[BUG] Solver failed, setting coefs to zeros in jupyter notebook 15_pysindy_lectures

[michaelkalz]

The inequality constraints part from the lectures code and lecture notebook seems not to work. It belongs to: Part 2d: use prior physical knowledge to constrain the model

Solver failed, setting coefs to zeros
ConstrainedSR3 model, inequality constraints:
(x)' = 0.000
(y)' = 0.000
(z)' = 0.000

Here is the code from the corresponding cell:

# Fit a regular SINDy model with 5% added Gaussian noise
sparse_regression_optimizer = ps.SR3(threshold=0.5)
model = ps.SINDy(feature_names=feature_names, optimizer=sparse_regression_optimizer)
model.fit(x_train_added_noise, t=dt)
print("SR3 model, no constraints:")
model.print()
x_sim = model.simulate(x0_test, t=t_test)

# Figure out how many library features there will be
library = ps.PolynomialLibrary()
library.fit(x_train)
n_features = library.n_output_features_

# Set constraints
n_targets = x_train.shape[1]
constraint_rhs = np.array([0, 28])

# One row per constraint, one column per coefficient
constraint_lhs = np.zeros((2, n_targets * n_features))

# 1 * (x0 coefficient) + 1 * (x1 coefficient) = 0
constraint_lhs[0, 1] = 1
constraint_lhs[0, 2] = 1

# 1 * (x0 coefficient) = 28
constraint_lhs[1, 1 + n_features] = 1

optimizer = ps.ConstrainedSR3(
    constraint_rhs=constraint_rhs,
    constraint_lhs=constraint_lhs,
    threshold=0.5,
    thresholder="l1",
)
model = ps.SINDy(
    optimizer=optimizer, feature_library=library, feature_names=feature_names
)
model.fit(x_train_added_noise, t=dt)
print("ConstrainedSR3 model, equality constraints:")
model.print()
constrained_x_sim = model.simulate(x0_test, t=t_test)
make_3d_plots(x_test, x_sim, constrained_x_sim,
              "ConstrainedSR3, equality constraints")

# Repeat with inequality constraints
eps = 0.5
constraint_rhs = np.array([eps, eps, 28])

# One row per constraint, one column per coefficient
constraint_lhs = np.zeros((3, n_targets * n_features))

# 1 * (x0 coefficient) + 1 * (x1 coefficient) <= eps
constraint_lhs[0, 1] = 1
constraint_lhs[0, 2] = 1

# -eps <= 1 * (x0 coefficient) + 1 * (x1 coefficient)
constraint_lhs[1, 1] = -1
constraint_lhs[1, 2] = -1

# 1 * (x0 coefficient) <= 28
constraint_lhs[2, 1 + n_features] = 1

optimizer = ps.ConstrainedSR3(
    constraint_rhs=constraint_rhs,
    constraint_lhs=constraint_lhs,
    threshold=0.5,
    inequality_constraints=True,
    thresholder="l1",
)
model = ps.SINDy(
    optimizer=optimizer, feature_library=library, feature_names=feature_names
)
model.fit(x_train_added_noise, t=dt)
print("ConstrainedSR3 model, inequality constraints:")
model.print()
constrained_x_sim = model.simulate(x0_test, t=t_test)
make_3d_plots(
    x_test, x_sim, constrained_x_sim,
    "ConstrainedSR3, inequality constraints"
)

Error message:

Solver failed, setting coefs to zeros
ConstrainedSR3 model, inequality constraints:
(x)' = 0.000
(y)' = 0.000
(z)' = 0.000

Unlike in the video (something like):
ConstrainedSR3 model, inequality constraints:
(x)' = 8.319 1 + -7.036 x + 7.536 y + -0.747 z + -0.027 x^2 + 0.057 x y + -0.076 x z + -0.029 y^2 + 0.068 y z + 0.014 z^2
(y)' = 5.460 1 + 23.951 x + 1.299 y + -0.865 z + -0.197 x^2 + 0.209 x y + -0.892 x z + -0.061 y^2 + -0.059 y z + 0.032 z^2
(z)' = 11.844 1 + 4.496 x + -2.701 y + -4.483 z + -0.239 x^2 + 1.061 x y + -0.128 x z + 0.052 y^2 + 0.080 y z + 0.059 z^2

PySINDy/Python version information:

python==3.10.15

pysindi==1.7.5