Mixing tee ROM failed

[jacktang]

Hello There!

I've read tutorial 1 and 2, and try to apply the same ROM workflow on my own tests of cold and hot flow in mixing tee.
The space lists below:

and there are four paramters:

• velocity of inlet1
• temperature of inlet1
• velocity of inlet2
• temperature of inlet2

The outputs are velocity of x, velocity of y, and pressure. I generated 300 snapshots by uniform sampling and splitted 200 snapshots for trainning, 50 for validation, and 50 for testing.

print(train_mus.shape)
print(test_mus.shape)
print(train_snapshots.shape)
print(test_snapshots.shape)

>(200, 4)
>(50, 4)
>(200, 1466)
>(50, 1466)

rom = ROM(db, POD(), RBF())
rom.fit();

errors = rom.kfold_cv_error(n_splits = 10)
print('Average error for each fold:')
for e in errors:
print('  ',e)
print('\nAverage error = {}'.format(errors.mean()))

Finally, the average error is 0.8
I don't figure out what's wrong with my experience. Could you please give me some hits on how to make it work? Thanks a lot!

[mtezzele]

Hi @jacktang, you can start by playing with the svd_rank of the POD and compute the projection error, that is the error on the training dataset. Maybe you have to many modes and the RBF interpolation creates a lot of oscillations that add up to a huge error. If you want to use RBF you can also check out the documentation: there is a smoothing parameter you can pass. Otherwise try with GPR.
Let us know it this helps.

[mtezzele]

Ok, great. Be aware that leave-one-out error is not the projection error. It is the prediction error on a single parameter point using all the other samples for the training.

[jacktang]

Hello @mtezzele, The "projection error" you mentioned above is using the snapshot vectors as the basis? I didn't find such method in EZyRB project, or I missed something important?

[mtezzele]

No, for the projection error use the predict method with the same parameters used in the training dataset and then compute the relative error: || snapshots - predictions || / || snapshots ||

[jacktang]

The projection errors on training dataset

error = []
for i, mu in enumerate(mus):
    predicted = rom.predict(mu)
    snapshot = snapshots[i]
    proj_err = np.mean(
            np.linalg.norm(predicted - snapshot) /
            np.linalg.norm(snapshot))
    error.append(proj_err)

error = np.array(error)
print(error)
max_idx = np.argmax(error, axis=0)
min_idx = np.argmin(error, axis=0)
print("max:", np.max(error), ",mu:", mus[max_idx])
print("min:", np.min(error), ",mu:", mus[min_idx])
print("mean:", np.mean(error))

===
[0.0016168  0.00151261 0.00086779 0.00109318 0.00108899 0.00119235
 0.00307508 0.00240418 0.00191264 0.00411363 0.00170633 0.00080376
 0.00129321 0.00534961 0.00349508 0.00265598 0.00449336 0.00086779
 0.00254334 0.00090921 0.00559876 0.0016168  0.00104805 0.00345684
 0.002048   0.00143418 0.00181505 0.00125449 0.00355256 0.00505084
 0.00134324 0.00146958 0.00106861 0.00108926 0.0016274  0.00136403
 0.00095908 0.00217046 0.00395786 0.00207823 0.00123911 0.0016274
 0.0012799  0.001744   0.00127547 0.00492846 0.00125449 0.00302543
 0.00109106 0.00109118 0.0045064  0.00199805 0.00164717 0.00505084
 0.00109318 0.00099218 0.00226732 0.00172054 0.00175106 0.00141783
 0.0011778  0.00169447 0.00189886 0.00128506 0.00175574 0.00697163
 0.00090921 0.00140073 0.00119235 0.00323317 0.00157576 0.00183056
 0.00141158 0.00095908 0.00176335 0.00134324 0.00125449 0.00181505
 0.00237149 0.00100616 0.00090921 0.00256155 0.00307508 0.00153445
 0.00155697 0.00140073 0.00281732 0.00164717 0.00110229 0.00112027
 0.00107876 0.00194808 0.00155886 0.00256155 0.00094619 0.00090921
 0.00120405 0.00104805 0.00120783 0.00183056 0.01036389 0.00140073
 0.00172054 0.01036389 0.00116751 0.0013469  0.00112027 0.00348566
 0.0043652  0.00119577 0.00481464 0.00119254 0.00163034 0.00094619
 0.0022829  0.00128506 0.00348566 0.0011778  0.00207823 0.00119254
 0.00211331 0.00297304 0.00170633 0.00258853 0.00100616 0.00090921
 0.00136403 0.00481464 0.00281732 0.00178162 0.00140172 0.00450088
 0.00080376 0.00254334 0.00125502 0.00395786 0.01079509 0.00155697
 0.00125449 0.0017337  0.00178162 0.00178162 0.00185159 0.00258853
 0.00395786 0.0011045  0.0022594  0.00251217 0.00534961 0.00090921
...
 0.00129396 0.00166423 0.00103717 0.0017337  0.00134324 0.00176335]
max: 0.010795091678056208 ,mu: [ 1.3  1.  20.  47. ]
min: 0.000803759999698049 ,mu: [ 0.1  1.5 23.  22. ]
mean: 0.00212359967701049

The snapshot with the largest projection error is the same as the snapshot in the loo error diagnose.

[jacktang]

svd-rank=3, mean-err: 0.021
svd-rank=10, mean-err: 0.0039
svd-rank=30, mean-err: 0.0020
svd-rank=100, mean-err: 0.000267

Based on the above projection error on training set, can I conclude that the large error of rom prediction because of no enough snapshots? and I should generate more snapshots as optimal_mu suggests. Thanks!