[Question]How model.predict() works for implicit ODEs function? about pysindy

[Jacob-Stevens-Haas]

PI is my least familiar part of the repo, but I see why it might not. But it looks like it creates coef_ in the correct shape, so what happens if you give it a try?

[niuyushuo]

PI is my least familiar part of the repo, but I see why it might not. But it looks like it creates coef_ in the correct shape, so what happens if you give it a try?

Thanks for your response. After getting the fitted implicit ODEs model, model.predict() works well.
To demonstrate the question, here are two models from my results:

x0_t = -0.031 1 + -0.104 x2 + 0.053 x5 + 0.132 x6 + 0.081 x0x1 + 0.024 x0x0 + -0.843 x5_t + 0.728 x0x0_t
x7_t = 0.015 1 + -0.044 x0 + 0.054 x5 + -0.156 x7 + 0.002 x0x1 + 0.030 x0x0

Follow your suggestion, save the model coefficient by: coefs = model.coefficients()
If I let the coefficients corresponding to x7_t (which has no x_t terms on the right hand side) loop the dataset, will get the same results compared to the resutls from model.predict(). It is consistent with the documentation which is 'result = [self.model.predict([xi]) for xi in x]'.
Then the question is how model.predict() loop data if there are x_t terms on the right hand side of implicit ODEs model?
Thanks.

[Jacob-Stevens-Haas]

I'm sorry, I don't understand everything you've done. How many models did SINDyPI fit in your example? And what do you mean when you say you "let the coefficients corresponding to x7_t loop the dataset?"

[niuyushuo]

I'm sorry, I don't understand everything you've done. How many models did SINDyPI fit in your example? And what do you mean when you say you "let the coefficients corresponding to x7_t loop the dataset?"

Hi thanks for your response.
For the first question, my dataset has 8 features. The library functions are defined below:

library_functions = [
    lambda x: x,
    lambda x, y: x * y,
    lambda x: x ** 2,
]
x_dot_library_functions = [lambda x: x]

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

So I got a total of 405 models (model0 -model404).
For the second question, I picked up model 45 and model 53 which are

x0_t = -0.031 1 + -0.104 x2 + 0.053 x5 + 0.132 x6 + 0.081 x0x1 + 0.024 x0x0 + -0.843 x5_t + 0.728 x0x0_t
x7_t = 0.015 1 + -0.044 x0 + 0.054 x5 + -0.156 x7 + 0.002 x0x1 + 0.030 x0x0

The reason I picked up those two as the first model has x_t terms on the right hand side and the second one does not.
I am using those two models to try to understand how model. predict () works.
As described in the documentation, the model.predict() works as 'result = [self.model.predict([xi]) for xi in x]'.
https://github.com/dynamicslab/pysindy/blob/master/pysindy/pysindy.py, at line 274
If I get the coefficients from x7_t, and loop the dataset. The results are consistent with the results model.predict(dataset)[:,53].
Then the question is just like the title, how model.predict() works if the fitted model (just like model x0_t here) has x_t terms on the right hand side? We only give x (to be input) to this function instead of x_t.
I test model.predict(dataset) by myself, and it works without any issues. Thanks.

[Jacob-Stevens-Haas]

Which library are you using? PDELibrary, or CustomLibrary?

[niuyushuo]

It is PDELibrary.
Here is my code:

sindy_library = ps.PDELibrary(
    library_functions=library_functions,
    temporal_grid=t,
    function_names=library_function_names,
    include_bias=True,
    implicit_terms=True,
    derivative_order=1
)


sindy_opt = ps.SINDyPI(      ### lambda = threshold^2 / (2 * nu)
    threshold=1e-2,
    tol=1e-8,
    thresholder="l1",
    max_iter=20000,
)

model = ps.SINDy(
    optimizer=sindy_opt,
    feature_library=sindy_library,
    differentiation_method=ps.SINDyDerivative(kind="kalman", alpha=0.6)
)

model.fit(X_sm_poly, t=t)
model.print()

sindy_library.get_feature_names()

[Jacob-Stevens-Haas]

My guess is that predict is giving you bad outputs. I don't think you can trust what you get out. My guess is that SINDyPI is reordering the features internally between each model it's fitting.

Also, you can format your code in Github comments. Heads up, I did this for a few of your comments.

[niuyushuo]

OK, thanks for your reply. I just wonder, for the multiple features implicit ODE model, is there any function/way in pysindy to evaluate each fitted model? If I follow the example 9_sindypi_with_sympy.ipynb. The method from 'Check all the model fits produce sensible models' to 'integrate and plot the new equations for x_dot' part, only works for single feature ODE model. I tested by myself, this method could not work for multiple features. Thanks.

[Jacob-Stevens-Haas]

I'm sorry, you would need to troubleshoot further. That code involves heavy use of sympy, which I've never used. Specifically, can you see where pysindy provides something unexpected?