If you have x_dot measurements and don't need to compute x_dot when using SINDyPI how do you implement that?

[yemialabipurpose]

I am practising with a seven-state system where only two of the equations are implicit. I am using SINDyPI. I have both x and x_dot measurements so I don't want Pysindy to compute x_dot for me. How do I feed x_dot into the algorithm when using SINDyPI? how do I define differentiation method? I omitted it when initializing the SINDy model and fed x_dot in when fitting it but I get this error instead. ValueError: operands could not be broadcast together with shapes (798,1,798,3) (1,3,1) how can i fix it?

I expected the following 7 equations

wr_dot = K1 + K2theta + k3theta_dot #implicit
theta_dot = K(wt-wr)
wt_dot = K4 + K5theta + k6theta_dot #implicit
iqs_dot= K7 + K8iqs +K9ids+ K10(wreqs), + K11eds
ids_dot = K12 -K8ids -K9iqs+ K10(wreds), + K11eqs
eqs_dot = K13 +K14ids -K11eqs+ eds - K10(wreds)
eds_dot = K13 -K14iqs - K11eds - eds +K10(wreqs)

#K are the coefficients.

Here is the code with which i was trying to implement it.

`feature_names=['wr', 'theta', 'wt', 'iqs', 'ids', 'eqs', 'eds']

Initialize custom SINDy library

x_library_functions = [
lambda x: x,
lambda x, y: x * y,
]
x_dot_library_functions = [lambda x: x]

library function names includes both the

x_library_functions and x_dot_library_functions names.

library_function_names = [
lambda x: x,
lambda x, y: x + y,
#lambda x: x,
]

sindy_library = ps.SINDyPILibrary(
library_functions=x_library_functions,
t=t_train.flatten(),
function_names=library_function_names,
include_bias=True
)

sindy_opt = ps.SINDyPI(
threshold=1e-6,
tol=1e-8,
max_iter=20000,
)
model = ps.SINDy(
optimizer=sindy_opt,
feature_library=sindy_library,
differentiation_method=ps.FiniteDifference(drop_endpoints=True),
feature_names=feature_names)
model.fit(x_train, t=t_train, x_dot=dx_train, quiet=True)
model.print()`

when I run this code i get the following errors:

---

ValueError Traceback (most recent call last)
Cell In[79], line 36
25 sindy_opt = ps.SINDyPI(
26 threshold=1e-6,
27 tol=1e-8,
28 thresholder="l1",
29 max_iter=20000,
30 )
31 model = ps.SINDy(
32 optimizer=sindy_opt,
33 feature_library=sindy_library,
34 differentiation_method=ps.FiniteDifference(drop_endpoints=True),
35 feature_names=feature_names)
---> 36 model.fit(x_train, t=t_train, quiet=True)
37 model.print()

File ~\AppData\Local\Packages\PythonSoftwareFoundation.Python.3.9_qbz5n2kfra8p0\LocalCache\local-packages\Python39\site-packages\pysindy\pysindy.py:343, in SINDy.fit(self, x, t, x_dot, u, multiple_trajectories, unbias, quiet, ensemble, library_ensemble, replace, n_candidates_to_drop, n_subset, n_models, ensemble_aggregator)
337 u = validate_control_variables(
338 x,
339 u,
340 trim_last_point=(self.discrete_time and x_dot is None),
341 )
342 self.n_control_features_ = u[0].shape[u[0].ax_coord]
--> 343 x, x_dot = self._process_multiple_trajectories(x, t, x_dot)
345 # Set ensemble variables
346 self.ensemble = ensemble

File ~\AppData\Local\Packages\PythonSoftwareFoundation.Python.3.9_qbz5n2kfra8p0\LocalCache\local-packages\Python39\site-packages\pysindy\pysindy.py:665, in SINDy._process_multiple_trajectories(self, x, t, x_dot)
663 x = [xi[:-1] for xi in x]
664 else:
--> 665 x_dot = [
666 self.feature_library.calc_trajectory(
667 self.differentiation_method, xi, ti
668 )
669 for xi, ti in _zip_like_sequence(x, t)
670 ]
671 return x, x_dot

