylim=(1e-7, 1e-2),
c_rel_error_ylim=(1e-7, 1e-2),
zoom=True,
zoom_loc=[75, 85],
)
sol = neoclassical_growth_matern(nu=2.5)
plot_neoclassical_growth(
sol,
"figures/neoclassical_growth_model_2_by_1_nu_2_5.pdf",
"figures/neoclassical_growth_model_2_by_1_nu_2_5_rel_error.pdf",
k_rel_error_ylim=(1e-7, 1e-2),
c_rel_error_ylim=(1e-8, 1e-2),
zoom=True,
zoom_loc=[75, 85],
)
sol = neoclassical_growth_matern(rho=2)
plot_neoclassical_growth(
sol,
"figures/neoclassical_growth_model_2_by_1_rho_2.pdf",
"figures/neoclassical_growth_model_2_by_1_rho_2_rel_error.pdf",
k_rel_error_ylim=(1e-7, 1e-2),
c_rel_error_ylim=(1e-7, 1e-2),
zoom=True,
zoom_loc=[75, 85],
)
sol = neoclassical_growth_matern(rho=20)
plot_neoclassical_growth(
sol,
"figures/neoclassical_growth_model_2_by_1_rho_20.pdf",
"figures/neoclassical_growth_model_2_by_1_rho_20_rel_error.pdf",
k_rel_error_ylim=(1e-7, 1e-2),
c_rel_error_ylim=(1e-7, 1e-2),
zoom=True,
zoom_loc=[75, 85],
)
"""
sol = neoclassical_growth_dae_matern()
plot_neoclassical_growth(
sol,
"figures/neoclassical_growth_model_2_by_1_dae.pdf",
"figures/neoclassical_growth_model_2_by_1_dae_rel_error.pdf",
k_rel_error_ylim=(1e-7, 1e-2),
c_rel_error_ylim=(1e-6, 1e-2),
zoom=True,
zoom_loc=[75, 85],
)
"""