SINDy example of a non-autonomous fit to a hidden latent layer

SINDy.py

import numpy as np
from sklearn.linear_model import Lasso

# ----------------------------
# USER INPUT: hidden layer & target
# ----------------------------
# Example synthetic data (replace with your arrays)
N = 1000
t = np.linspace(0, 10, N)
hidden_layer = np.sin(2*np.pi*1*t) + 0.5*np.sin(2*np.pi*3*t)  # latent forcing
target = 2*np.sin(2*np.pi*1*t + 0.2) + 0.7*np.cos(2*np.pi*3*t - 0.3)  # observed output

# ----------------------------
# Parameters
# ----------------------------
max_harmonic = 3        # max multiple of the latent phase to include
alpha = 1e-3            # Lasso sparsity regularization
fit_intercept = True    # include intercept in regression

# ----------------------------
# Build library of sin/cos functions
# ----------------------------
library_list = []
for n in range(1, max_harmonic+1):
    library_list.append(np.sin(n * hidden_layer))
    library_list.append(np.cos(n * hidden_layer))

Theta = np.column_stack(library_list)  # shape (N, 2*max_harmonic)

# ----------------------------
# Fit sparse regression (non-autonomous SINDy)
# ----------------------------
lasso = Lasso(alpha=alpha, fit_intercept=fit_intercept)
lasso.fit(Theta, target)
Xi = lasso.coef_
intercept = lasso.intercept_

# ----------------------------
# Prediction
# ----------------------------
y_pred = Theta @ Xi + intercept

# ----------------------------
# Diagnostics / display
# ----------------------------
print("Selected coefficients (Xi):")
for i, coef in enumerate(Xi):
    func_type = 'sin' if i%2==0 else 'cos'
    harmonic = (i//2)+1
    print(f"{func_type}({harmonic}*latent) -> {coef:.4f}")
print(f"Intercept: {intercept:.4f}")

# Optional: plot
import matplotlib.pyplot as plt
plt.figure(figsize=(10,4))
plt.plot(t, target, label='Target')
plt.plot(t, y_pred, '--', label='SINDy Pred')
plt.xlabel('Time')
plt.ylabel('Observable')
plt.legend()
plt.show()

SINDy, KAN, Koopman views:
https://chatgpt.com/share/690f5eea-267c-8006-8c8d-f7d584714fbd

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