File ~\AppData\Local\Packages\PythonSoftwareFoundation.Python.3.9_qbz5n2kfra8p0\LocalCache\local-packages\Python39\site-packages\pysindy\pysindy.py:666, in (.0)
663 x = [xi[:-1] for xi in x]
664 else:
665 x_dot = [
--> 666 self.feature_library.calc_trajectory(
667 self.differentiation_method, xi, ti
668 )
669 for xi, ti in _zip_like_sequence(x, t)
670 ]
671 return x, x_dot

File ~\AppData\Local\Packages\PythonSoftwareFoundation.Python.3.9_qbz5n2kfra8p0\LocalCache\local-packages\Python39\site-packages\pysindy\feature_library\base.py:87, in BaseFeatureLibrary.calc_trajectory(self, diff_method, x, t)
85 def calc_trajectory(self, diff_method, x, t):
86 axes = x.dict
---> 87 x_dot = diff_method(x, t=t)
88 return AxesArray(x_dot, axes)

File ~\AppData\Local\Packages\PythonSoftwareFoundation.Python.3.9_qbz5n2kfra8p0\LocalCache\local-packages\Python39\site-packages\pysindy\differentiation\base.py:49, in BaseDifferentiation.call(self, x, t)
48 def call(self, x, t=1):
---> 49 return self._differentiate(x, t)

File ~\AppData\Local\Packages\PythonSoftwareFoundation.Python.3.9_qbz5n2kfra8p0\LocalCache\local-packages\Python39\site-packages\pysindy\differentiation\finite_difference.py:251, in FiniteDifference._differentiate(self, x, t)
249 interior = interior + x[tuple(s)] * coeffs[i]
250 else:
--> 251 coeffs = self._coefficients(t)
252 interior = self._accumulate(coeffs, x)
253 s[self.axis] = slice((self.n_stencil - 1) // 2, -(self.n_stencil - 1) // 2)

File ~\AppData\Local\Packages\PythonSoftwareFoundation.Python.3.9_qbz5n2kfra8p0\LocalCache\local-packages\Python39\site-packages\pysindy\differentiation\finite_difference.py:93, in FiniteDifference._coefficients(self, t)
90 self.stencil = np.transpose(t[self.stencil_inds])
92 pows = np.arange(self.n_stencil)[np.newaxis, :, np.newaxis]
---> 93 matrices = (
94 self.stencil
95 - t[
96 (self.n_stencil - 1) // 2 : -(self.n_stencil - 1) // 2,
97 np.newaxis,
98 ]
99 )[:, np.newaxis, :] ** pows
100 b = np.zeros(self.n_stencil)
101 b[self.d] = np.math.factorial(self.d)

ValueError: operands could not be broadcast together with shapes (798,1,798,3) (1,3,1)

[Jacob-Stevens-Haas]

Hey, thanks for your question. 1) You're correct to pass x_dot to SINDy.fit(), not SINDy(). BUT the traceback shows that the code you ran wasn't the code you posted:

Posted:

model = ps.SINDy(
optimizer=sindy_opt,
feature_library=sindy_library,
differentiation_method=ps.FiniteDifference(drop_endpoints=True),
feature_names=feature_names)
model.fit(x_train, t=t_train, x_dot=dx_train, quiet=True)
model.print()`

Traceback:

31 model = ps.SINDy(
32 optimizer=sindy_opt,
33 feature_library=sindy_library,
34 differentiation_method=ps.FiniteDifference(drop_endpoints=True),
35 feature_names=feature_names)
---> 36 model.fit(x_train, t=t_train, quiet=True)
37 model.print()

When you send x_dot to fit(), it pre-empts the differentiation method, so setting it does nothing. 2) I also think SINDyPILibrary is deprecated, so I want to say it's the PDELibrary you're supposed to use? I believe it's in the docstring for that module. 3) Can you please format your code with triple backticks? (```)