pswpswpsw / skdmd Goto Github PK

Dear Dr. Pan @pswpswpsw ,
My system has a simple nonlinear sine function. The hyperparam selection figure is as follows so that I choose rank=90 and sigma=4. But the reconstruction error plot looks very strange, and the error is also huge. My system is as follows:

def F_omib_2d_system(x):
    Pm = 1.2
    Pe = 1.6382
    Damp = 5
    w0 = np.math.pi*2*50
    TJ = 6

    F = np.zeros(x.shape)
    F[0] = x[1]
    F[1] = w0*(Pm - Pe*np.math.sin(x[0]) - Damp*x[1]/w0)/TJ

    return F

The phase space range is phase_space_range = [[-.2, 3], [-9.5, 9.5]]
All the other codes are exactly the same as the lusch example. Can you help provide some hints on how I can improve to get better results?

Hi Dr. Pan @pswpswpsw ,
I used your code and data sample to create the result-num.png to select sigma and r. However, from the figure, it's hard to tell why you choose sigma=3 and r=180. Can you give me some hints on how to interpret the figure? Thanks.

Dear Dr. Pan @pswpswpsw ,
When I was trying out the multi-task learning mode selection with my own data, sklearn raised the convergence warning. It said you might want to increase the number of iterations. But my iteration is already 1e5 and it was really a very simple system. My data was generated using a 2-dimensional ODE, which was very similar to the example in 4.1. The different part is that I use feature tractories as training data. I randomly selected N initial point in the space and used RK45 to integrate along time, containing M+1 time steps. 1 to M data points were saved as X, and 2 to M+1 data points were saved as Xnext. So the number of rows of both X and Xnext is N*M, and the number of column is 2. So in my data generation code, X and Xnext were previously stored, unlike code line 70-71 in the cv_kdmd_hyp.py file. I don't know if that caused the convergence warning.