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utils.py
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utils.py
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import dataclasses
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
import tensorflow as tf
from tqdm.notebook import tqdm
# set plotting syle
def set_style():
sns.set_context('notebook')
sns.set_style('darkgrid')
plt.rc('axes', linewidth=1)
plt.rc('axes', edgecolor='k')
plt.rc('figure', dpi=100)
# custom progress bar for long training
class tqdm_callback(tf.keras.callbacks.Callback):
def __init__(self, num_epochs, desc, loss=None, val_loss=None):
self.num_epochs = num_epochs
self.desc = desc
self.metrics = {'loss':loss, 'val_loss':val_loss}
def on_train_begin(self, logs={}):
self.epoch_bar = tqdm(total=self.num_epochs, desc=self.desc)
def on_train_end(self, logs={}):
self.epoch_bar.close()
def on_epoch_end(self, epoch, logs={}):
for name in self.metrics:
self.metrics[name] = logs.get(name, self.metrics[name])
self.epoch_bar.set_postfix(mse=self.metrics['loss'], val_mse=self.metrics['val_loss'], refresh=False)
self.epoch_bar.update()
# plot Lorenz 1963 trajectory
def plot_l63_traj_truth_obs(
x_truth,
x_raw,
dt,
Nt_shift,
t_plot,
linewidth,
):
Nt_plot_t = int(t_plot/dt)
Nt_plot_r = int(t_plot/dt/Nt_shift)
palette = sns.color_palette('deep')
sub_palette = [
palette[0],
palette[3],
palette[2],
]
fig = plt.figure(figsize=(linewidth, linewidth/3))
for (n, variable) in enumerate('xyz'):
plt.plot(
dt*np.arange(Nt_plot_t),
x_truth[:Nt_plot_t, n],
label='${}$'.format(variable),
c=sub_palette[n],
)
plt.plot(
dt*Nt_shift*np.arange(Nt_plot_r),
x_raw[:Nt_plot_r, n],
'.',
c = sub_palette[n],
)
plt.xlabel('time (MTU)')
plt.ylabel('L63 variables')
plt.title('True L63 trajectory (lines) and observations (dots)')
plt.xlim(0, t_plot)
plt.ylim(-30, 50)
plt.legend()
plt.show()
# plot any learning curve
def plot_learning_curve(
loss,
val_loss,
title,
linewidth,
):
palette = sns.color_palette('deep')
sub_palette = [
palette[0],
palette[3],
]
fig = plt.figure(figsize=(linewidth, linewidth/3))
plt.plot(loss, c=sub_palette[0], label='training loss')
plt.plot(val_loss, c=sub_palette[1], label='validation loss')
plt.xlabel('Number of epochs')
plt.ylabel('MSE')
plt.yscale('log')
plt.title(title)
plt.legend()
# standard L96 model
@dataclasses.dataclass
class Lorenz1996Model:
Nx: 'number of variables'
F: 'forcing'
dt: 'integration time step'
steps: 'integration scheme steps' = dataclasses.field(init=False)
weights: 'integration scheme weights' = dataclasses.field(init=False)
def __post_init__(self):
self.steps = np.array([0, self.dt / 2, self.dt / 2, self.dt])
self.weights = np.array([1, 2, 2, 1])
self.weights = self.weights / self.weights.sum()
def tendency(self, x):
xp = np.roll(x, shift=-1, axis=-1)
xmm = np.roll(x, shift=+2, axis=-1)
xm = np.roll(x, shift=+1, axis=-1)
return (xp - xmm)*xm - x + self.F
def forward(self, x):
averaged_dx_dt = np.zeros_like(x)
current_dx_dt = np.zeros_like(x)
for (w, dt) in zip(self.weights, self.steps):
current_x = x + current_dx_dt * dt
current_dx_dt = self.tendency(current_x)
averaged_dx_dt += w * current_dx_dt
return x + averaged_dx_dt * self.dt
# plot single Lorenz 1996 trajectory
def plot_l96_traj(
x,
model,
linewidth,
):
fig = plt.figure(figsize=(linewidth, linewidth/3))
plt.grid(False)
im = plt.imshow(
x.T,
aspect = 'auto',
origin = 'lower',
interpolation = 'spline36',
cmap = sns.diverging_palette(240, 60, as_cmap=True),
extent = [0, model.dt*x.shape[0], 0, model.Nx],
vmin = -10,
vmax = 15,
)
plt.colorbar(im)
plt.xlabel('Time (MTU)')
plt.ylabel('Lorenz 96 variables')
plt.tick_params(direction='out', left=True, bottom=True)
plt.show()
# plot comparative Lorenz 1996 trajectories
def plot_l96_compare_traj(
x_ref,
x_pred,
model,
linewidth,
):
error = x_pred - x_ref
fig = plt.figure(figsize=(linewidth, linewidth))
ax = plt.subplot(311)
ax.grid(False)
im = plt.imshow(
x_ref.T,
aspect = 'auto',
origin = 'lower',
interpolation = 'spline36',
cmap = sns.diverging_palette(240, 60, as_cmap=True),
extent = [0, model.dt*x_pred.shape[0], 0, model.Nx],
vmin = -10,
vmax = 15,
)
ax.set_title('true model integration')
plt.colorbar(im)
ax.set_ylabel('Lorenz 96 variables')
ax.tick_params(direction='out', left=True, bottom=True)
ax.set_xticklabels([])
ax = plt.subplot(312)
ax.grid(False)
im = plt.imshow(
x_pred.T,
aspect = 'auto',
origin = 'lower',
interpolation = 'spline36',
cmap = sns.diverging_palette(240, 60, as_cmap=True),
extent = [0, model.dt*x_pred.shape[0], 0, model.Nx],
vmin = -10,
vmax = 15,
)
ax.set_title('surrogate model integration')
plt.colorbar(im)
ax.set_ylabel('Lorenz 96 variables')
ax.tick_params(direction='out', left=True, bottom=True)
ax.set_xticklabels([])
ax = plt.subplot(313)
ax.grid(False)
im = ax.imshow(
error.T,
aspect = 'auto',
origin = 'lower',
interpolation = 'spline36',
cmap = sns.diverging_palette(240, 10, as_cmap=True),
extent = [0, model.dt*error.shape[0], 0, model.Nx],
vmin = -15,
vmax = 15,
)
ax.set_title('signed error')
plt.colorbar(im)
ax.set_xlabel('Time (MTU)')
ax.set_ylabel('Lorenz 96 variables')
ax.tick_params(direction='out', left=True, bottom=True)
plt.show()
# plot Lorenz 1996 forecast skill
def plot_l96_forecast_skill(
fss,
model,
p1,
p2,
xmax,
linewidth,
):
fig = plt.figure(figsize=(linewidth, linewidth/2))
palette = sns.color_palette('deep')
palette.pop(1)
for (c, key) in zip(palette, fss):
time = (model.dt/model.lyap_time)*np.arange(fss[key].shape[0])
rmse_m = fss[key].mean(axis=1) / model.model_var
rmse_p1 = np.percentile(fss[key], p1, axis=1) / model.model_var
rmse_p2 = np.percentile(fss[key], p2, axis=1) / model.model_var
plt.plot(time, rmse_m, color=c, label=key)
plt.fill_between(time, rmse_p1, rmse_p2, color=c, alpha=0.1)
plt.axhline(np.sqrt(2), c='k', ls='--', label='$\sqrt{2}$')
plt.xlabel('Time (Lyapunov time)')
plt.ylabel('normalised RMSE')
plt.ylim(0, 2)
plt.xlim(0, xmax)
plt.title('Forecast skill')
plt.legend()
plt.show()