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b17b2ba a410163 b17b2ba a410163 b17b2ba a410163 b17b2ba a410163 b17b2ba a410163 b17b2ba a410163 b17b2ba a410163 b17b2ba a410163 b17b2ba a410163 b17b2ba a410163 b17b2ba a410163 | 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 | import numpy as np
import matplotlib.pyplot as plt
import umap
def damped_oscillator(t, omega, zeta):
"""
Solve x'' + 2*zeta*omega*x' + omega^2*x = 0
Initial conditions: x(0)=1, x'(0)=0
"""
if zeta < 1:
# Underdamped
omega_d = omega * np.sqrt(1 - zeta**2)
x = np.exp(-zeta * omega * t) * (
np.cos(omega_d * t) + (zeta * omega / omega_d) * np.sin(omega_d * t)
)
elif zeta == 1:
# Critically damped
x = np.exp(-omega * t) * (1 + omega * t)
else:
# Overdamped
s1 = -omega * (zeta + np.sqrt(zeta**2 - 1))
s2 = -omega * (zeta - np.sqrt(zeta**2 - 1))
c1 = -s2 / (s1 - s2)
c2 = s1 / (s1 - s2)
x = c1 * np.exp(s1 * t) + c2 * np.exp(s2 * t)
return x
# Parameters
np.random.seed(456)
omega_min, omega_max = 0.75, 2.0
zeta_min, zeta_max = 0.5, 1.5
n_samples = 100
n_points = 200
t = np.linspace(0, 5, n_points)
my_noise = 0.005
# Generate data
time_series = []
labels = []
# Class 0: Underdamped (oscillatory)
for i in range(n_samples):
omega = np.random.uniform(omega_min, omega_max)
zeta = np.random.uniform(zeta_min, zeta_max)
y = damped_oscillator(t, omega, zeta)
y += np.random.normal(0, my_noise, len(t))
time_series.append(y)
if zeta < 1:
labels.append(0)
else:
labels.append(1)
# Convert to arrays
X = np.array(time_series) # Shape: (100, 200)
y_true = np.array(labels) # Shape: (100,)
print(f"Generated {len(X)} time series")
print(f"Shape: {X.shape}")
print(f"Class distribution: {np.bincount(y_true)}")
# Visualize some examples
fig, axes = plt.subplots(4, 6, figsize=(16, 8))
fig.suptitle("Example Time Series from Each Class")
axes = axes.flatten()
for i, ax in enumerate(axes):
# Underdamped
ax.plot(t, X[i])
ax.set_xlabel("Time")
ax.set_ylabel("x(t)")
ax.grid(alpha=0.3)
plt.tight_layout()
plt.savefig("outputs/test_data_examples.png", dpi=150, bbox_inches="tight")
# Stack time series (N_s × N)
Y = X
# UMAP to 2D
reducer = umap.UMAP(n_components=2, n_neighbors=15, min_dist=0.1)
embedding = reducer.fit_transform(Y)
# Visualize
fig, axes = plt.subplots()
plt.scatter(embedding[:, 0], embedding[:, 1], alpha=0.6)
# plt.show()
plt.savefig("outputs/umap_decomp.png", dpi=150, bbox_inches="tight")
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